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The hybrid nanofluids can enhance cooling systems in microelectronics by enhancing heat dissipation from processes which makes them vital for maintaining optimal performance. They are also beneficial in solar systems where efficient heat transfer is essential for exploiting the energy detention. Thus, this study has studied the three-dimensional flow of a water-based hybrid nanofluid comprising of Fe3O4 and CuO nanoparticles on a bi-directional extending sheet. The bi-directional extending sheet is subjected to thermal convective and velocity slip conditions. In addition, the effects of heat source, magnetic field, thermal radiation, viscous dissipation, and Joule heating are employed. The partial differential equations (PDEs) that represent the mathematical model are subsequently converted to ordinary differential equations (ODEs) by applying the appropriate similarity variables. The shooting technique is incorporated to determine the computational solution of the converted ODEs. The effectiveness of the current study is confirmed by published results, which also validate the current outcomes. Based on the results, it is concluded that CuO and Fe3O4 solid nanoparticle volume fractions improved the thermal distribution while decreasing the velocity distributions along x and y-axes. The thermal distribution is improved by the thermal heat source, thermal radiation, thermal Biot number, and thermal Eckert numbers. CuO-water nanofluid has a higher velocity panel than CuO-Fe3O4/water hybrid nanofluid. Conversely, the CuO-Fe3O4/water hybrid nanofluid has a higher thermal profile than the CuO-water nanofluid. CuO-water nanofluid flow has higher surface drags than CuO-Fe3O4/water hybrid nanofluid flow. CuO-water nanofluid has a lower heat transfer rate than CuO-Fe3O4/water hybrid nanofluid.

In this work, a comparative analysis on magnetohydrodynamic nanofluid flow containing spherical and cylindrical-shaped alumina nanoparticles over a stretching curved surface is mainly focused. The effects of Brownian motion, Joule heating, thermophoresis, chemical reaction and activation energy are taken into consideration in this work. It is important to mention that this analysis considers a 4 % volume fraction of the alumina nanoparticles. A thermal convective and zero-mass flux conditions are imposed to scrutinize the heat transfer analysis. The leading equations are transformed into dimensionless form by using suitable similarity variables. A numerical solution is obtained using the shooting technique. The acquired outcomes depict that greater magnetic factor enhances the skin friction coefficient. The greater magnetic factor, thermal Biot number, Eckert number, and interfacial layer thickness augment the heat transfer rate, while a greater nanoparticle diameter diminishes the thermal transfer rate. A higher magnetic factor has an increasing impact on thermal distribution and a reducing impact on velocity distribution. A greater curvature factor enhances both the velocity and thermal distributions. The concentration distribution is enhanced by the higher interfacial layer thickness and activation energy factor, while it is reduced by a higher nanoparticle diameter, Brownian motion factor, and chemical reaction factor. From the comparative analysis, it is found that the velocity, thermal, and concentration distributions are higher for the cylindrical-shaped nanoparticles compared to spherical-shaped nanoparticles.

When applied to a rotating disk, Maxwell nanofluids have a wide range of applications in various fields. They provide increased heat transfer efficiency in cooling systems, which is essential for preserving the ideal operating temperatures of spinning gears like disk brakes and turbines. Furthermore, Maxwell nanofluids in microfluidic devices provide improved fluid manipulation and control, improving performance in applications such as microscale pumps and lab-on-a-chip systems. This article has numerically examined the magneto-bio-convection flow of Maxwell, which includes nanofluid, past a disk surface based on these applications. We present the model equations in PDE format, then shift them to ODEs using the appropriate variables. We utilize the bvp4c approach to obtain numerical solutions to the modeled equations. We also take into account the effects of thermal radiation, heat sources, Brownian motion, thermophoresis, chemical reactivity, and activation energy. We find that a higher stretching/shrinking variable has enhanced the radial velocity profile, while simultaneously diminishing the axial and angular velocity field. While the velocity profiles in the axial direction and redial direction have reduced with larger magnitude of Maxwell fluid variable. The thermal distributions have risen due to higher magnetic, Brownian motion, thermophoresis, heat sources, and thermal radiation components. Thermophoresis, magnetic and thermal radiation, heat sources, and Brownian motion all contribute to an increase in heat transfer rates.

Abstract Nanofluid is a specially crafted fluid comprising a pure fluid with dispersed nanometer-sized particles. Incorporation these nanoparticles into pure fluid results in a fluid with improved thermal properties in comparison of pure fluid. The enhanced properties of nanofluids make them highly sought after, in diverse applications, consisting of coolant of devices, heat exchangers, and thermal solar systems. In this study hybrid nanofluid consisting of copper, alumina and titanium nanoparticles on a curved sheet has investigated with impact of chemical reactivity, magnetic field and Joule heating. The leading equations have converted to normal equations by using appropriate set of variables and has then evaluated by homotopy analysis method. The outcomes are shown through Figures and Tables and are discussed physically. It has revealed in this study that Cu-nanofluid flow has augmented velocity, temperature, and volume fraction distributions than those of Al2O3-nanofluid and TiO2-nanofluid. Also, the Cu-nanofluid flow has higher heat and mass transfer rates than those of Al2O3-nanofluid and TiO2-nanofluid.

The combination of microbes and nanofluids has noteworthy consequences for technological and engineering progress, particularly in the realm of heat transfer applications. This study explains radiative flow with chemical reactions affect the emergence of microorganisms in magnetic mixed convective Williamson nanofluid flow. The Cattaneo-Christov heat flux theory and the effects of heat source/sink have been examined about the energy equation. The prime idea of this analysis is to enhance heat and mass transport. The modelled equations have been converted to dimensionless by considering suitable alteration. The dimensionless expression is then numerically tackled using MATLAB's bvp4c approach. The graphs for different profiles—that is, momentum, temperature, concentration and concentration of microorganisms that move—are made visible for particular nondimensional factors. Furthermore, entropy generation minimization has been obtained through law of thermodynamics. The drag friction, heat and mass transfer rate, and microbe density are also computed in a tabular manner. The most important findings that are pertinent to this study are that an increase in the values of the Brownian motion, thermal radiation and thermophoresis significantly enhance heat transfer characteristics. A consistent pattern can be observed when comparing the current results with earlier research.

Abstract The fluid flow over an extending sheet has many applications in different fields which include, manufacturing processes, coating, thin film decomposition, heat and mass transfer, biomedical applications, aerospace engineering, environmental science, energy production. Keeping in mind these applications, the non-Newtonian hybrid nanofluid flow comprising of Cu and CuO nanoparticles over an extending sheet is analyzed in this work. Two different base fluids called kerosene oil and water have been incorporated. The sheet is considered to be thermally convective along with zero mass flux condition. The main equations of modeled problem have been transformed to dimensionless form by using similarity variables. The designed problem is evaluated computationally by using bvp4c Matlab function. Validation of the present results is also performed. The impacts of magnetic, Brownian motion, chemical reaction, suction and thermophoresis factors are analyzed and discussed in details. The outcomes of the present investigation declare that the kerosene oil-based hybrid nanofluid flow has greater velocity and concentration profiles than that of the water-based hybrid nanofluid flow. The water-based hybrid nanofluid has greater temperature distribution than that of kerosene oil-based hybrid nanofluid flow. The streamlines of the kerosene oil-based Newtonian and non-Newtonian hybrid nanofluid flows are more stretched than water-based Newtonian and non-Newtonian hybrid nanofluid flows.

This work inspects the thermal transportation of the magnetohydrodynamic Casson trihybrid nanofluid flow over a convectively heated bidirectional elongating sheet. The flow is considered as three dimensional passing over the sheet, which is placed in a porous medium. The effects of thermal radiations and space- and thermal-dependent heat sources are used in energy equations, while magnetic effects are used in momentum equations. Appropriate variables have been used to convert the modeled equations into a dimensionless form, which have then been solved using the homotopy analysis method. In this work, it is uncovered that both the primary and secondary velocities are weakened with an upsurge in porosity and magnetic factors. The thermal transportation is augmented with growth in thermal- and space-dependent heat source factors and the thermal Biot number. The convergence of the method used in this work is ensured through ℏ-curves. The results of this investigation have also been compared with the existing literature with a fine agreement among all the results that ensured the validation of the model and method used in this work.

The current study intends to talk about the unsteady Williamson hybrid nanofluid flow with heat transport across a stretching surface comprising the magnetic hydrodynamic, thermal radiative, suction/injection, and convective boundary condition effects respectively. The study focused on the hybrid Williamson nanofluid, comprising of an EG ethylene glycol (C2H6O2) and two types of nano-solid particles, c zinc oxide and molybdenum disulphide ZnO-MOS2. To accomplish this goal, the modelled expressions are transmitted into dimensionless ODE by making use of several highly established transformations. The aim of the numerical result of the current exploration is studied through Keller Box Analysis (KBA). Tabular data and statistical bar plots are used to compare this strategy. The impact of physical variables such as Magnetic field parameter γ, Williamson fluid variable We, Porous media β, Thermal radiation Rd, Biot number Bi and Prandtl number Pr are analyzed through plots and tables. An augmentation in the strength of the magnetic field and Williamson fluid parameter results in a reduction in velocity. However, a temperature rise is observed for higher values of the Williamson fluid parameter and magnetic parameters. The surface friction drag is diminished by the Forchheimer and Weissenberg values. The rate of mass transfer is strongly positively correlated with both the Schmidt number and chemical reaction. The present study has a remarkable agreement with the results that were previously published, which confirms the application and validation of the Keller-Box scheme.

Abstract This article presents the two-dimensional flow of hybrid nanofluid comprising of gyrotactic microorganisms under the consequences of multiple slip conditions, magnetic field and thermal radiation across an elongating curved surface using porous media. The nanoparticles of TiO2 and Fe3O4 have dispersed in water for composition of hybrid nanofluid. Main equations of the problem are converted to ODEs by using an appropriate set of variables. Solution of the present model is determined with the help of bvp4c technique, which is explained in detail in the coming section. Validation of the current results is done versus the published work. The effects of various emerging factors on flow distributions have been considered and explained. Additionally, the slips conditions are incorporated to analyze various flow distributions. The present outcomes show that the rising magnetic factor lessens the velocity profile, whereas rises the temperature profile. The curvature factor has supported both temperature and velocity distributions. Growth in velocity, thermal, concentration, and microorganisms slip factors reduce the corresponding distributions. The greater impact of the embedded parameters is found on hybrid nanofluid flow when matched to nanofluid flow.

Abstract 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 A stratified flow may be seen regularly in a number of significant industrial operations. For instance, the stratified flow regime is typically used by gas-condensate pipelines. Clearly, only a limited set of working situations for which this flow arrangement is stable allow for the achievement of the stratified two-phase flow zone. In this paper, the authors are considered the laminar, steady and incompressible magnetohydrodynamic flow of a non-Newtonian Casson fluid flow past a stratified extending sheet. The features of bio-convection, Brownian motion, thermal radiation thermophoresis, heat source, and chemically reactive activation energy have been employed. The set of equations administered flow of fluid is converted into ordinary differential equation by suitable variables. A semi-analytical investigation of the present analysis is performed with homotopy analysis method. Endorsement of the current results with previous results is also investigated. The outcomes showed that the velocity distribution of the fluid flow lessens with higher Casson and magnetic factors. The temperature profiles of fluid flow shrinkage as the Prandtl number and Casson factor increase and enlarges with higher values of thermal radiation, magnetic, and Brownian motion factors. It is found that the growing thermophoretic and Brownian motion factors reduce the rate of thermal flow of the Casson fluid flow. In contrast, the increasing thermal stratification parameter increases the thermal flow rate of fluid.

The present article describes the hydrothermal characteristics of hybrid nanofluid flow over an extending curved Darcy surface. Darcy-Forchheimer effect communicates the nanofluid flow through the permeable surface. The effects of magnetic strength, suction/injection and nonlinear radiation have been also considered. Magnesium-oxide (MgO) and Silver (Ag) nanoparticles (NPs) are dispersed in the base fluid, to produce the hybrid nanofluids (HNF). The modeled equations are numerically computed through the Parametric Continuation Method (PCM). The upshot of flow constraints on the energy, mass and velocity contour is graphically presented and explained. The result shows that when the curvature component is taken into account, the energy is lowered, but the velocity curve is elevated. The consequences of thermal Biot number intensify the heat transportation rate. By raising the amount of nanoparticle in the base fluid, energy and velocity profiles are enhances. It has been detected that the energy transmission rate improves up to 27.3% by using nanofluid (MgO-water) as the range of volume friction parameter rises from 0.02 to 0.04. However, 39.97% enhancement is observed in the energy transmission rate between nanoliquid and hybrid nanofluid (Ag–MgO/water) as the range of volume friction parameter rises from 0.01 to 0.04.

Abstract Entropy creation by a blood-hybrid nanofluid flow with gold-tantalum nanoparticles in a tilted cylindrical artery with composite stenosis under the influence of Joule heating, body acceleration, and thermal radiation is the focus of this research. Using the Sisko fluid model, the non-Newtonian behaviour of blood is investigated. The finite difference (FD) approach is used to solve the equations of motion and entropy for a system subject to certain constraints. The optimal heat transfer rate with respect to radiation, Hartmann number, and nanoparticle volume fraction is calculated using a response surface technique and sensitivity analysis. The impacts of significant parameters such as Hartmann number, angle parameter, nanoparticle volume fraction, body acceleration amplitude, radiation, and Reynolds number on the velocity, temperature, entropy generation, flow rate, shear stress of wall, and heat transfer rate are exhibited via the graphs and tables. Present results disclose that the flow rate profile increase by improving the Womersley number and the opposite nature is noticed in nanoparticle volume fraction. The total entropy generation reduces by improving radiation. The Hartmann number expose a positive sensitivity for all level of nanoparticle volume fraction. The sensitivity analysis revealed that the radiation and nanoparticle volume fraction showed a negative sensitivity for all magnetic field levels. It is seen that the presence of hybrid nanoparticles in the bloodstream leads to a more substantial reduction in the axial velocity of blood compared to Sisko blood. An increase in the volume fraction results in a noticeable decrease in the volumetric flow rate in the axial direction, while higher values of infinite shear rate viscosity lead to a significant reduction in the magnitude of the blood flow pattern. The blood temperature exhibits a linear increase with respect to the volume fraction of hybrid nanoparticles. Specifically, utilizing a hybrid nanofluid with a volume fraction of 3% leads to a 2.01316% higher temperature compared to the base fluid (blood). Similarly, a 5% volume fraction corresponds to a temperature increase of 3.45093%.

The current investigation explores the effect of activation energy on the MHD radiative Williamson nanofluid flow across a wedge using heat generation and binary chemical reactivity. The flow model consists of partial differential equations (PDEs) by transforming them into ordinary differential equations (ODEs). Numerical computations have been carried out through the bvp4c MATLAB package. The most effective solutions for flow profiles have been displayed through graphs, while the numeric solutions for the drag friction, heat, and mass transport have been displayed via tables. Numerical findings demonstrate that the temperature field is accelerated by the increase in radiation parameter. In addition, it is intriguing to discover that the concentration boundary layer thickness improves as the activation energy increases. A fundamental study further reveals that the local skin friction coefficient is a rising function of thermal and concentration Grashof numbers. Moreover, it is concluded that the enhanced Brownian motion, thermophoresis, and Eckert number decline the heat transfer rate.

This research presents an innovative alteration to the solar collector's design by integrating a 4-lobed tube with helical tape. The choice of a working fluid, a combination of water and alumina nanoparticles, is purposeful, aiming to reduce irreversibility. Extensive numerical simulations, along with thorough benchmark verification, meticulously assess the system's performance, demonstrating strong alignment with established benchmarks.This study delves into the interaction among pivotal parameters—D* (diameter ratio), Re (Reynolds number), and N (revolution number)—and their impact on essential performance metrics, encompassing ηII (second law performance), Xd (exergy drop), and Φx (exergy drop ratio). With the elevation of all three parameters, the intensified swirl flow facilitates improved heat absorption by the nanofluid, resulting in reduced entropy generation and subsequently, a decrease in exergy drop. More precisely, the increments in Re, N, and D* lead to significant reductions in the value of Xd, with approximately 52.1 %, 4.02 %, and 5.03 %, respectively. When N = 4, D*=0.02, the amount of ηII for Re = 2e4 is 8.38 times greater than that of Re = 4e3. Increasing D* and N leads to substantial improvements in ηII, with approximately 50.02 % and 30.15 % enhancements, respectively. The highest ηII, reaching 0.582, is attained when D*=0.048, N = 7, and Re = 2e4.

Casson nanofluid have gained significant attention in recent years due to their unique rheological; properties and potential applications in science and technology such as heat transfer enhancement, biomedical applications, microfluidics, oil and gas industry, and electronics. This study examines the gyrotactic bioconvection flow of Casson nanofluid across a bidirectional linear stretching sheet with the effects of inclined magnetic field. We examine the impact of velocity, temperature, solute, and microorganism slip on the flow of Casson nanoliquid over a bi-directional linear stretching sheet. Blood is considered as base liquid while magnesium nanoparticles are suspended in base liquid to make homogenous mixture of nanofluid. Also, Brownian and thermophoresis phenomena are taken in the model. Thermal, solutal and microorganism’s stratifications are taken along with thermal and solutal slip conditions. The nonlinear partial differential equations are transformed into ordinary differential equations utilizing the proper similarity transformations. The solution of the flow model is acquired through Homotopic analysis method. Graphical discussions are provided for the effects of various embedded parameters include in fluid model. Some well-known findings have been identified as specific examples of the current investigation. Graphs are used to show how physical factors affect the nanofluid flow. It can be seen that when the magnetic factor, volume fraction parameter, and mixed convection parameter increase, the fluid velocities decreases. On the other hand, the buoyancy ratio factor and Rayleigh number cause to enhance the velocity outline. Temperature outline improves with the enhancement of volume fraction parameter and thermal slip factor. Concentration outline decelerates with the accelerating estimations of solutal slip and stratification parameters. Peclet number reduces the microorganism’s profile.

This paper shows the stagnant point flow of Powell-Eyring hybrid nanofluids due to a stretching sheet. The Xue and Yamada-Ota based on hybrid nanoliquid have been subjected to a comparison study that has been scrutinized. The suspension of two nanoparticles AA 7072 and AA 7075 with base fluid Ethylene glycol ( EG ) is studied through hybrid nanoliquid. With the implementation of the noteworthy suitable alteration, the system of equations in terms of ODEs is established. The bvp4c technique is then applied to obtain the numerical solution of reduced ODEs. The significance of physical quantities over thermal, velocity, force friction, and heat transport are elaborated in tabular form and also in graphical form. During this analysis, the Xue model produced less heat transport as compared to the Yamada-Ota hybrid nanofluid. The result shows that the Xue model produces less heat gradient equated to the Yamada-Ota model. The velocity profile is enhanced and the thermal profile has decayed with the larger value of the fluid parameter.

Hybrid nanofluids have specific features that make them suitable for various industrial and engineering applications. The engineering and industrial applications of hybrid nanofluids are refrigeration, air conditioning, drug delivery, cancer therapy, electronic cooling, gearboxes, power plants, engines, bearings, air pollution control, solar thermal collectors, and water treatment. The existing model is presented for the theoretical examination of the hybrid nanofluid flow at the stagnant point of a gyrating sphere. With applications of the quadratic Rosseland thermal radiation, the variations in quadratic density temperature is scrutinized. In this analysis, two different nanoparticles such as silver Ag and manganese zinc ferrite MnZnFe2O4 nanoparticles have mixed with kerosene oil. The main equations of the existing problem are framed by using the concepts of boundary layer theory. On the basis of this theory, the nonlinear PDEs are used in the formulation of the existing problem. HAM technique is used for evaluation of current flow problem. Some significant findings of the current model are that the heat transmission intensifies for upsurge in radiation factor and nanoparticles volume fractions. Also, it is found that the velocity distribution decreases for rise in the positive constant. Further, it has discovered that thermal distribution is higher for growth in radiation factor and temperature ratio factor.

The energy transition to enhance heat transport during the flow of ternary hybrid nanofluid comprised of Copper (Cu), Iron oxide (Fe3O4), Silicon dioxide (SiO2) 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-Fe3O4 nanoparticles in the base fluid remarkably magnifies the energy transmission rate. The unitary ternary hybrid nanofluid (Cu, Fe3O4, SiO2) has higher velocity profiles as compared to unitary nano fluid (Cu) and hybrid nano-fluid (Cu-Fe3O4).

Recent studies have shown that non-Newtonian fluid flows over stretching sheets have received a lot of interest. These fluids have extensive practical applications in various fields of engineering and industries. The significance of the present study is that it is used in copper wire thinning and annealing, aerodynamic emission of plastic films, the liquid film compression process, etc. In this article, a semi-analytical simulation of the magnetohydrodynamic Maxwell nanofluid flow containing nanoparticles and microorganisms over a stretching surface has been addressed. The nanofluid flow is examined through a bi-directional linearly stretched surface. The impacts of chemical reaction, Soret, and Dufour numbers on Mawell nanofluid flow are taken into account. The aim of the existing problem is to deliberate the Cattaneo-Christov heat and mass flux model in order to examine the thermal and mass transport phenomena. In the methodology section, the computation of the higher-order ODEs are solved by means homotopy analysis method. Some interesting results are found here. The increasing Soret number and chemical reaction have reduced the temperature distribution, whereas the greater Dufour number has increased the thermal profile. In the case of the Fourier law, the temperature is greater, while in the case of the Cattaneo-Christov heat flux model, the temperature is smaller. In the case of the Fick model, the concentration is greater, while in the case of the Cattaneo-Christov mass flux model, the concentration is smaller. The greater Dufour number and reducing Soret number or the greater Soret number and reducing Dufour number have significantly declined the heat rate transport. The greater Dufour number and reducing Soret number have increased the mass transfer rate, while the greater Soret number and reducing Dufour number have reduced the mass transfer rate.

This investigation theoretically describes the exact solution of an unsteady fractional a second-grade fluid upon a bottom plate constrained by two walls at the sides which are parallel to each other and are normal to the bottom plate. The flow in the fluid is induced by the time dependent motion of the bottom plate. Initially the flow equation along with boundary and initial conditions are considered which are then transformed to dimensionless notations using suitable set of variables. The Laplace as well as Fourier transformations have been employed to recover the exact solution of flow equation. The time fractional differential operator of Caputo-Fabrizio has been employed to have constitutive equations of fractional order for second-grade fluid. After obtaining the general exact solutions for flow characteristics, three different cases at the surface of bottom plate are discussed; namely (i) Stokes first problem (ii) Accelerating flow (iii) Stokes second problem. It has noticed in this study that, for higher values of Reynolds number the flow characteristics have augmented in all the three cases. Moreover, higher values of time variable have supported the flow of fractional fluid for impulsive and constantly accelerated motion and have opposeed the flow for sine and cosine oscillations.

Abstract 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 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.

Non-Newtonian fluids flow with mixed convection has got the researcher’s attention due to its widespread application in engineering and manufacturing systems. Furthermore, the thermal radiation in convective thermal transmission plays a key role in regulating the thermal transmission. That’s why the authors’ interest comes to the point to present a detailed analysis of the mixed convective flow of Casson and Oldroyd-B fluids through a linearly stratified stretching sheet. Also, the flow of Casson and Oldroyd-B fluids are considered as chemically reactive, thermally radiative, and magnetized by a strong magnetic field. The mathematical model of the present analysis is presented in PDEs (partial differential equations) format which is transformed into ODEs (ordinary differential equations) by employing suitable variables. The transformed ODEs are treated with an analytical technique called HAM (Homotopy analysis method) which provides an analytical solution for both linear and nonlinear differential equations. Through the use of diagrams, the converging exploration of HAM is depicted. An interesting result has been introduced that, the streamlines of Casson liquid are highly affected by a strong magnetic field as compared to Oldroyd-B liquid. The strong magnetic field and buoyancy ratio parameter moderate the velocity profile, while an opposite trend is found in the motion of liquid by using mixed convectional factors. Additionally, the impacts of magnetic and buoyancy ratio parameters are greater for Oldroyd-B fluid as associated with Casson liquid. On the other hand, the mixed convection parameter is stronger for Casson liquid as equated to Oldroyd-B fluid. The present results have a great agreement with previously published results.

The objective of this research is to examine the two-dimensional flow of a non-Newtonian water-based hybrid nanofluid containing silver and alumina nanoparticles over a stretching surface with convective conditions. The flow is considered to be steady, laminar and incompressible. The mathematical modeling of the flow analysis is considered in the form of partial differential equations which are then transformed into ordinary differential equations by mean of suitable similarity transformations. The present problem is solved with the help of semi-analytical technique called HAM. Convergence of HAM is shown with the help of Figure. The impacts of embedded parameters like magnetic parameter, Joule heating, activation energy and nonlinear thermal radiation on the flow profiles are displayed with the help of Figures and Tables. Our results showed that the greater magnetic parameter reduced the velocity profile, while a reverse impact magnetic parameter is found against temperature profile, skin frication and heat transfer rate of the hybrid nanofluid. Concentration profiles of the hybrid nanofluid flow are augmented with the increasing activation energy while reduced against chemical reaction parameter. Sherwood number has shown increasing behavior due to larger value of Schmidt number and decreasing on larger value of temperature relative parameter.

Abstract 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 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 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.

The flow of fluid over a spinning disk has a broad scope of numerous applications. It is employed in various things, including medical equipment, the braking system of cars, gas turbines, plastic films, and glass production. As a result of these applications, we considered the phenomena of Darcy Forchheimer's three-dimensional flow on TiO2−Fe3O4 nanoparticles suspended in based CMC-water fluid. The influence of thermal radiation and convective conditions is studied. Moreover, the Buongiorno model is utilized to compute the Brownian motion and the thermophoretic effect. To generate the non-dimensionalized governing equations, suitable alterations are put into use. These equations are then utilized with Matlab BVP4c. Graphs are used to analyze the behavior of velocity distributions, and thermal and concentration profiles at different parameter values. In addition, the solutions to the flow problem have been analyzed in terms of several other physical variables on velocity, temperature, concentration, drag force, heat, and mass transfer. According to the findings, it is clear that an escalates in the value of the rotation parameter leads to an increase in the radial velocity and axial velocity. In contrast, an opposite pattern is followed in the Forchheimer number. Finally, some engineering quantities are evaluated numerically and presented in tabular forms.

Jet flows are employed in a variety of applications. It can be found in daily life as well as in agriculture, for example, jet flow assists with irrigation and harvest protection. The current problem is related to the study of energy and mass transference on the hybrid nanoliquid flow with mixed convection effect due to the vertical stretching surface conveying the cobalt ferrite CoFe2O4 and titanium dioxide TiO2 nanoparticles (NPs) with the base fluid water H2O. Further, the role of the chemical reaction, heat source/sink, and activation energy are investigated. By exploiting the idea of the modified Buongiorno model, the thermophoretic and Brownian diffusivity effects have discoursed on the existing flow behavior. The existing mathematical problem is framed with the application of the nonlinear higher-order PDEs. Higher-order PDEs of the mathematical model are changed into highly nonlinear ODEs by using the concepts of suitable similarity transformations. The modified higher-order nonlinear ODEs are cracked by manipulating the bvp4c technique in MATLAB. The impacts of the numerous physical flow parameters on the velocity, energy, and concentration are computed in graphical forms. Key findings from the present problem revealed that the velocity of the nanoliquid and hybrid nanofluid decreased due to greater nanoparticles volume fraction. Furthermore, the heat transportation is greater for mixed convection and thermophoresis parameter.

This article presents the magnetohydrodynamic (MHD) flow of a nanoliquid due to a rotating sphere at a stagnation point. The flow is considered to be influenced by the magnetic field, dissipative, thermally radiative, and chemically reactive. Also, the thermophoretic and Brownian motion influences are taken into consideration. Some restrictions in the present analysis are taken: like there is no-slip and convective conditions, joule heating, Hall effects and buoyancy-driven. The solution of the present analysis is derived through the homotopy analysis method (HAM). The significance of several physical parameters on velocities, thermal and concentration profiles are shown with the help of Figures. Also, the significance of different physical factors on skin frictions, local Nusselt number and Sherwood number are demonstrated with the help of Tables. The outcomes show that the Nusselt number is lower for the larger Brownian motion parameter, Eckert number, and thermophoretic parameter, while the increment in the thermal radiation parameter augmented the Nusselt number. It is established that the increasing rotation, magnetic and positive constant parameters have increased the velocity profiles along the x-direction while reducing the velocity profiles along the z-direction of the nanoliquid flow. The increasing positive constant parameter reduces the thermal graph of the nanoliquid flow. Furthermore, the intensifying Eckert number, thermophoresis, Brownian motion, and thermal radiation factor have escalated the thermal profiles of the nanoliquid flow.

Recent research has linked the improvement of extrusion features, rotatary heat process and biofuel production to the use of nanoparticles. The prime proposes of the current scrutinization is to inspect the MHD flow of Powell-Eyring fluid induce by the nanofluid and bioconvection flow through a spinning disk. Together with nanofluids, a blend of bioconvective is employed to improve the system's thermal performance which has applications in different technological systems. The flow is considered over a stretable spinning disk. The Buongiorno model has been produced to adequately reflect how the role of nanoliquid affects Brownian motion and thermophoresis characteristics. Arrhenius's activation energy has also been considered. By applying the suitable transformation, the obtained boundary layer expressions are altered into a set of ordinary differential expressions. The three stages Lobatto BVP4c technique is utilized for ordinary differential expressions. The influences of pertinent variables on different profiles are represented graphic form. The study demonstrates tangential and axial velocity reduces with larger magnitude of Ma as the opposite effect is noted for fluid parameters α1. Moreover, the concentration distributions enhance with rising values of κ and Ea . The results are calculated using previously published research, and excellent conformity is discovered.

Abstract 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.

The present study addressed the physical significance of the entropy generation for the mixed convection time-dependent flow of cross-hybrid nanoliquid due to the stretched surface at a stagnation point. The Plot for heat transport is discoursed by applying the role of thermal radiation under convective conditions. For hybrid nanofluid, engine oil is used as a base liquid with copper (II) oxide CuO and titanium dioxide TiO2 nanoparticles. The existing model is framed in the highly partial differential equation system. The governing equations have been transformed into a set of ODS's using a similar scaling operation. Following this, the resulting ODEs are solved numerically through the BVP4c. The primary goal of this research is to analyze the results of varying the stretching ratio parameter (λ), Weissenberg parameter (We), thermal radiation (Rd), and Biot number (Bi) for both pure TiO2 and CuO + TiO2/ EO hybrid nanofluid, on the velocity, temperature, drag force, heat transfer as well as entropy generation, and Bejan number was studied. A drop in velocity is observed with increasing values of the We and upsurge in velocity for rising value of unsteady parameter (A), while increasing values of both of these parameters are associated with rising temperatures. Copper and titanium oxide nanoparticles are used to increase Engine oil (EO) thermal enactment, making it a more useful base fluid. Further, some significant industrial and engineering applications are related to the present problem discourse.

The amalgamation of microorganisms in the nanofluid is significant in beautifying the thermal conductivity of several systems, such as microfluid devices, chip-shaped microdevices, and enzyme biosensors. The current investigation studies mixed convective flow of the entropy minimization of unsteady MHD tangent hyperbolic nanoliquid because a stretching surface has motile density via convective and slip conditions. For the novelty of this work, the variable transport characteristics caused by dynamic viscosity, thermal conductivity, nanoparticle mass permeability, and microbial organism diffusivity are considered. It is considered that the vertical sheet studying the flow. By using the appropriate alteration, the governing equations for the most recent flow analysis were altered into a non-dimension relation. Through MATLAB Software bvp4c, the PDE model equations have been made for these transformed equations. Engineering-relevant quantities against various physical variables include force friction, Nusselt number, Sherwood number, and microorganism profiles. The results showed good consistency compared to the current literature. Moreover, these outcomes revealed that augmentation in the magnitude of the magnetic field and velocity slip parameter declines the velocity profile. The reverse impact is studied in We. In addition, heat transfer is typically improved by the influence of thermal radiation parameters, Brownian movement, and thermophoretic force. The physical interpretation has existed through graphical and tabular explanations.

The current problem is concerned with the study of magnetohydrodynamic ternary hybrid nanofluid flow over two distinct geometries i.e., cone and wedge. The ternary hybrid nanoliquid with MHD has a lot of engineering and industrial applications. In polymer data processing, cone and wedge geometries are frequently utilized. Therefore, the present problem is designed to the flow of ternary hybrid nanoliquid over multiple geometries. Hybrid nanoliquids performed well in the heat transport rate as compared to the nanoliquid and conventional liquid. Here in this study, the idea of ternary hybrid nanoliquid is introduced to improve the energy and mass transmissions which show more satisfactory results in the thermal and mass transmission performance. The impacts of chemical reaction and thermal radiation are also executed in this model. The formulation of the present study is performed in the form of PDEs which are then transformed into the ODEs by using suitable similarity transformations. The homotopic analysis scheme is implemented for the semi-analytical solution of the existing model. Some major results that materialize from the present simplification are that; the tri-hybrid nanoliquid velocity is greater for the rising nanoparticles volume fractions. The enlargement in radiation parameter enlarged the tri-hybrid nanoliquid thermal profile. The mass transfer rate of the ternary hybrid nanoliquid is lesser for the Schmidt number and chemical reaction. Intensification in nanoparticles volume fractions and radiation parameter has increased the ternary hybrid nanofluid heat rate transfer for both cone and wedge geometries.

This article explores the analysis of magnetized blood-based nanofluids flows over an extending cylinder. The nanofluid contains copper, copper oxide and iron oxide nanoparticles which are mixed with blood. The mathematical model has been built-up in partial differential equations (PDEs) form and then changed into ordinary different equations by mean of suitable similarity variables and then has been evaluated by homotopy analysis method (HAM). The convergence of the applied technique is presented in graphical form. During the solution process, the influences of physical parameters like magnetic parameter, unsteadiness parameter, curvature parameter and thermal relaxation time parameter on the flow profiles have been investigated and depicted in Figures and Tables. The correctness of the present model has also been presented in tabular form. The results show that the greater curvature factor reduces the radius of cylinder due to which thickness of layer becomes thin at the boundaries and therefore the velocity distribution declines, while the greater curvature parameter has the increasing impact on the temperature distribution for constant wall temperature (CWT) case and decreases the temperature distribution for prescribed surface temperature (PST) case.

In engineering and manufacturing industries, stretching flow phenomena have numerous real-world implementations. Real-world applications related to stretched flow models are metalworking, crystal growth processes, cooling of fibers, and plastics sheets. Therefore, in this work, the mechanical characteristics of the magnetohydrodynamics of the non-Newtonian Maxwell nanofluid flow through a bi-directional linearly stretching surface are explored. Brownian motion, thermophoresis, and chemical reaction impacts are considered in this analysis. Additionally, thermal convective and mass flux conditions are taken into consideration. The mathematical framework of the existing problem is constructed on highly non-linear partial differential equations (PDEs). Suitable similarity transformations are used for the conversion of partial differential equations into ordinary differential equations (ODEs). The flow problem is tackled with the homotopy analysis method, which is capable of solving higher-order non-linear differential equations. Different flow profiles against various flow parameters are discussed physically. Heat and mass transference mechanisms for distinct flow factors are analyzed in a tabular form. The outcomes showed that both primary and secondary velocities are the declining functions of magnetic and Maxwell fluid parameters. The heat transfer rate rises with the cumulative values of the Brownian motion and thermal Biot number. In addition, the mass transfer rate decreases with the rising Schmidt number, Brownian motion parameter, and chemical reaction parameter, while it increases with the augmenting thermophoresis parameter. It has been highlighted that streamlines in the current work for Maxwell and Newtonian models are in fact different from one another.

Fluid flow through a porous media has many industrial applications such as water flowing through rocks and soil and purification of gas and oil mixed in rocks. Also, heat transfer enhancement has been introduced in various thermal and mechanical systems by improving the thermal conductance of base fluids. In this article, the flow of an electrically conducting water-based hybrid nanofluid comprising GO and Fe3O4 nanoparticles over an extending sheet using a porous medium has been investigated. The space-dependent heat source, Joule heating, Brownian motion, thermophoresis, thermal radiation, chemical reaction, and activation energy impacts are taken into account. For the solution of the modeled equations, the homotopy analysis method is considered. The homotopic convergence is shown with the help of a figure. This analysis is contrasted with previous outcomes and has found a great agreement. The impacts of embedded factors on different flow characteristics, skin friction coefficient, and Nusselt and Sherwood numbers are displayed using figures and tables. The outcomes of the present analysis show that the increasing magnetic and suction factors have reduced the fluid motion while amplifying the thermal profiles. Additionally, the suction factor has a reducing impact on both temperature and concentration profiles. The thermal profiles have increased with the increasing thermal Biot number, Eckert number, thermophoresis, and Brownian motion factors. The Nusselt numbers have increased with the increasing thermal Biot number and stretching factor but reduced with the increasing thermal radiation and temperature difference factors.

Abstract 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 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 k 1, inertial parameter k 2, 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.

The suspension of nanoparticles in base liquids has found extensive applications in various industrial processes like nanomedicines, microsystem cooling, and energy conversion. Owing to its important applications, this article investigates the hybrid nanofluid flow over a three-dimensional stretching surface. The fluid is influenced by thermal radiation, chemical reaction, and a variable thermal source/sink. The set of equations that administer the fluid behavior has been transformed to dimensionless form by a suitable set of similarity transformations that are further solved by the homotopy analysis method. It was found that as the ratio parameter increased, the velocity of hybrid nanofluid velocity decreased along the primary direction and increased along the secondary direction. The temperature characteristic was augmented with greater values of nonlinear thermal radiation and source/sink factors. Growth in the chemically reactive factor and Schmidt number has an adverse effect on the concentration profile of the hybrid nanofluid flow. A comparative analysis of the current results and those established in the literature was conducted. A close agreement with those published results was found. It was noted that temperature and concentration increase more quickly for the MoS2+MgO/H2O hybrid nanofluid than the MoS2/H2O,MgO/H2O nanofluids.

In comparison to Newtonian fluids, non-Newtonian fluids have fascinating features in heat transportation. Here, newly type of Reiner-Rivlinnanoliquid flow over the revolving disk for viscous dissipation (VD) is being explored in a multiple-slip effect. The inclusion of gyrotactic microorganisms in the nanoliquid enhances the tendency of the nanoparticles. The idea of the intended model is enhanced by considering in the impact of activation energy, thermal radiative, heated convective conditions and entropy minimization. The system of nonlinear PDE is constructed into nonlinear ODE's by applying the von-Karman similarity method and later solved numerically using the BVP4c solver which is considered to study the complicated ordinary differential equations. TheInfluence of various parameters is elaborated and plotted physically through the graphical illustration. By contrasting the reported data in the restricted form to a previously published article, the accuracy of the current model has examined. The impact of a non-Newtonian fluid parameter over the velocity field appeared to showdpreciation in it. The results elucidate that when the wall slip coefficient is larger more torque is needed to maintain constant disk revaluation. Surface heat transmission and wall skin friction are computed for a wide variety of factors. These flows have several real world-applications, including modeling cases that occur in oceanography and geophysics, various industrial fields (such as lumber production).

Abstract 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 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 The current study provides a detailed analysis of steady two-dimensional incompressible and electrically conducting magnetohydrodynamic flow of a couple stress hybrid nanofluid under the influence of Darcy–Forchheimer, viscous dissipation, joule heating, heat generation, chemical reaction, and variable viscosity. The system of partial differential equations of the current model (equation of motion, energy, and concentration) is converted into a system of ordinary differential equations by adopting the suitable similarity practice. Analytically, homotopy analysis method (HAM) is employed to solve the obtained set of equations. The impact of permeability, couple-stress and magnetic parameters on axial velocity, mean critical reflux condition and mean velocity on the channel walls are discussed in details. Computational effects show that the axial mean velocity at the boundary has an inverse relation with couple stress parameter while the permeability parameter has a direct relation with the magnetic parameter and vice versa. The enhancement in the temperature distribution evaluates the pH values and electric conductivity. Therefore, the $$SWCNTs\,\,{\text{and}}\,\,MWCNTs$$ S W C N T s and M W C N T s hybrid nanofluids are used in this study for medication purpose.

Abstract 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.