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In contemporary times, there has been a significant focus among researchers on hybrid nanofluids derived from oils, owing to their remarkable and substantial utility in the domains of engineering, mechanics, and industrial applications. The aim of this research is to determine the impact of incorporating tantalum and nickel nanoparticles in mineral oil on thermal characteristics and flow patterns, with the objective of predicting possible improvements. The dependence of the role of both nanoparticles on their shapes is evaluated for column, platelet, lamina, cylinder, and tetrahedron-type shapes. This work analyzes the thermal performance of two different nanofluids individually made of tantalum and nickel nanoparticles while also examining the synergistic effects produced due to the simultaneous suspension of these particles. A profound understanding of the intricate flow dynamics and thermal energy transfer phenomena along a vertical surface holds paramount importance in the pursuit of optimizing heat exchange procedures, formulating effective cooling systems, and designing thermally efficient devices. Furthermore, it contributes to the advancement of climate modeling, the precision of weather forecasting, and the refinement of the operational effectiveness of solar thermal systems. The basic mathematical model is formulated subject to free convection, time-dependent flow and heat conditions, and thermal radiation. This governing system is made non-dimensional to lessen the intricacy and provide the basis for the utilization of fractional operators. In order to assess the effectiveness of fractional modeling techniques, constant proportional Caputo (CPC) and Atangana–Baleanu (ABC) derivatives are operated for the model generalization. Most of the time, solving fractional models via an analytic method are not a feasible technique because it produces extremely complex and implicit mathematical expressions. However, in this study, the Laplace transform is served as a solution procuring technique, and series and integral form exact solutions are extracted for CPC and ABC derivative-based models, respectively. To interpret modifications in thermal and velocity patterns arising from diverse physical phenomena, numerous graphical depictions of exact solutions are communicated. Moreover, the implications of varying a number of critical factors, including the fractional parameter, nanoparticles' shapes and proportions, and radiation term, on shear stress and thermal productivity of the hybrid nanofluid are discussed using the tabulated findings. On comparing shape effects and individual suspensions of considered nanoparticles, it is observed that lamina shape and nickel nanoparticles are relatively more effective regarding the improvement of thermal performance. The model based on the CPC derivative yields lower profiles of temperature and flow functions as compared to the ABC derivative-based model. The results indicate that introducing homogeneous proportions of tantalum and nickel nanoparticles into mineral oil raises its heat-transferring capacity by up to 47.60%. These findings suggest that the examined hybrid nanofluid performs extremely well as a lubricant and a cooling agent. [ABSTRACT FROM AUTHOR]

Mineral Oil [MO] has significant importance because of its vast variety of applications in various arenas of manufacturing, technology, and industrial processes. The applications of the Mineral Oil [MO] are PVC production, polystyrene production, as a lubricating, cutting fluid, thermoplastics rubber production, glossing product, wood products, cleaning products, lamp oil, glues, toys, veterinary, cosmetics, food preparation, as a brake fluid in some cars, and so forth. Due to these applications of Mineral Oil [MO], in the existing work, the two-dimensional mixed convective flow of micropolar fluid with the applications of the aluminum oxide nanoparticles in a Mineral Oil [MO] base liquid is taken into consideration. The melting heat phenomenon is discussed for the interpretation of heat transmission. Further, the flow analysis is discussed through the impacts of inclined magnetic field, heat generation, Joule heating and thermal radiation. Mass diffusivity is deliberated through the implementation of homogenous and heterogeneous chemical reactions. Entropic behavior is analyzed for the discussion of irreversibility analysis. Suitable similarity transformations are employed to renovate modeled systems of the PDEs into ODEs. Analytical simulation of the proposed model has been accomplished with the utilization of the homotopy analysis technique. Some significant outcomes from the existing work are that the velocity outline is reduced but the energy curve is greater for the melting parameter. Nanofluid entropy generation is increased due to the improvement of the Brinkman parameter and material parameter. Heat transportation is augmented due to the amplification of the radiation parameter, and nanoparticle volume fraction. The present study is useful in different fields of industries, technological processes, mechanical processes, and electrical processes due to the applications of mineral oil. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. However, this technology is not ended here; binary and ternary nanofluids are now used to improve the efficiency of regular fluids. Therefore, this paper aims to analyze the natural convection Newtonian ternary nanofluid flow in a vertical channel. The tri‐hybridized nanoparticles of zinc oxide ZnO, Aluminum oxide Al2O3, and titanium oxide TiO2 is dissolved in base fluid distilled water (DW) to form a homogenous suspension. The impact of thermal radiation, joule heating, and viscous dissipation are also assumed. The classical Newtonian ternary nanofluid model has been generalized by using fractal‐fractional derivative (FFD) operator. The generalized model has been discretized by using the Crank–Nicolson scheme and then solved by using computational software. To analyze the behavior of fluid flow and heat distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is noted from the figure that when the volume fraction ϕ reaches to 0.04 (4% of the base fluid), the ternary nanofluid flow shows a significant amount of enhancement in heat transfer rate as compared to binary and unary nanofluid flows. This enhancement in the rate of heat transfer leads to improve the thermophysical characteristics such as viscosity, thermal expansion, and heat capacity etc. of the base fluid. It is also worth mentioning here that the thermal field is also enhance with the higher values of Eckert number Ec$Ec$, radiation parameter Rd$Rd$, and joule heating parameter Jh${J_h}$. [ABSTRACT FROM AUTHOR]

Diathermal oils have piqued the interest of several researchers in recent years due to their numerous industrial applications. The core aim of this study is the development of a novel fractal-fractional model to analyze the thermal performance of an oil-based tripartite hybrid nanofluid for channel flows. Graphene (Gr), magnesium oxide (MgO), and copper (Cu) nanoparticles are simultaneously dispersed in engine oil to obtain a tripartite hybrid nanofluid. To evaluate the impacts of the shape factor on thermal performance, five different shapes (brick, blade, spherical, platelet, and cylindrical) of nanoparticles are considered. The flow of considered fluid starts due to the constant motion of the right wall, which also encounters constant heating. Meanwhile, the left wall absorbs uniform radiation impacts. The mathematical model to explain this physical process is formulated by utilizing a fractal-fractional derivative, which involves a power-law kernel in its working. This model is exposed to joint employment of classical and fractal Laplace transforms to acquire the analytic solutions. These solutions are further used to develop expressions for skin friction coefficient and Nusselt number. Based on these quantities, heat transfer rate and shear stress are estimated to analyze augmentation in the thermal potential of engine oil and to observe variation in shear stress because of parametric effects. By conducting a comparative analysis between graphs of fractional and fractal-fractional models, it is concluded that a better elucidation of memory effects can be provided through the fractal-fractional approach. Furthermore, this work highlights that dispersing three different types of nanoparticles in engine oil makes it a more effective industrial fluid with a 9.58% higher heat-conduction capacity. This significant enhancement in the thermal performance of engine oil signifies its effectiveness for lubrication and cooling applications. [ABSTRACT FROM AUTHOR]

In this article, the authors have presented the MHD hybrid nanoliquid flow comprised of CuO and Ag nanoparticles (nps) over a rotating disk under the effects of thermophoresis, Brownian motion, activation energy, heat source and chemical reaction. The flow is considered over a spinning disc with convective conditions. The proposed model is solved with the help of HAM. The convergence of the HAM is also shown in order to verify the convergence of the modeled problem. The effects of embedded parameters on the velocity, energy and mass profiles of the magnetohydrodynamic flow of hybrid nanoliquid are shown with the help of Figures. Also, the effects of embedded parameters on skin friction, heat and mass transfer rate are calculated with the help of Tables. The results showed that the velocity and energy profiles are augmented with the increasing solid volume fraction. The increasing magnetic parameter reduces both the radial and tangential velocities of the hybrid nanofluid flow. The increasing effects of heat source, thermophoresis and Brownian motion factors on energy profiles are found. The increasing influence of thermophoresis and activation energy factors on concentration profile of the hybrid nanofluid flow is found, while the increasing Brownian motion, chemical reaction and Schmidt number reduce the concentration profile. [ABSTRACT FROM AUTHOR]

Engine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape CuO , platelet shape Al 2 O 3 and cylindrical shape TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil. [ABSTRACT FROM AUTHOR]

The current article aims to examine the magnetohydrodynamics (MHD) impact on the flow of MgO–Ag/water-based hybrid nanoliquid with motile microorganisms and the fluid is allowed to flow over a Riga plate subject to slip effects and activation energy. Furthermore, the presence of a uniform heat source/sink is also addressed in the energy equation. In addition to this, the thermophoresis effect is highlighted in the concentration equation. From the present proposed model, we get a non-linear system of the governing equations. The obtained system of partial differential equations (PDEs) is converted to the dimensionless system of ordinary differential equations (ODEs) using the similarity transformation. The obtained high non-linear system of equations has been solved numerically, using the parametric continuation method (PCM). In the present analysis, the main motivation is to highlight the heat transfer rate of MgO–Ag/water-based hybrid nanofluid flow over a Riga plate. The second motivation of the present research is to highlight the impact of slip conditions on the velocity, energy, and mass profiles. From the graphical analysis, it is depicted that the slip conditions reduce the velocity, energy, and mass outlines. From the present analysis, we concluded that volume friction reduced the flow profile while increasing the temperature of the fluid flow over a Riga plate. All the parameters of the present research are highlighted in velocity temperature and concertation of the fluid. In addition to this in all the figures we have compared the hybrid nanofluid with mono nanofluid and the also the comparison between slip and no-slip conditions have carried out through graphs for velocity, temperature, and concentration. [ABSTRACT FROM AUTHOR]

Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. Based on the characteristics of nanofluids, this study examines generalized Brinkman-type nanofluid flow in a vertical channel. Three different types of ultrafine solid nanoparticles such as GO, Al 2 O 3 , and TiO 2 are dispersed uniformly in regular water to form nanofluid.  Partial differential equations (PDEs) are used to model the phenomena. Fick's and Fourier's laws of fractional order were then used to formulate the generalized mathematical model. The exact solution of the generalized mathematical model has been obtained by the joint use of Fourier sine and the Laplace transform (LT) techniques. The obtained solution is represented in Mittag-Leffler function. To analyze the behavior of fluid flow, heat and mass distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is worth noting from the analysis that the heat transfer efficiency of regular water has been improved by 25% by using GO nanoparticles, 23.98% by using Al 2 O 3 , and 20.88% by using TiO 2 . [ABSTRACT FROM AUTHOR]

The fluid containing solid nanoparticles "nanofluid" performed more effectively compared to conventional fluids. The thermal scientists and scholars considered nanofluid in their research due to its useful applications in different thermal systems. But nanofluid still not enough for the required thermal transport properties. Therefore, the researchers tried to disperse two or more than two nanoparticles which are called hybrid and tri‐hybrid nanofluid. It was tested experimentally that these hybrid nanofluids are more efficient fluids in different cooling systems compared to nanofluid and regular fluids. The present article carried out the research about the suspension of three different kinds of nanoparticles in various shapes for advance cooling applications in industries and engineering problems. The three nanoparticles are cylindrical carbon nanotubes(CNT)$({CNT})$, spherical aluminum oxide(Al2O3)$({A{l_2}{O_3}})$, and platelet shaped(Graphene) are mixed in water flowing in a rotating disk. This advance fluid has remarkable enhancement in the heat transfer rate in comparison with regular fluid, mono nanofluid and hybrid nanofluid. In this study viscoelastic radiative ternary hybrid nanofluid is considered on a rotating disk. The solutions are obtained by using the HAM method. For physical interpretation, all the flow parameters are discussed through graphs. The impact of volume fraction on the flow and heat transfer is also evaluated and presented in graphs. From the comparison, it was declared that tri‐hybrid nanofluid has the best thermal performance compared to hybrid and mono nanofluid. Furthermore, radiation increases the temperature of the fluid, while viscoelastic parameter decreases the radial and tangential velocity. From the present study, we noticed that by considering the tri‐hybrid mixture in water, the rate of heat transfer can be enhanced up to 33.69%. Finally, the results obtained show that the tri‐hybrid nanofluid has excellent performance in the heat transfer rate. [ABSTRACT FROM AUTHOR]

In the modern era, the heat transfer is the basic need in every field of sciences and engineering. To augment the energy transfer, the ternary hybrid nanofluid (Thnf) has been used. After the successful nanofluid working performance, the researchers used this idea in many physical situations. Later on, the researchers tried to further improve the performance of nanofluid with high stability. Motivated from the unique practical applications of hybrid nanofluid, in the present analysis, we have considered ternary nanoliquid, which is obtained by the suspension of three nano particulates in base fluids. The aim of the present research is to highlight the thermal applications of ternary nanofluid in the vertical stretching wall jet flow. The suspension of three different nano solid particles is considered in a base liquid water a jet flow over a vertical extending sheet is addressed. In addition to this, the presence of chemical reaction in the concentration, thermophoresis effect in the energy equation and heat source is also addressed. To model the present phenomena of flow using the modified Buongiorno's model, that highlights the impact of Brownian motion and thermophoresis effect. The present flow problem is modelled in terms of PDE's. To transform the obtained model, we use appropriate similarity variables. The transform model is then solved numerically, using the fast convergence numerical PCM approach (parametric continuation method). The solution obtained is shown through graphical representation by indicating the impact of pertinent flow parameters. Finally, from the present results, we obtained that the performance of Thnf is effective in water as compared to hybrid nanoliquid and mono nanofluid. Furthermore, the motile gyrotactic microbes profile gets lower with the varying values of bioconvection Lewis number and Peclet number. [ABSTRACT FROM AUTHOR]

Fractional calculus gets more attention in applied and pure science from the last two decay due to their valuable contribution. Due to extensive applications of fractional derivatives, the main aim of this article is focused on the multi fractional comparative study of entropy generation of magnetohydrodynamic (MHD) flow of Casson nanofluid with slipping and ramped wall heating effect on the plate. Set of partial differential equations forms governing equation and by using constant proportional–Caputo hybrid (CPC), Atangana–baleanu (AB) and Caputo Fabrizio (CF) fractional derivative generalized the model. Using the Laplace transform approach, a closed form of the solution is attained. Entropy production for Casson nanofluid is explored and compared using triple fractional modelled and for four different nanoparticles. Furthermore, the Bejan number is compared for the previously mentioned fractional derivatives. The graphs depict the effect of several parameters on the minimization and maximisation of multi generalised entropy generation. Instead of Atangana–baleanu and Caputo Fabrizio fractional operators, the newly proportional Caputo hybrid operator has a strong memory effect. It is concluded that CPC fractional model is more realistic then other two fractional model in case of ramped wall temperature while in case of isothermal wall temperature the results are vice versa. [ABSTRACT FROM AUTHOR]

During last decades the research of nanofluid is of great interest all over the World, particularly because of its thermal applications in engineering, and biological sciences. Although nanofluid performance is well appreciate and showed good results in the heat transport phenomena, to further improve conventional base fluids thermal performance an increasing number of researchers have started considering structured nanoparticles suspension in one base fluid. As to make an example, when considering the suspension of three different nanoparticles in a single base fluid we have the so called "ternary hybrid nanofluid". In the present study three different shaped nanoparticles are uniformly dispersed in blood. In particular, the three different shaped nanoparticles are spherical shaped ferric oxide Fe 3 O 4 , platelet shaped zinc Zn , and cylindrical shaped gold Au , which are considered in blood base fluid because of related advance pharmaceutical applications. Accordingly, we focused our attention on the sharp evaluation of heat transfer for the unsteady couple stress Casson tri-hybrid nanofluid flow in channel. In particular, we formulated the problem via momentum and energy equations in terms of partial differential equations equipped with realistic physical initial and boundary conditions. Moreover, we transformed classical model into their fractional counterparts by applying the Atangana–Baleanu time-fractional operator. Solutions to velocity and temperature equations have been obtained by using both the Laplace and the Fourier transforms, while the effect of physical parameters on velocity and temperature profiles, have been graphically analyzed exploiting MATHCAD. In particular, latter study clearly shows that for higher values of volume fraction ϕ hnf of the nanoparticles the fluid velocity declines, while the temperature rises for the higher values of volume fraction ϕ hnf of the nanoparticles. Using blood-based ternary hybrid nanofluid enhances the rate of heat transfer up-to 8.05%, spherical shaped Fe 3 O 4 enhances up-to 4.63%, platelet shaped Zn nanoparticles enhances up-to 8.984% and cylindrical shaped gold Au nanoparticles enhances up-to 10.407%. [ABSTRACT FROM AUTHOR]

The core devotion of this study is to develop a generalized model by means of a recently proposed fractional technique in order to anticipate the enhancement in the thermal efficiency of engine oil because of the dispersion of graphene and magnesia nanoparticles. In addition to investigating the synergistic attributes of the foregoing particles, this work evaluates shape impacts for column, brick, tetrahedron, blade, and lamina-like shapes. In the primary model, the flow equation is coupled with concentration and energy functions. This classical system is transmuted into a fractional environment by generalizing mathematical expressions of thermal and diffusion fluxes by virtue of the Prabhakar fractional operator. In this study, ramped flow and temperature slip conditions are simultaneously applied for the first time to examine the behavior of a hybrid nanofluid. The mathematical analysis of this problem involves the incorporation of dimension-independent parameters into the model and the execution of the Laplace transform for the consequent equations. By doing so, exact solutions are derived in the form of Mittag–Leffler functions. Multiple illustrations are developed by dint of exact solutions to chew over all aspects of temperature variations and flow dynamics. For the preparation of these illustrations, the details of parametric ranges are as follows: 0.00 ≤ Υ ≤ 0.04 , 2.0 ≤ G r 1 ≤ 8.0 , 0.5 ≤ S c ≤ 2.0 , 0.1 ≤ τ ≤ 4.0 , 0.1 ≤ d ≤ 0.6 , 0.2 ≤ λ 1 ≤ 1.5 , and 1.0 ≤ G r 2 ≤ 7.0 . The contribution of differently shaped nanoparticles, volume proportions, and fractional parameters in boosting the heat-transferring attributes of engine oil is also anticipated. In this regard, results for Nusselt number are provided in tabular form. Additionally, a brief analysis of shear stress is carried out for fractional parameters and various combinations of magnesia, graphene, and engine oil. This investigation anticipates that engine oil's hybridization with magnesia and graphene would result in a 33% increase in its thermal performance, which evidently improves its industrial significance. The enhancement in Schmidt number yields an improvement in the mass transfer rate. An increment in collective volume fraction leads to raising the profile of the thermal field. However, the velocity indicates a decreasing behavior. Nusselt number reaches its highest value ( N u = 8.1363 ) for the lamina shape of considered particles. When the intensity of the buoyancy force augments, it causes the velocity to increase. [ABSTRACT FROM AUTHOR]

An incredible eradication of thermal indulgence is required to enhance the flow and heat transfer enhancement in micro/nanofluidic devices. In addition, the rapid transport and instantaneous mixing of colloidal suspensions of metallic particles at nanoscale are exceptionally crucial at ascendency of inertial and surface forces. To address these challenges, the present work is intended to investigate the role of trimetallic nanofluid comprising of three kinds of nano-sized granules (titanium oxide, Silica and Aluminium dioxide) with pure blood through a heated micropump in the presence of inclined magnetic field and axially implemented electric field. To ensure rapid mixing in unidirectional flow, the pump internal surface is lined-up with mimetic motile cilia with slip boundary. The embedded cilia whip in pattern due to dynein molecular motion controlled by time and produce a set of metachronal waves along the pump wall. The shooting technique is executed to compute the numerical solution. In a comparative glance it is revealed that the trimetallic nanofluid exhibits 10% higher heat transfer efficiency as compared to bi-hybrid and mono nanofluids. Moreover, the involvement of electroosmosis results in almost 17% decrease in the heat transfer rate if it values jumps from 1 to 5. The fluid temperature in case of trimetallic nanofluid is higher and thus keeps the heat transfer entropy and the total entropy lower. Furthermore, involvement of thermal radiated and momentum slip significantly contribute in reducing heat losses. [ABSTRACT FROM AUTHOR]

The present problem is offered for the visualization of the MHD flow of non-Newtonian Cross-hybrid nanoliquid with the application of Darcy–Forchheimer through the porous medium toward the moving thin needle. Further, the present work described the engineering applications of the non-Newtonian fluids. Commonly, the non-Newtonian liquids are useful for lubricating purposes including greases and Engine oil (EO), etc. Additionally, the computations for Hall current and viscous dissipation are deliberated for the enhancement of flow behavior. The heat transmission phenomenon is discussed under the Cattaneo–Christov heat flux theory instead of Fourier's law. Engineering applications of the homogeneous and heterogeneous chemical reactions are analyzed in the current analysis. EO has an enormous application in the engineering fields, and therefore in the present work EO is used as a base liquid and molybdenum disulfide MoS 2 and graphene oxide GO are the nanoparticles. The hybrid nanofluid showed more satisfactory results in the enhancement of the heat transport in the engineering fields as compared to the nanofluids and regular fluids; therefore the MoS 2 and GO are mix-ups in the EO. The present model is developed in the form of PDEs which can be altered into ODEs through the execution of suitable similarity transformations. A homotopic analysis scheme is adopted for the analytic simulation of the transformed ODEs. The velocity, energy, and mass curves are computed against different flow parameters in a pictorial form. Skin friction and Nusselt in contour graphs are discussed. Key findings from this inspection are that both nanoparticle volume fractions declined the velocity profile but augmented the temperature of the hybrid nanoliquid. Further, it is noted that boosting the Schmidt has significantly reduced the hybrid nanofluid concentration. [ABSTRACT FROM AUTHOR]

The energy transition to enhance heat transport during the flow of ternary hybrid nanofluid comprised of Copper (Cu), Iron oxide (Fe 3 O 4), Silicon dioxide (SiO 2) nanoparticles and Polymer as base liquid over a revolving disk surface has been reported. From the several existing techniques, adding nanoparticles to standard working fluids is an effective approach that might dramatically improve the rate of heat transfer. The Hall and radiation impacts are also considered. A mathematical model is developed by assuming the flow as incompressible and purely radial in a cylindrical coordinate system and appropriate similarity variables are introduced for problem simplification and dimensionless analysis. The solution of complex generated PDEs was calculated using semi analytical method known as Homotopy Analysis Method (HAM) after translating them into corresponding ODEs. It has been observed that the consequences of thermal radiation, dissipation term, unsteadiness and rotation parameters boost the energy transmission rate and enhances the heat transfer rate of tri hybrid nanofluids. However, Cu - Fe 3 O 4 nanoparticles in the base fluid remarkably magnifies the energy transmission rate. The unitary ternary hybrid nanofluid (Cu, Fe 3 O 4 , SiO 2) has higher velocity profiles as compared to unitary nano fluid (Cu) and hybrid nano-fluid (Cu-Fe 3 O 4). [ABSTRACT FROM AUTHOR]

In the pump of different machines, the vacuum pump oil (VPO) is used as a lubricant. The heat rate transport mechanism is a significant requirement for all industries and engineering. The applications of VPO in discrete fields of industries and engineering fields are uranium enrichment, electron microscopy, radio pharmacy, ophthalmic coating, radiosurgery, production of most types of electric lamps, mass spectrometers, freeze-drying, and, etc. Therefore, in the present study, the nanoparticles are mixed up into the VPO base liquid for the augmentation of energy transportation. Further, the MHD flow of a couple stress nanoliquid with the applications of Hall current toward the rotating disk is discussed. The Darcy-Forchheimer along with porous medium is examined. The prevalence of viscous dissipation, thermal radiation, and Joule heating impacts are also considered. With the aid of Cattaneo-Christov heat-mass flux theory, the mechanism for energy and mass transport is deliberated. The idea of the motile gyrotactic microorganisms is incorporated. The existing problem is expressed as higher-order PDEs, which are then transformed into higher-order ODEs by employing the appropriate similarity transformations. For the analytical simulation of the modeled system of equations, the HAM scheme is utilized. The behavior of the flow profiles of the nanoliquid against various flow parameters has discoursed through the graphs. The outcomes from this analysis determined that the increment in a couple-stress liquid parameter reduced the fluid velocity. It is obtained that, the expansion in thermal and solutal relaxation time parameters decayed the nanofluid temperature and concentration. Further, it is examined that a higher magnetic field amplified the skin friction coefficients of the nanoliquid. Heat transport is increased through the rising of the radiation parameter. [ABSTRACT FROM AUTHOR]

The research of fluid containing nanoparticles for the heat transport characteristics is very famous because of its variety of real-life applications in various thermal systems. Although the thermal efficiency of the nanofluid was effective but still the nano scientists were trying to introduce some new advance class of fluid. Therefore, an advance class of fluid is developed by the dispersion of two different nano sized particles in the conventional base fluid known as "Hybrid nanofluid" which is more effective compared to simple nanofluids in many engineering and industrial applications. Therefore, motivated from the hybrid type of nanofluids in the current research we have taken two-dimensional laminar and steady flow of second grade fluid passing through porous plate. The engine oil base fluid is widely used fluid in the engineering and industrial problems. Keeping these applications in mind the engine oil is considered and two different nanoparticles Copper and aluminum oxide are added in ordered to get the required thermal characteristics. In addition to this the thermal radiation, chemical reaction, activation energy, Brownian motion and thermophoresis are also addressed during the current research. The present proposed higher-order PDE's is transformed to the non-linear system of ODE's. For the solution of the proposed high non-linear model HAM method is employed. As the hybrid nanofluid are highlighted on the second-grade fluid flow over a horizontal porous flat plate. During the present analysis and experimental study, it has been proved that the performance of hybrid nanofluid is efficient in many situations compared to nanofluid and regular fluid. For physical interpretation all the flow parameters are discussed through graphs. The impact of volume fraction is also addressed through graphs. Moreover, the comparative analysis between hybrid and nanofluid is carried out and found that hybrid nanofluid performed well as compared to nanofluid and regular fluid. The engineering quantities obtained from the present research have been presented in tables. [ABSTRACT FROM AUTHOR]

To control the complicated rheological behavior of fluid models, several mathematical approaches have been established. Empirical, statistical, iterative, and analytical approaches are used to study such mathematical models. Consequently, this paper provides an analytical analysis and assessment of the Laplace, and Sumudu transforms for the unsteady MHD flow prediction of a second‐grade hybrid nanofluid in a rotating frame. The mathematical model is built using a nonfractional technique with ramping conditions. To explore the velocity field and heat transfer, we used Laplace and Sumudu transforms to uncover the unseen characteristics of magnetized second‐grade hybrid nanofluid flow. For the purposes of comparison, a graphical picture is given that represents successful outcomes in the literature for the first time. In conclusion, numerical simulations show that the derived outlines of velocity and temperature fields using Sumudu and Laplace transformations correspond well. In addition, the variation of velocity of fluid against time is reported for ramped wall temperature, while it is constant for isothermal wall temperature. [ABSTRACT FROM AUTHOR]

Compared with methanol (pure) and blood, methanol‐ and blood‐based nanofluids are significant with numerous characteristics, including thermophysical effects and immersion rate of CO2 in tray column absorber. Blood‐based liquids show importance in biological treatments like digestion as well as breathing systems. Mixed convective conditions and suction or injection are helpful in controlling the heating or the cooling in industrial applications. Keeping this in view, we examined the physical perception of entropy generation (EG) in a mixed convective hybrid nanofluid (HBN) flow with chemical reaction, cross‐diffusion, and transpiration in a curved surface with activation energy and thermal radiation. Transformed principal equations are determined with the assistance of a fourth‐order Runge–Kutta method with a shooting technique. We obtained solutions for two different cases, that is, for hybrid (mixture of cases) (magnetite + hematite + blood) and (magnetite + hematite + methanol). Obtained results are discussed via graphs and tables. Also, we discussed the effects of the Bejan number and the EG. We found that the EG appears more conspicuously in the case of magnetite + hematite + methanol compare to magnetite + hematite + blood case. We also found that in the magnetite + hematite + methanol case the flow and heat transfer characteristics are more pronounced compared with that in the case of magnetite + hematite + blood. This helps us to choose magnetite + hematite + blood or magnetite + hematite + methanol compositions in the manufacturing industry. Furthermore, the rate of heat transfer can be enhanced up to 16.42% in the case of methanol‐based HBN while the rate of heat transfer can be enhanced up to 19.16% in the case of blood‐based HBN. [ABSTRACT FROM AUTHOR]

The industry level enhancement of the thermal conductivities of various base fluids is greatly aided by a nanofluid. Most engineering phenomena call for the removal of heat in order to improve industrial machinery performance. These fluids have a variety of uses, such as coolants for electric gadgets, car engines, heat exchangers and nuclear reactors. In this article, the authors have investigated the micropolar water‐based hybrid nanofluid containing silver and alumina nanoparticles over an extending surface. The flow problem also takes into account the Joule heating, variable heat source/sink, thermal radiation, chemical reaction, and activation energy. The flow problem is taken in the form of PDEs which are then transformed to ODEs by means of suitable similarity variables. The flow problem is solved with the help of HAM, which is capable of solving highly nonlinear partial and ordinary differential equations. The convergence of the HAM is also shown with the help of Figure 1. The results showed that the physical parameters have a greater influence on the velocity profile of nanofluid flow than hybrid nanofluid flow. However, the upshots of the physical constraints on the thermal profiles have a dominant impact on the hybrid nanoliquid flow relative to nanofluid. Also, it found that the physical parameters have a greater influence on the energy and mass transfer rates of the hybrid nanofluid flow than the nanofluid. [ABSTRACT FROM AUTHOR]

In this investigation, the thin‐film flow of Maxwell nanofluid has been considered on an inclined stretched sheet by using the idea of double diffusion. Non‐Newtonian fluids are mostly used in biological processing, chemical reactions, and industrial applications. Magnetic effects have been applied to the flow system in the normal direction. The variable thickness of the liquid film varied during the double diffusion under the influence of the embedded parameters. Equations that handled the flow phenomenon have been changed to dimension‐free format and then have been solved by employing the homotopy analysis method (HAM). The substantial parameters were traced out during the conversion of flow equations and discussed theoretically using a graphical view. Higher values of the double diffusion parameters decay the thermal and concentration profiles. It has been revealed in this study that fluid motion has retarded with augmenting values of magnetic field effects, unsteadiness parameter, and thin‐film thickness. Temperature distribution upsurges with higher values of Brownian motion, and thermophoresis parameters while decreasing with growth in film thickness factor and thermal Maxwell parameter. Concentration profiles upsurge with augmenting values of thermophoresis parameter and retard with growth in Brownian motion. [ABSTRACT FROM AUTHOR]

This work explores a semi‐analytical solution of the Magnetohydrodynamics (MHD) viscoelastic water‐based hybrid nanoliquid flow containing TiO2 and CoFe2O4 nanoparticles past a rotating disk along with velocity slip condition. The impact of solar radiation is incorporated in the temperature equation. The current study consists of non‐Newtonian viscoelastic hybrid nanofluid flow problem which is comprised of momentum and temperature equations. By using suitable similarity transformations, the higher‐order nonlinear ordinary differential equations are transformed into the nonlinear ordinary differential equations and then resolved with the execution of the homotopy analysis scheme in MATHEMATICA 10.0. The behavior of the involved physical parameters on the hybrid nanoliquid radial and tangential velocities and temperature profiles are calculated in a graphical form. Also, the skin friction and Nusselt number for TiO2−CoFe2O4/${\rm{Ti}}{{\rm{O}}_2}-{\rm{CoF}}{{\rm{e}}_2}{{\rm{O}}_4}/$/water nanoliquid are described in tabular form. Some major results related to the current work are that by rising the values of the viscoelastic parameter, nanoparticle volume fraction of the titanium dioxide and cobalt oxide increases the skin friction coefficient Cgr${C_{gr}}$. The viscoelastic parameter, nanoparticles volume fraction of the cobalt oxide and magnetic parameter reduced the skin friction coefficient Cfr${C_{fr}}$ of the hybrid nanofluid. It is noted that Nusselt number is lower for both QSR=0${Q_{SR}} = 0$ and QSR>0${Q_{SR}} > 0$ cases against the absorption factor. The expansion in hybrid nanofluid temperature is examined for both QSR=0${Q_{SR}} = 0$ and QSR>0${Q_{SR}} > 0$ cases. It is obtained that the temperature and heat rate transfer of the hybrid nanofluid are dominant in the presence of solar radiation. [ABSTRACT FROM AUTHOR]

Electro-osmotic flow via a microchannel has numerous uses in the contemporary world, including in the biochemical and pharmaceutical industries. This research explores the electroosmotic flow of Casson-type nanofluid with Sodium Alginate nanoparticles through a vertically tilted microchannel. In addition, the transverse magnetic field is also considered. In this flowing fluid, the influence of heat and mass transmission is also explored. The aforementioned physical process is represented by partial differential equations. Utilizing suitable dimensionless variables for nondimensionalized. Furthermore, the non—dimensional classical system is fractionalized with the use of generalized Fourier and Fick's law. Generalizations are made using the Caputo derivative's description. The analytical solution of the velocity, temperature, and concentration profiles is obtained by combining the methods of Laplace and Fourier. Interestingly, the influence of several physical characteristics such as the fractional parameter, Casson fluid parameter, the thermal and mass Grashof numbers, and the zeta potential parameter is displayed. Moreover, the results show that the volume fractional of nanoparticles enhances the rate of heat transfer up to 39.90%, Skin friction up to 38.05%, and Sherwood number up to 11.11%. Also, the angle of inclination enhances the fluid velocity. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids play a significant role in the advancement of thermal characteristics of pure fluids both at experimental and industrial levels. This work explores the mixed convective MHD micropolar hybrid nanofluid flow past a flat surface. The hybrid nanofluid flow is composed of alumina and silver nanoparticles whereas water is used as a base fluid. The plate has placed vertical in a permeable medium with suction and injection effects. Furthermore, viscous dissipation, thermal radiation and Joule heating effects are taken into consideration. Specific similarity variables have been used to convert the set of modeled equations to dimension-free form and then has solved by homotopy analysis method (HAM). It has revealed in this investigation that, fluid motion upsurge with growth in magnetic field effects and mixed convection parameter and decline with higher values of micropolar factor. Micro-rotational velocity of fluid is upsurge with higher values of micropolar factor. Thermal flow behavior is augmenting for expended values of magnetic effects, radiation factor, Eckert number and strength of heat source. The intensification in magnetic strength and mixed convection factors has declined the skin friction and has upsurge with higher values of micropolar parameter. The Nusselt number has increased with the intensification in magnetic effects, radiation factor and Eckert number. [ABSTRACT FROM AUTHOR]

Scientists and researchers are much interested in studying graphene and silver nanoparticles for the enhancement of heat transport due to their extensive variety of applications in different areas of industrial and engineering such as drug delivery, medical devices, ultra-light, excellent electrical conductivity, strong medical strength, health care, consumer, food, etc. Therefore, in the existing investigation, the MHD flow of a mixed convective hybrid nanoliquid with graphene and silver nanoparticles past a rotating disk is considered. Water and ethylene glycol (50:50) is used as a base liquid in the existing model. The mechanism for heat transport is computed with the existence of thermal radiation and thermal convective condition. Homogeneous and heterogeneous chemical reactions are assumed in the flow behavior. The mathematical formulation of the proposed problem is based on the nonlinear PDEs which are then transformed to nonlinear ODEs by manipulating the appropriate similarity transformation. The simulation of the existing problem has been performed with the help of the homotopy analysis technique. The outcomes of the different flow parameters on the velocities, temperature, concentration, skin friction coefficient, and Nusselt number of the hybrid nanofluid are attained via graphs and tables. Some significant results from the existing problem demonstrate that the rate of heat transport is greater for the thermal Biot number and nanoparticles volume fraction. Further, it is noticed that the velocity of the liquid particles becomes lower for a higher magnetic field parameter. [ABSTRACT FROM AUTHOR]

This article aims to study entropy generation and heat transfer due to free convection. Two types of base fluids (water and kerosene oil) are taken with a suspension of titanium alloy nanoparticles. An external magnetic field is applied in a perpendicular direction and the induced magnetic field is neglected. Scientific analysis is performed on magnetohydrodynamic flow through a Darcy medium. Free convection and the sudden motion of the heated plate cause the fluid to flow. The problem is formulated in terms of differential equations with associated physical conditions. Relations for entropy generation and Bejan numbers are also provided. The Laplace transform technique has been used for finding the exact solution to the problem. Results are plotted using Mathcad software and a comparison is made between water-titanium alloy and kerosene oil-titanium alloy nanoparticles for velocity, temperature, entropy generation, and Bejan number. It is concluded that kerosene oil base fluid has a greater velocity and temperature profile in all parametric studies as compared to water-based fluid. While in the case of entropy generation and Bejan number, near to the plate and for away the plate the behaver is distinct. Entropy generation and Bejan number are boosting up via using different base fluid. For larger estimation of Brinkman number, both Bejan number and entropy rate have the opposite effect. The volume fraction of nanofluid enhance the rate of heat transfer in case of both nanofluid. While the water base nanofluid enhance the rate of heat transfer up to 19.14% and kerosene oil base fluid is enhanced up to 30.01%. [ABSTRACT FROM AUTHOR]

In this investigation, a 2D flow of micropolar hybrid nanofluid (HNF) is considered over stretching/shrinking sheet. The magnetic effect is employed in a perpendicular direction to the surface of sheet. To improve the thermal conductivity of the fluid flow, the nanoparticles (NPs) of iron oxide and graphene oxide are mixed with water to obtain the HNF and water is used as a base fluid(Fe3O4+GO/H2O)$\;({{\rm{F}}{{\rm{e}}_3}{{\rm{O}}_4} + {\rm{GO}}/{{\rm{H}}_2}{\rm{O}}})$. The proposed equations of the modeled problem are converted to dimensionless form by implementing the similar variables. The analytical solution of the modeled equations is evaluated by mean of homotopy analysis method. The impacts of the embedded constraints on the HNF flow profiles are discoursed theoretically by incorporating a graphical view. Special cases (stretching, shrinking) are considered for the HNF in order to examine the impacts of the embedded parameters on the HNF flow profiles. The results showed that the expanding values of the stretching parameter, the HNF flow particles are pushed in a forward direction due to which fluid moves swiftly for both shrinking/stretching cases. The velocity profiles are increased with the increasing material parameter for the stretching case, while a reducing impact is found for the shrinking case. Also, the increasing material parameter enhances the microrotation profiles the HNF flow. Furthermore, the material parameter shows the same behavior for both stretching and shrinking cases. The increasing volume fraction of the solid NPs reduces the velocity profiles for stretching case, while augments for shrinking case. On the other hand, it is observed that the increasing volume fractions of the NPs increase the microrotation and temperature profiles for both stretching and shrinking cases. [ABSTRACT FROM AUTHOR]

Entropy generation in unsteady magneto‐bioconvection Casson nanofluid flow with gyrotactic microorganisms in the presence of Cattaneo–Christov heat and mass flux theory is analyzed. Buongiorno nanofluid model is followed taken into account the influences of viscous dissipation, Brownian motion, and thermophoresis. Mathematica is used to compute the transformed equations through homotopy analysis method (HAM) resulting from the implementation of similarity transformations on governing equations and boundary conditions. The effects of pertinent parameters on different profiles are shown in graphs and discussed in detail. [ABSTRACT FROM AUTHOR]

This report presents the three-dimensional electromagnetohydrodynamic flow of a zinc-oxide–water nanofluid past a bidirectional Riga plate with velocity slips and thermal and mass convection conditions. The Cattaneo–Christov heat and mas flux model, thermal radiation, chemical reaction and activation energy are considered to analyze the flow problem. The volume fraction of the ZnO nanoparticles is taken 6% in this analysis. An appropriate set of similarity variables is used to transform the partial differential equations into ordinary differential equations. During this process, some parameters are found and influences of these factors on the flow profiles are shown and discussed in detail. A numerical technique called NDSolve is considered for the solution of the nanofluid flow problem. The results showed that higher solid volume fraction and slip parameter have reduced velocities profiles and the increasing solid volume fraction and thermal Biot number have increased the temperature profile. Additionally, the concentration Biot number has increased the concentration profile. The modified Hartmann number has significantly increased the velocity profile. Dual impacts in velocity profiles along primary and secondary direction has been observed due to stretching ratio parameter. A comparison of current results has been carried with a fine agreement amongst current and established results. [ABSTRACT FROM AUTHOR]

This article investigates graphite-aluminum oxide hybrid nanoparticles in water-base fluid with the addition of heat generation in the presence of a porous medium. The problem is formulated in terms of momentum and energy equations with sufficient initial and boundary conditions. The solution is investigated by using the Laplace transform method. It is observed that the velocity of the drilling fluid is controlled by adding hybrid nanoparticles as compared to simple nanofluids. In a similar way, the temperature of the fluid is reduced. Also, the heat transfer rate is boosted up to 37.40741% by using hybrid nanofluid compared to regular nanofluid. Moreover, the heat transfer rate was increased up to 11.149% by using different shapes of nanoparticles in the base fluid water. It is also observed that by using hybrid nanofluid skin fraction is boosted up at y = 0 and boosted down at y = 1. [ABSTRACT FROM AUTHOR]

Vacuum pump oil (VPO) is used as a lubricant in pumps of different machines. The rate of heat transport is a fundamental requirement of all phenomena. To enhance the rate of heat transmission and reduce the amount of energy consumed as a result of high temperatures. For this reason, the vacuum pump oil (VPO) is taken as a base fluid and Fe3O4 is the nanoparticles suspended in VPO. That's why, the present study inspected the consequence of Hall current, Joule heating effect and variable thickness on these three-dimensional magnetohydrodynamics bidirectional flow of nanoliquid past on a stretchable sheet. Further, the Cattaneo-Christove heat flux and radiation impacts are also considered. The VPO−Fe3O4 nanofluid model is composed of momentum equations in x−direction, y−direction and temperature equations. The leading higher-order non-linear PDEs of the current study have been changed into non-linear ODEs with the implementation of appropriate similarity transformations. The procedure of the homotopy analysis method is hired on the resulting higher-order non-linear ODEs along with boundary conditions for the analytical solution. The significance of distinct flow parameters on the velocities in x−direction, y−direction and temperature profiles of the nanofluid have been encountered and briefly explained in a graphical form. Some important findings of the present modelling are that with the increment of nanoparticles volume fraction the nanofluid velocities in x−direction and y−direction are increased. It is also detected that higher estimations of magnetic field parameter, Prandtl number and thermal relaxation time parameter declined the nanofluid temperature. During this examination of the model, it is found that the Fe3O4-Vacuum pump oil (VPO) nanofluid enhanced the rate of heat transfer. Also, the vacuum pump oil (VPO) has many industrial and engineering applications. The current study will help to improve the rate of heat transmission by taking this into account due to which working machines will do better performance and the loss of useful energy will be decayed. Lastly, the skin friction coefficient and Nusselt number are also illustrated in a tabular form. Some major findings according to the numerical computation of the problem are that the enhancing estimations of magnetic parameter, nanoparticles volume fraction and wall thickness parameter augmented the skin friction coefficient in x−direction and Nusselt number. The reduction in skin friction coefficient of the nanofluid in y−direction is examined for Hall current and shape parameter. [ABSTRACT FROM AUTHOR]

Motivated by the temporal relaxation feature of the Jeffrey model and its practical uses in the rheological modeling of several vital liquids, this study aimed to present a theoretical analysis of three-dimensional MHD Jeffrey nanofluid flows over a dual stretching surface with velocity slip conditions. By adopting the nonhomogeneous nanofluid model along with the passive control approach of nanoparticles, the current flow problem is solved semi-analytically via the homotopy analysis method for convective heating and multiple slip conditions. Dynamically, the magnetic and viscoelastic parameters have a declining effect on the velocity distributions in both directions in the existence and absence of slip effects, while the Deborah number has generally an escalating influence on the flow distributions. On the other hand, the variations of the velocity profiles in both directions are always greater in the presence of slip effect as compared to the nonslip case. Besides, the velocity stretching factor rises the velocity profiles in both directions. Furthermore, this increasing impact is dominant for the velocity distribution along the y-direction as compared to the velocity field along the x-direction. Thermally, the greater Biot number increases the temperature distribution. However, the bigger Schmidt number reduces the concentration distribution. [ABSTRACT FROM AUTHOR]

In the current century, hybrid nanofluids are considered one of the modified forms of heat transferring fluids because of their advanced thermal characteristics. The main motive of this article is the formulation of two different fractional models to explain flow patterns and thermal behavior of sodium alginate (NaAlg/SA) based hybrid nanofluid. The improvement in the thermal performance of NaAlg due to the addition of molybdenum-disulfide ( MoS 2 ) and cobalt (Co) nanoparticles is also analyzed. The ramped motion of an unbounded inclined plate leads to execute the flow of hybrid nanofluid through a porous material. The considered hybrid nanofluid also encounters magnetic effects. The heat transfer process starts due to the application of the ramped heating condition at the inclined boundary and thermal radiation, shape factor of nanoparticles, and heat injection/suction also affect this process. The mathematical modeling of the considered problem is carried out and two different fractional models are developed through Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) fractional derivatives. Using the powerful Laplace transform technique, double mathematical and fractional analysis is performed to establish the analytic solutions. To clearly understand the heat transfer mechanism and behavior of shear stress, numerical simulations are performed for temperature and velocity gradients at the boundary. For a comprehensive physical investigation, several graphs and tables are furnished to evaluate the role of involved thermal and physical parameters in developing the flow patterns and temperature field. This study concludes that even dispersion of Co and MoS 2 nanoparticles in NaAlg enhances the heat transfer rate of host fluid up to 21%. Comparative analysis suggests that AB fractional derivative is more adequate to describe the flow patterns and temperature field. Furthermore, maximum values of Nusselt number are observed when both nanoparticles are considered of blade shape. [ABSTRACT FROM AUTHOR]

In biological systems, the MHD boundary layer bioconvection flow through permeable surface has several applications, including electronic gadgets, heating systems, building thermal insulation, geological systems, renewable energy, electromagnetism and nuclear waste. The bioconvection caused by the hydromagnetic flow of a special form of water-based nanoliquid including motile microorganisms and nanoparticles across a porous upright moving surface is investigated in this report. The combination of motile microbes and nanoparticles causes nanofluid bioconvection is studied under the cumulative impact of magnetic fields and buoyancy forces. The Brownian motion, thermophoresis effects, heat absorption/generation, chemical reaction and Darcy Forchhemier impact are also unified into the nonlinear model of differential equations. The modeled boundary value problem is numerically computed by employing a suitable similarity operation and the parametric continuation procedure. The parametric study of the flow physical parameters is evaluated versus the velocity, energy, volume fraction of nanoparticles, motile microorganisms' density, skin friction, Sherwood number and Nusselt number. It has been observed that the velocity profile reduces with the effect of porosity parameter k1, inertial parameter k2, Hartmann number and buoyancy ratio. While the energy transition profile significantly enhances with the flourishing values of Eckert number Ec, heat absorption/generation Q and Hartmann number respectively. [ABSTRACT FROM AUTHOR]

Nanoparticles are used in industrial and engineering by allowing for faster heat transfer rates in microchips, vehicle cooling, food processing, and nuclear reactors. This research aims to scrutinize the three-dimensional bioconvectional flow performances of viscoelastic nanofluids through a elongating sheet with motile microorganisms. Radiative impact and solutal boundary conditions are studied here. The impacts of thermophoresis, Brownian motion, and bioconvection are also considered. By using suitable similarity transformations, the PDEs are converted into ODEs. The numerical and graphical results are calculated with the help of shooting scheme built-in function Bvp4c in computational tool MATLAB. The graphical and numerical importance of physical engineering parameters like local skin friction, local Nusselt, local Sherwood, and local motile microorganism numbers are discussed here. The thermal profile is enhanced for the higher estimations of the Brownian motion and thermophoresis parameter. The heat profile is boosted up for the increasing variations of the thermal radiation and the thermophoresis parameter. The energy profile is improved by increasing the estimations of solutal Biot number while declining for mixed convection parameter and unsteadiness parameter. The microorganism profile decays for Peclet and bioconvection Lewis number while rising for buoyancy ratio parameter and bioconvection Rayleigh number. [ABSTRACT FROM AUTHOR]

The study of thermo-physical characteristics is essential to observe the impact of several influential parameters on temperature and velocity fields. The transportation of heat in fluid flows and thermal instability/stability is a charming area of research due to their wider applications and physical significance because of their utilization in different engineering systems. This report is prepared to study thermal transportation in Maxwell hybrid nanofluid past over an infinite stretchable vertical porous sheet. An inclusion of hybrid nanofluid is performed to monitor the aspects of thermal transportation. Keeping in mind the advantages of thermal failure, non-Fourier theory for heat flux model is utilized. Aspects of external heat source are also considered. The mathematical formulation for the considered model with certain important physical aspects results in the form of coupled nonlinear PDEs system. The obtained system is reduced by engaging boundary layer approximation. Afterwards, transformations have been utilized to convert the modeled PDEs system into ODEs system. The converted nonlinear ODEs system is then handled via finite element method coded in symbolic computational package MAPLE 18.0. Grid independent survey is presented for the validation of used approach and the comparative analysis has been done to confirm the reliability of obtained solution. The obtained solution is discussed and physical aspects have been explored and recorded against numerous involved influential variables. Motion into hybrid nanoparticles and nanoparticles becomes slow down versus higher values of Forchheimer and Darcy's porous numbers. Thermal growth is enhanced for the case of hybrid nano-structures rather than for case of nanofluid. Thickness regarding momentum layer is dominated for hybrid nanoparticles rather than case of nanoparticles. [ABSTRACT FROM AUTHOR]

The present study is related to the analytical investigation of the magnetohydrodynamic flow of Ag − MgO/ water hybrid nanoliquid with slip conditions via an extending surface. The thermal radiation and Joule heating effects are incorporated within the existing hybrid nanofluid model. The system of higher-order partial differential equations is converted to the nonlinear system of ordinary differential equations by interpreting the similarity transformations. With the implementation of a strong analytical method called HAM, the solution of resulting higher-order ordinary differential equations is obtained. The results of the skin friction coefficient, Nusselt number, velocity profile, and temperature profile of the hybrid nanofluid for varying different flow parameters are attained in the form of graphs and tables. Some important outcomes showed that the Nusselt number and skin friction are increased with the enhancement in Eckert number, stretching parameter, heat generation parameter and radiation parameter for both slip and no-slip conditions. The thermal profile of the hybrid nanofluid is higher for suction effect but lower for Eckert number, stretching parameter, magnetic field, heat generation and radiation parameter. For both slip and no-slip conditions, the hybrid nanofluid velocity shows an upward trend for both the stretching and mixed convection parameters. [ABSTRACT FROM AUTHOR]

Fluid motion is caused by the surface stretching, the temperature difference or the concentration difference etc. In this study, we will focus exclusively on the 3D nanofluid flow due to expanding surface of Oldroyd-B fluid which is extended in two directions. The flow over expanding surface has several applications in engineering and industrial processes for instance plastic sheet extrusion, hot rolling, paper processing, wire drawing, plastic films painting, and fiber glass etc. In current investigation, we have discussed the nanofluid flow over an expanding surface for Oldroyd-B fluid. It is possible to use nanofluids to enhance the fluid's thermal conductivity. The equations that governs the flow are converted into nonlinear coupled ODE's. The problem's series solution was found using the method of homotopy analysis. Effects of Deborah number, thermophoretic and Brownian diffusion parameters, Prandtl and Schmidt numbers on the flow field are explored and discussed graphically. The relaxation/retardation times are noted to have contrasting effects on fluid velocity. Further, the diffusion parameter of nanoparticles enhance the temperature and nanofluid concentration. [ABSTRACT FROM AUTHOR]

The study concerns with the mechanical characteristics of rotating system of two double disks. Hall current effect, entropy generation, Arrhenius activation energy and binary chemical reactions are investigated in heat and mass transfer bioconvection flow of Maxwell nanofluid. Brownian motion and thermophoresis with thermal radiation and buoyancy effects are encountered in the governing equations. The mechanical system has been investigated by the governing equations and boundary conditions which are simplified by the use of suitable similarity transformations. Optimal homotopy analysis method is implemented to obtain the series solution of non‐linear ordinary differential equations. Physical behaviors of heat and mass transfer flow with entropy generation are investigated through the effects of embedded parameters. [ABSTRACT FROM AUTHOR]

Fractional calculus characterizes a function at those points, where classical calculus failed. In the current study, we explored the fractional behavior of the stagnation point flow of hybrid nano liquid consisting of TiO2 and Ag nanoparticles across a stretching sheet. Silver Ag and Titanium dioxide TiO2 nanocomposites are one of the most significant and fascinating nanocomposites perform an important role in nanobiotechnology, especially in nanomedicine and for cancer cell therapy since these metal nanoparticles are thought to improve photocatalytic operation. The fluid movement over a stretching layer is subjected to electric and magnetic fields. The problem has been formulated in the form of the system of PDEs, which are reduced to the system of fractional-order ODEs by implementing the fractional similarity framework. The obtained fractional order differential equations are further solved via fractional code FDE-12 based on Caputo derivative. It has been perceived that the drifting velocity generated by the electric field E significantly improves the velocity and heat transition rate of blood. The fractional model is more generalized and applicable than the classical one. [ABSTRACT FROM AUTHOR]

The current research investigates the thermal radiations and non-uniform heat flux impacts on magnetohydrodynamic hybrid nanofluid (CuO-Fe2O3/H2O) flow along a stretching cylinder, which is the main aim of this study. The velocity slip conditions have been invoked to investigate the slippage phenomenon on the flow. The impact of induced magnetic field with the assumption of low Reynolds number is imperceptible. Through the use of appropriate non-dimensional parameters and similarity transformations, the ruling PDE's (partial differential equations) are reduced to set of ODE's (ordinary differential equations), which are then numerically solved using Adams–Bashforth Predictor–Corrector method. Velocity and temperature fields with distinct physical parameters are investigated and explored graphically. The main observations about the hybrid nanofluid and non-uniform heat flux are analyzed graphically. A decrease in the velocity of the fluid is noted with addition of Hybrid nanofluid particles while temperature of the fluid increases by adding the CuO-Fe2O3 particles to the base fluid. Also, velocity of the fluid decreases when we incorporate the effects of magnetic field and slip. Raise in curvature parameter γ caused enhancement of velocity and temperature fields at a distance from the cylinder but displays opposite behavior nearby the surface of cylinder. The existence of heat generation and absorption for both mass dependent and time dependent parameters increases the temperature of the fluid. [ABSTRACT FROM AUTHOR]

In this study, the effects of variable characteristics amalgamated with chemical reaction and Arrhenius activation energy are analyzed on a two-dimensional (2D) electrically conducting radiative Casson nanoliquid flow past a deformable cylinder embedded in a porous medium. The surface of the cylinder is deformable in the radial direction i.e., the z-axis. The impression of Soret and Dufour's effects boosts the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of momentum slip, convective heat, and mass conditions. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless protuberant parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the velocity slip parameter and porosity parameter velocity field depreciates. Also, on escalating the radiation parameter and heat transfer Biot number a prominent difference is noticed in an upsurge of the thermal field. For growing values of Brownian motion and thermophoretic parameters, temperature field augments. On escalating the curvature parameter and porosity parameter, drag force coefficient upsurges. The outcome of the Soret number, mass transfer Biot number, and activation energy parameter is quite eminent on the concentration distribution for the sheet in comparison to the deformable cylinder. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem. [ABSTRACT FROM AUTHOR]

In this paper, a numerical study of MHD steady flow due to a rotating disk with mixed convection, Darcy Forchheimer's porous media, thermal radiation, and heat generation/absorption effects are explored. A strong magnetic field is applied in perpendicular direction to the flow which governs the Hall current effects. Homogeneous and heterogeneous reactions are also taken into account. For the simplification of partial differential equations (PDEs) into the nonlinear ordinary differential equations (ODEs), the method of generalized Von Karman similarity transformations is employed, and the resulting non-dimensional ordinary differential equations are solved by using the homotopy analysis method (HAM). Effects of different parameters on the axial, radial and tangential velocity profiles, temperature and concentration of chemical reaction profiles are analyzed and discussed. The present work's remarkable finding is that with the expansion of nanoparticles size, dimensionless constant parameter, local Grashof number, porosity parameter, Hall current, and suction parameter, the nanofluid radial velocity is enhanced. For the higher values of magnetic field parameter, the tangential velocity and nanofluid temperature are enhanced. The magnetic field parameter and the disk thickness coefficient parameter have similar impacts on the axial velocity profile. Heterogeneous chemical reaction parameter decreases the concentration of chemical reaction profile. The nanoparticles volume fraction increases the concentration of chemical reaction profile. Furthermore, the present results are found to be in excellent agreement with previously published work in tabulated form. [ABSTRACT FROM AUTHOR]

The study concerns with the mechanical characteristics of heat and mass transfer flow of a second grade nanofluid as well as gyrotatic microorganism motion past a thin needle with dipole effect, entropy generation, thermal radiation, Arrhenius activation energy and binar chemical reaction. The governing equations and boundary conditions are simplified by the use of suitable similarity transformations. Homotopy analysis method is implemented to obtain the series solution of non-linear ordinary differential equations. Physical behaviors of heat and mass transfer flow with gyrotatic microorganisms and entropy generation are investigated through the embedded parameters. The nanofluid velocity is enhanced for higher values of the ferromagnetic parameter, local Grashof number, bioconvection Rayleigh number and radiation parameter. The Reynolds number, radiation parameter and Eckert number decrease the nanofluid temperature. The entropy generation is increased with the enhancement of radiation parameter, Eckert number, Lewis number, temperature difference parameter, dimensionless constant parameter, Curie temperature, Prandtl number and concentration difference parameter. [ABSTRACT FROM AUTHOR]

To enhance the surface properties of solids the mechanism of thin films is frequently used. Penetration, degradation, stiffness, illumination, diffusion, absorption, and electric performance are all characteristics of a bulk substance medium that a thin film can improve. In nanotechnology, thin film processing can be extremely useful. Therefore, the time-dependent nonlinearly convective stream of thin film nanoliquid over an inclined stretchable sheet with magnetic effect is investigated in current work. The features of mass and heat transport processes are explained using important factors like thermophoresis and Brownian movement. Nonlinear partial differential equations are obtained to model the time-dependent liquid film flow over an inclined surface, which are then turned into couple ordinary differential equations utilizing appropriate alterations. The results of the computation of the model problem are collected using an analytical approach Homotopy Analysis Method and presented the final finding numerically and graphically. During the flow assessment, the impact of individual flow factors such as magnetic, Brownian, and thermophoresis parameters on regular profiles (temperature, velocity, and concentration) are analyzed and found to be quite remarkable. Furthermore, the consequence of M and Nt factors on the velocity, concentration and thermal distribution leads to diminishing conduct. On the other hand, the thermal profile of the liquid film rises in response to the thermophoresis factor. The % wise variation in the skin friction, Nusselt number and Sherwood number versus physical parameters has been obtained and discussed. [ABSTRACT FROM AUTHOR]

The entropy generation for a reactive Williamson nanofluid flow past a vertical Riga system is the subject of this article. The effects of MHD, thermophoresis, nonlinear heat radiation and varying heat conductivity are modeled into the heat equation in the established model. Suitable similarity transformations are examined to bring down the partial differential equations into ordinary differential equations. The Homotopy analysis approach is used to solve the dimensionless transport equations analytically. The graphic information of the various parameters that emerged from the model is effectively collected and deliberated. The temperature field expands with thermophoresis, Brownian motion and temperature ratio parameters as the modified Hartmann number forces an increase in velocity, according to the findings of this analysis. With the increase in the fluid material terms, the entropy generation and Bejan number increase. Riga plate has numerous applications in improving the thermo-physics features of a fluid, the value of magnetic field embraces an important role in fluid mechanics. An external electric field can be used to control flow in weak electrically conductive fluids. The Riga plate is one of the devices used in this regard. It's a device that creates electromagnetic fields. They produce the Lorentz force which is a force that directs fluid flow. The authors have discussed the entropy optimization for a reactive Williamson nanofluid flow past a vertical Riga plate is addressed. This is the first investigation on mass and heat transfer flow that the authors are aware of, and no similar work has yet been published in the literature. A thorough mathematical examination is also required to demonstrate the model's regularity. The authors believe that the results acquired are novel and have not been plagiarized from any other sources. [ABSTRACT FROM AUTHOR]

This investigation describes the hydromagnetic flow of gravity-driven couple stress hybrid nanofluid past a heated plate. The carbon nanotubes (CNTs) are used to characterize the hybrid nanofluid. The heated plate is placed vertically with an application of homogenous-heterogeneous reactions to the assumed flow system. The homogeneous reaction governs by isothermal cubic autocatalytic kinetics while the heterogeneous reaction governs by the first order kinetics. For current study the couple stress hybrid nanofluid is presumed to be conducted electrically with impact of non-uniform magnetic effects. An appropriate set of dimensionless quantities has employed to governing equations and then has solved by homotopy analysis method. The influence of emerging parameters encountered in this work has discussed in detail with the help of graphs. In this study it has examined that, flow of fluid reduces with upsurge in magnetic parameter and volumetric concentrations, whereas thermal and concentration characteristics augment with increase in volumetric concentrations. Moreover, growth in Prandtl number leads to a reduction in thermal characteristics and growth in Schmidt number result a reduction in concentration profile. The impact of various emerging parameters has also studied numerically upon physical quantities. It has established that, with augmentation in values of buoyancy parameter there is a growth in the values of skin friction. A comparison has also carried out between current and established results with a fine agreement in both results. [ABSTRACT FROM AUTHOR]

This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid f ′ ξ , g ξ are decayed for high values of ϕ 1 , ϕ 2 , F r and k 1 factors. [ABSTRACT FROM AUTHOR]

In this research, the phenomenon of heat and mass transfer in 3D radiative flow of hybrid nanofluid over a rotational disk is investigated. Nanoparticles of Al 2 O 3 and Cu are being used with water (H 2 O) as base fluid. The mathematical flow model in terms of PDEs is constructed by considering the heat transport mechanism due to Joule heating and viscous dissipation. This set of PDEs is converted into a system of ODEs by introducing the proper similarity transformations, which is then solved with the computational strength of Lobatto IIIA method. Demonstrations of graphical and numerical data are offered to examine the variation of velocity and thermal field against various physical constraints. The variable trend of heat transfer rate and skin friction coefficient through numerical data are also investigated. It is found that rate of heat transfer is proportional to Brinkman number, magnetic effect and concentration of nanoparticles. Achieved accuracy in term of relative error upto the level of 1e-14 shows the reliability and worth of solution methodology. [ABSTRACT FROM AUTHOR]