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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]

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]

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]

Inclusion of nanoparticles boosts thermal performance and is essential for thermal transport. The current investigation has been made to conduct research on heat mass transport in synovial material with the mixing of hybrid and tri-hybrid comprising variable viscosity past over a heated surface having constant density and a steady environment. The conservation laws have been considered in the presence of Lorentz force, heat generation/absorption, modified heat and mass fluxes together with chemical reaction. The mathematical model is developed in Cartesian coordinate in the form of coupled partial differential equation (PDEs). The derived PDEs are simplified by a boundary layer approach (BLA) and reduced PDEs have been converted into ordinary differential equation (ODEs) using scaling group Similarity transformation. The converted ODEs are highly nonlinear and have been solved numerically by finite elements scheme (FES). The used scheme is effective for nonlinear problem and can be frequently utilized to tackle nonlinear problems arising in mathematical physics. [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]

Numerical simulations of non-linear Casson nanofluid flow were carried out in a microchannel using the fractal-fractional flow model. The nano-liquid is prepared by dispersing Cadmium Telluride nanoparticles in common engine oil. Using relative constitutive equations, the system of mathematical governing equations has been formulated along with initial and boundary conditions. Dimensionless variables have been used to obtain the non-dimensional form of the governing equations. The fractal-fractional model has been obtained by employing the fractal-fractional operator of the exponential kernel. As the exact solution of the non-linear fractal-fractional model is very tough to find, therefore the formulated model has been solved numerically via the Crank-Nicolson scheme. Various plots are generated for the inserted parameters. From the analysis, it has been observed that a greater magnitude of the electro-kinetic parameter slows down the fluid's velocity. It is also worth noting that the fractional and classical models can also be derived from the fractal-fractional model by taking the parameters tend to zero. From the analysis, it is also observed that in response to 0.04 volume fraction of cadmium telluride nanoparticles, the rate of heat transfer (Nusselt number) and rate of mass transfer (Sherwood number) increased by 15.27% and 2.07% respectively. [ABSTRACT FROM AUTHOR]

The mechanism of thermal transport can be enhanced by mixing the nanoparticles in the base liquid. This research discusses the utilization of nanoparticles (tri-hybrid) mixture into Carreau–Yasuda material. The flow is assumed to be produced due to the stretching of vertical heated surface. The phenomena of thermal transport are modeled by considering Joule heating and heat generation or absorption involvement. Additionally, activation energy is engaged to enhance heat transfer rate. The mathematical model composing transport of momentum, heat and mass species is developed in Cartesian coordinate system under boundary layer investigation in the form of coupled nonlinear partial differential equations. The complex partial differential equations are converted into coupled nonlinear ordinary differential equations by using the appropriate similarity transformation. The conversion of PDEs into ODEs make the problem easy to handle and it overcome the difficulties to solve the PDEs. The transformed ordinary differential equations are solved with the help of help of finite element scheme. The obtained solution is plotted against numerous involved parameters and comparative study is established for the reliability of method and accuracy of obtained results. An enhancement in fluid temperature is recorded against magnetic parameter and Eckert number. Also, decline in velocity is recorded for Weissenberg number and concentration is controlled against higher values of Schmidt number. Furthermore, it is recommended that the finite element scheme can be implemented to handle complex coupled nonlinear differential equation arising in modeling of several phenomena occurs in mathematical physics. [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]

Following to improved thermal impact of hybrid nanomaterials, wide range applications of such materials is observed in the thermal engineering, extrusion systems, solar energy, power generation, heat transfer devices etc. The hybrid nanofluid is a modified form of nanofluid which is beneficial for improving energy transfer efficiency. In current analysis, the solid nanoparticles aluminium ( ϕ Al 2 O 3 ) and copper ( ϕ Cu ) have been mixed with water to produce a new hybrid nanofluid. The investigation of a steady two-dimensional mixed convection boundary layer flow of the resultant hybrid nanofluid on a vertical exponential shrunk surface in the existence of porous, magnetic, thermal radiation, velocity, and thermal slip conditions is carried out. Exponential similarity variables are adopted to transform the nonlinear partial differential equation into a system of ordinary differential equations which has been then solved by employing the shooting method in Maple software. The obtained numerical results such as coefficient of skin friction f ″ 0 , heat transfer rate - θ ′ 0 , velocity f ′ η and temperature θ η distributions are presented in the form of different graphs. The results revealed that duality exists in solution when the suction parameter S ≥ S ci in assisting flow case. Due to non-uniqueness of solutions, a temporal stability analysis needs to be performed and the result indicates that the upper branch is stable and realizable compared to the lower branch. [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]

The Jeffrey fluid model is capable of accurately characterizing the stress relaxation behavior of non-Newtonian fluids, which a normal viscous fluid model is unable to perform. The primary objective of this paper is to provide a comprehensive investigation into the effects of MHD and thermal radiation on the 3D Jeffery fluid flow over a permeable irregular stretching surface. The consequences of the Darcy effect, variable thickness and chemical reaction are also considered. The phenomena have been modeled as a nonlinear system of PDEs. Using similarity substitution, the modeled equations are reduced to a dimensionless system of ODEs. The parametric continuation method (PCM) is used to determine the numerical solution to the obtained sets of nonlinear differential equations. The impact of physical parameters on temperature, velocity and mass profiles are presented through Figures and Tables. It has been noticed that the energy profile magnifies with the increment of porosity term, thermal radiation and heat source term, while diminishing with the flourishing upshot of power index and Deborah number. Furthermore, the porosity term and wall thickness parameter enhance the skin friction. [ABSTRACT FROM AUTHOR]

The thermal distribution in a convective-radiative concave porous fin appended to an inclined surface has been examined in this research. The equation governing the temperature and heat variation in fin with internal heat generation is transformed using non-dimensional variables, and the resulting partial differential equation (PDE) is tackled using an analytical scheme, generalized residual power series method (GRPSM). Moreover, a graphical discussion is provided to examine the consequence of diverse non-dimensional variables including the parameters of convection-conduction, ambient temperature, radiation, heat generation, and porosity effect on the thermal field of the fin. Also, a graph is plotted to analyze the variations in unsteady temperature gradient using the finite difference method (FDM) and generalized residual power series method (GRPSM). The major result of this investigation unveils that as the convection-conduction parameter scale upsurges, the distribution of temperature in the fin diminishes. For the heat-generating parameter, the thermal distribution inside the fin increases. [ABSTRACT FROM AUTHOR]

The researchers are continuously working on nanomaterials and exploring many multidisciplinary applications in thermal engineering, biomedical and industrial systems. In current problem, the analytical simulations for performed for thermos-migration flow of nanofluid subject to the thermal radiation and porous media. The moving wedge endorsed the flow pattern. The heat source effects are also utilized to improves the heat transfer rate. The applications of thermophoresis phenomenon are addressed. The formulated set of expressions are analytically treated with implementation of variational iteration method (VIM). The simulations are verified by making the comparison the numerical date with existing literature. The VIM analytical can effectively tackle the nonlinear coupled flow system effectively. The physical impact for flow regime due to different parameters is highlighted. Moreover, the numerical outcomes are listed for Nusselt number. [ABSTRACT FROM AUTHOR]

The dynamic of fluids and coolants in automobiles are achieved by enhancement in heat energy using ternary hybrid nanostructures. Ternary hybrid nanomaterial is obtained by suspension of three types of nanofluid (aluminum oxide, silicon dioxide and titanium dioxide) in base fluid (EG). Prime investigation is to address comparison study in thermal energy involving various flow models termed as Maxwell fluid and Williamson fluid. This exploration is carried out by partially ionized fluidic particles in the presence of ternary hybrid nanomaterial over cone. Heat transfer is carried out by heat source and thermal radiation. Equations regarding Ordinary differential are achieved from PDEs using variable transformations. The numerical consequences are obtained implementing finite element method. Flow into fluid particles is enhanced versus higher values of Hall and ion slip parameters. Thermal performance as well as flow performance for the case Williamson fluid is better than for case of Maxwell fluid. Production via energy is boosted versus heat source parameter. [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]

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 energy transmission through micropolar fluid have a broad range implementation in the field of electronics, textiles, spacecraft, power generation and nuclear power plants. Thermal radiation's influence on an incompressible thermo-convective flow of micropolar fluid across a permeable extensible sheet with energy and mass transition is reported in the present study. The governing equations consist of Navier–Stokes equation, micro rotation, temperature and concentration equations have been modeled in the form of the system of Partial Differential Equations. The system of basic equations is reduced into a nonlinear system of coupled ODE's by using a similarity framework. The numerical solution of the problem has been obtained via PCM (Parametric Continuation Method). The findings are compared to a MATLAB built-in package called bvp4c to ensure that the scheme is valid. It has been perceived that both the results are in best agreement with each other. The effects of associated parameters on the dimensionless velocity, micro-rotation, energy and mass profiles are discussed and depicted graphically. It has been detected that the permeability parameter gives rise in micro-rotation profile. [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]

Bioconvection has recently been the subject of dispute in a number of biotechnological fields that depend on fluids and their physical properties. When mixed nanofluids are subjected to heat and mass transmission, the process of bioconvection occurs. This attempt conveys the theoretical analysis of two-dimensional electrically conducting and magnetically susceptible binary fluid containing nanoparticles and gyrotactic microorganisms past a stratified stretching surface. Furthermore binary chemical reaction, thermal radiation, and activation energy are taken into assumptions. The analytical solution based on HAM has been performed. The convergence of HAM is presented with the help of figures. The present study is compared with previously published results and has established an excessive agreement which validate the present study. It is perceived that the presence and absence of an electric field influences the variations in fluid velocities due to presence of magnetic field. The micropolar constant heightens the velocity and microrotation of the fluid flow. The buoyancy parameter and bioconvection Rayleigh number diminish the velocity function while these parameters show dual impact on microrotation function. The skin friction and couple stress escalates with the increasing buoyancy ratio parameter and bioconvection Rayleigh number. [ABSTRACT FROM AUTHOR]

This article focused on the comparative study of entropy generation for natural convection flow of the newly proportional Caputo hybrid and Atangana baleanu fractional derivative. The governing equation is formed as the set of partial differential equations with the physical boundary conditions. The report of entropy generation is investigated for the first time for proportional–Caputo hybrid model and comparison are sorts out with generalized Atangana baleanu fractional derivative. The Bejan number is also compared for the mention fractional derivatives. Graphs show the impact of various factors on the minimization and maximizing of entropy production. The newly proportional Caputo hybrid operator has a good memory effect rather than Atangana baleanu fractional operator. [ABSTRACT FROM AUTHOR]

Fractal-fractional derivative is a new class of fractional derivative with power Law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional derivatives with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper new concept of fractal-fractional derivative for the modeling of couple stress fluid (CSF) with the combined effect of heat and mass transfer have been used. The magnetohydrodynamics (MHD) flow of CSF is taken in channel with porous media in the presence of external pressure. The constant motion of the left plate generates the CSF motion while the right plate is kept stationary. The non-dimensional fractal-fractional model of couple stress fluid in Riemann–Liouville sense with power law is solved numerically by using the implicit finite difference method. The obtained solutions for the present problem have been shown through graphs. The effects of various parameters are shown through graphs on velocity, temperature and concentration fields. The velocity, temperature and concentration profiles of the MHD CSF in channel with porous media decreases for the greater values of both fractional parameter α and fractal parameter β respectively. From the graphical results it can be noticed that the fractal-fractional solutions are more general as compared to classical and fractional solutions of CSF motion in channel. Furthermore, the fractal-fractional model of CSF explains good memory effect on the dynamics of couple stress fluid in channel as compared to fractional model of CSF. Finally, the skin friction, Nusselt number and Sherwood number are evaluated and presented in tabular form. [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]

Involvement of hybrid nanoparticles a vital role to improve the efficiency of thermal systems. This report covers the utilization of different nanoparticles mixed in Carreau Yasuda material for the improvement of thermal performance. The configuration of flow situation is considered over a rotating porous cone by considering the Hall and Ion slip forces. Transport of momentum is considered to be in a rotating cone under generalized ohm's law and heat transfer is presented by considering viscous dissipation, Joule heating and heat generation. Rheology of considered model is derived by engaging the theory proposed by Prandtl. Modeled complex PDEs are reduced into ODEs under similarity transformation. To study the physics behind this phenomenon, solution is essential. Here, FEM (Finite Element Method) is adopted to compute the solution. Furthermore, the grid independent study is reported with several graphs and tables which are prepared to note the influence of involved parameters on thermal and velocity fields. It is worth mentioning that heat transport is controlled via higher radiation parameter and it upsurges for Eckert number. Moreover, Hall and ion slip parameters are considered significant parameters to produce the enhancement in motion of fluid particles but speed of nano and hybrid nanoparticles becomes slow down versus large values of Forchheimer and Weissenberg numbers. Additionally, an enhancement in production of heat energy is addressed via large values of heat generation number and Eckert number while reduction in heat energy is occurred due to positive values of thermal radiation and Hall and ion slip parameters. [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]

This study presents the magnetized and non-magnetized Casson fluid flow with gyrotactic microorganisms over a stratified stretching cylinder. The mathematical modeling is presented in the form of partial differential equations and then transformed into ordinary differential equations (ODEs) utilizing suitable similarity transformations. The analytical solution of the transformed ODEs is presented with the help of homotopy analysis method (HAM). The convergence analysis of HAM is also presented by mean of figure. The present analysis consists of five phases. In the first four phases, we have compared our work with previously published investigations while phase five is consists of our new results. The influences of dimensionless factors like a magnetic parameter, thermal radiation, curvature parameter, Prandtl number, Brownian motion parameter, Schmidt number, heat generation, chemical reaction parameter, thermophoresis parameter, Eckert number, and concentration difference parameter on physical quantities of interests and flow profiles are shown through tables and figures. It has been established that with the increasing Casson parameter (i.e. β → ∞ ), the streamlines become denser which results the increasing behavior in the fluid velocity while on the other hand, the fluid velocity reduces for the existence of Casson parameter (i.e. β = 1.0 ). Also, the streamlines of stagnation point Casson fluid flow are highly wider for the case of magnetized fluid as equated to non-magnetized fluid. The higher values of bioconvection Lewis number, Peclet number, and microorganisms' concentration difference parameter reduces the motile density function of microorganisms while an opposite behavior is depicted against density number. [ABSTRACT FROM AUTHOR]

The numerical analysis of MHD boundary layer non-Newtonian micropolar fluid due to an exponentially curved stretching sheet is developed in this study. In the energy equation effects of viscous dissipation are included. For the mathematical description of the governing equations curvilinear coordinates are used. By utilizing exponential similarity variables, the modelled partial differential equations (PDEs) are reduced into ordinary ones. The resultant non-linear ODEs are numerically solved with two methods shooting and Keller box method. The study reveals that the governing parameters, namely, radius of curvature, material parameter, magnetic parameter, Prandtl number and Eckert number have major effects on the fluid velocity, micro-rotation velocity, surface friction, couple stress and heat transfer rate. The results indicate that the magnetic field diminishes the fluid velocity inside the hydrodynamics boundary layer whereas it enhances the temperature inside the thermal boundary layer. Microrotation profile decreases near the surface, as the magnetic parameter and radius of curvature increases but far away behavior is opposite. The material parameter enhances the velocity and microrotation profile whereas, opposite behaviors is noticed for the temperature distribution. Obtained outcomes are also compared with the existing literature and the comparison shows a good agreement with existing studies. [ABSTRACT FROM AUTHOR]

The first author Muhammad Arif appreciates the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship (Grant No. 14/2562 and Grant No. 25/2563)." The first author Muhammad Arif appreciate the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship (Grant No. 14/2562 and Grant No. 25/2563)." now reads: "The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. [Extracted from the article]

Muhammad Ramzan, Poom Kumam and Raees Khan have not responded to correspondence from the Editors about this retraction. As the authorship could not be verified the Editors no longer have confidence in the content of this article. Retraction of: I Scientific Reports i https://doi.org/10.1038/s41598-021-98881-1, published online 29 September 2021 The Editors have retracted this article. [Extracted from the article]

The authors would like to thank the Deanship of Scientific Research at Umm Al-Qura University for supporting this work by Grant Code: 22UQU4331317DSR25." This research was funded by National Science, Research and Innovation Fund (NSRF), and King Mongkut's University of Technology North Bangkok with Contract no. [Extracted from the article]

Kamel SMIDA would like to express his gratitude to AlMaarefa University, Riyadh, Saudi Arabia, for providing funding (TUMA-2021-17) to do this research. Kamel SMIDA would like to express his gratitude to AlMaarefa University, Riyadh, Saudi Arabia, for providing funding (TUMA-2021-17) to do this research. [Extracted from the article]