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This research work executes the activation energy and covalent bonding reaction aspects in the flow of hybrid ferroliquid across a stream-wise and crosswise position. Substance of Fe3O4 and CoFe2O4 are mixed with base liquid water + EG is considered as hybrid ferroliquid. Usual form of heat absorption and heat generation is taken in the thermal equation and magnetic field is taken in the momentum equation. The ODEs are obtained by conversion of PDEs through transformation and solved by RKF-45 scheme. Comparison of ferroliquid and hybrid ferroliquid is made with flow variables and presented in graph format. Computational values of heat transportation rate, mass transportation rate and drag friction are displayed through tabular data. Upshot bring out that the reaction rate decays the concentration while activation energy enrich the temperature. Also in both stream-wise and crosswise position, hybrid ferroliquid is lower than ferroliquid and which is same in concentration but reverted in temperature.

Double diffusion flow of Jeffrey fluid in presence of nanoparticles is studied theoretically under time dependent thermal conductivity. The considered nanoparticles are evaporated over convectively heated surface which moves periodically in its own plane. The appropriate dimensionless variables are employed to obtain the dimensionless forms of governing equations. We computed the analytical solution of non-linear differential equations by utilizing homotopy analysis method. The present investigation reveals the features of various emerging parameters like Deborah number, combined parameter, oscillation frequency to stretching rate ratio, Prandtl number, Lewis number, thermophoresis parameter, Brownian motion parameter, nano Lewis number, modified Dufour parameter, and Dufour solutal Lewis number. A useful enhancement in movement of nanoparticles is observed by utilizing the combined magnetic and porosity effects. Unlike traditional studies, present analysis is confined with the unsteady transportation phenomenon from periodically moving surfaces. Such computation may be attributable in flow results from tensional vibrations due to stretching and elastic surfaces. The simulation presented here can be attractable significance in the bioengineered nanoparticles manufacturing. It is observed that the heat transportation of nanoparticles may efficiently enhance through the utilization of variable thermal conductivity. The solutal concentration decreases with increasing Deborah number and Lewis number. It is further noted that the nano Lewis number causes reduction of nanoparticles concentration.

The development of advanced-performance thermal frameworks for increased heat transport has proved to be of remarkable interest these days. Therefore, present attempt is intended to deal with entropy generation and heat transfer analysis for the peristaltic flow of an electrically conducting silver-water nanoliquid through a symmetric channel. System is supposed to be affected by an external magnetic field and electrical conductivity of nanofluid is considered to vary with temperature. Mixed convection, joule heating aspects along with thermal and velocity slip conditions are considered in analysis. Two phase model of nanofluids is adopted. Mathematical modeling for entropy generation is carried out via second law of thermodynamics. Making use of numerical solver NDSolve, graphical analysis for entropy generation, heat transfer, Bejan number and velocity is presented. Results reveal that by enhancing electrical conductivity parameter entropy generation increases. It is further deduced that entropy generation can be minimized by addition of silver nanoparticles. Bejan number increases by increasing Grashoff number. For large values of Hartman number temperature increases. Temperature of nanofluid increases by enhancing thermal slip parameter. Increase in Grashoff number provides better rate of heat transport at the boundary. Moreover, velocity decreases by enhancing velocity slip parameter.

Nanomaterials are quite significant in the physiological and engineering processes. Such materials have motivated the recent scientists in view of their enhanced thermophysical characteristics than conventional liquids. With this in mind, the intention here is to address the peristaltic activity of Sisko nano-liquid subject to Hall and Ohmic heating effects. Fluid-saturated porous space is modeled using the modified Darcy’s law. Thermal radiation is also accounted. In addition, the analysis carried out is subject to thermal jump, velocity slip and zero mass flux condition. Numerical solution to the resulting nonlinear problem through the lubrication approach is developed. Solution analysis is made by pointing out the impacts of sundry variables. The temperature profile increases by increasing the Hartman number due to the Joule heating effect. However, temperature decreases by increasing the Hall parameter.

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.

In this work, Bodewadt flow over a stretchable rotating disc is executed by considering three types of hybrid nanoliquids. In addition, heat transport nature is analysed by incorporating the effect...

No doubt the nanomaterial has superior thermophysical characteristics when compared with traditional fluid in numerous engineering and biological phenomena. Here, model is constructed for mixed convective peristaltic motion in the presence of Joule heating. Analysis has been organized for Sisko fluid. Brownian motion and thermophoresis are used to examine the nanomaterial effects. Velocity and thermal slip conditions are utilized. Zero mass flux condition is imposed. Small Reynolds number and large wavelength arguments are employed. Governing problem is nonlinear in terms of both differential equation and boundary conditions. Numerical solution to incoming nonlinear problem is computed. The solutions for velocity, temperature, concentration and pressure gradient are examined for the influential variables. It represents that concentration of nanomaterial rapidly enhances for higher N $$_{{\rm t}}$$ . Concentration of nanomaterial against Brinkman number is increased throughout the channel.

The enhancement of energy by introducing nanoparticles is a hot topic in the present century, due to industrial and technological applications. Therefore, current article investigates the peristaltic flow of $$\mathrm{Ag}{-}\mathrm{H}_2\mathrm{O}$$ nanofluid with entropy generation through a uniform channel. Hall and Radiation effects are incorporated. Two-phase formulation for nanofluid is employed. Long-wavelength approximation is used in the mathematical modelling. Built-in numerical solver NDSolve is utilized. Numerical results of the coupled equations are sketched for several quantities of interest. Outcomes of the study reveals that entropy significantly reduces for large values of Hall parameter, whereas opposite behaviour is noted for velocity. Increase in the values of radiation parameter reduces the velocity, temperature, and entropy generation. Increase in Bejan number is observed for enhancement in Brinkman number. Rate of heat transfer at walls increases when heat source parameter is increased. Additionally, comparison of different nanoparticles is also furnished through tables.

The basic idea of the present article is to model and study the aspects of curvature-dependent channel walls on peristalsis of laminar viscous material flow through a curved geometry. Mathematical modeling for such flow configuration is being presented for the first time. Lubrication theory assumptions are used for mathematical modeling of the problem. Moreover, the numerical method is used to solve the resulting system of equation. The impacts of different flow quantities on the heat transfer rate, velocity and temperature profiles are discussed via graphs. Results indicate that the curvature parameter considerably influences the mechanical and thermal aspects of the flow and hence must be included in the modeling of flows through curved a channel.

Entropy generation in peristaltic transport of nanomaterial with iron oxide is discussed. MHD and Joule heating are analyzed. Energy equation further consists of heat source/sink and viscous dissipation. Velocity slip and temperature jump conditions are also accounted. Large wavelength analysis is carried out. Results for velocity, temperature, pressure and entropy generation are presented graphically. Temperature decreases by increasing nanomaterials’ volume fraction. Larger velocity slip parameter yields lower pressure gradient. Entropy generation is increased for Hartmann number and nanoparticle volume fraction.

Nanofluids have attracted many scientists due to their remarkable thermophysical properties. Small percentage of nanoparticles when added to conventional fluid significantly enhances the heat transfer features. Sustainability and efficiency of nanomaterials have key role in the advancement of nanotechnology. This article analyzes the Hall, Ohmic heating and velocity slip effects on the peristalsis of nanofluid. Convective boundary conditions and heat generation/absorption are considered to facilitate the heat transfer characteristics. Governing equations for the peristaltic flow through a curved channel are derived in curvilinear coordinates. The equations are numerically solved under the assumption of long wavelength and small Reynold number. It has been observed that nanofluid enhances the heat transfer rate and reduces the fluid temperature. Hartman number and Hall parameter show reverse behavior in fluid motion and heat transfer characteristics. In the presence of velocity slip, the pressure gradient rapidly decreases and dominant effect is seen in narrow portion of channel.

Mesoscopic theory is applied to show the nanoparticles migration through a porous 3D cavity. Various amounts of Lorentz forces, buoyancy and Darcy number on working fluid behavior are considered and depicted. Al2O3-H2O is selected including Brownian motion effect. Outputs are illustrated in views of streamlines, isokinetic and isotherms contours. Outputs display that the enhancing magnetic forces lead to rise in conduction mode. Nu_ave augments with the decrease in Lorentz forces while it improves for stronger Lorentz forces.

Entropy generation analysis for peristalsis of nanofluid with temperature dependent viscosity has been carried out. Mathematical formulation is executed using “long wavelength” approximation. Hall effects and Ohmic heating are also included. Arising non-linear equations are solved using Homotopy Perturbation Method. Analytical solutions for temperature, axial velocity, Bejan number and entropy generation are obtained and examined through graphs. Results show that for enhanced values of nanoparticles volume fraction both velocity and temperature decreases. Increasing values of viscosity parameter decreases the temperature. Moreover, entropy generation and Bejan numbers show decreasing behaviors for increase in nanoparticles volume fraction.

This paper reports numerical study for peristalsis of Carreau–Yasuda nanofluid in a symmetric channel. Constant magnetic field is applied. Modified Darcy’s law and nonlinear thermal radiation effects are considered. Viscous dissipation and Ohmic heating effects are also present. Long wavelength and small Reynolds number are considered. Resulting nonlinear problems are solved numerically. Graphical illustrations depict that temperature increases for larger Hartmann number and it decays for thermophoresis parameter.

In this article, the flow of an incompressible nanoliquid induced due to unsteady contracting cylinder is investigated. Analysis of heat transport phenomenon is reported under uniform heat absorption/generation and convective type boundary condition. A set of transformations is implemented to reduce PDEs to ODEs. The obtained coupled nonlinear equations are treated numerically through the help of RKF 45 technique. Physical evaluation of convective condition and heat absorption/generation on thermal analysis is discussed through graphs. Output shows that both the parameters of convective condition and heat absorption/generation give an increment in liquid temperature and its related thickness of boundary layer. Keywords: Unsteadiness, MHD, Contracting cylinder, Nanoliquid, Uniform heat generation, Numerical solutions

This is a speculative investigation of the magnetohydrodynamic flow of Eyring-Powell liquid under suspension of nano-particles and dust. A simulation is executed by fraternization of Ferrous oxide (Fe3O4) and aluminum oxide (Al2O3) nanoparticles in Eyring-Powell dusty fluid. Dispersion of ferrous oxide (Fe3O4) and aluminum oxide (Al2O3) nano-particles in dusty fluid have applications in heat exchanger system, biocompatibility, biosensors, nuclear reactor heating process, detection and cancer treatment, in monitoring stem cells differentiation etc. Ferrous oxide (Fe3O4) and aluminum oxide (Al2O3) mixtures are substantially useful in optimizing the heat transport occurrences. Implementation of similarity variables leads to the systems of ordinary differential expressions. These nonlinear systems of ODEs are tackled with the use of Runge-Kutta-Fehlberg Scheme (RKFS). The analysis of dimensionless temperature and velocity fields is given via plots. The numerical benchmarks of friction-factors and heat transport rate are for different constraints are given and examined. Obtained results are matched with previously published material and noted to be satisfactory. This model expresses that the rate of heat transportation is more in aluminum oxide nanofluid compared to ferrous oxide nanofluid with existing of viscous variation parameter. The presence of thermal and momentum slips correspond the enhancement in local Nusselt number in case of ferrous oxide nanoparticles when compared to aluminum oxide nanoparticles.

Time-dependent, two-dimensional Sakiadis flow of quiescent fluid is considered. The flow is induced by stationary flat plate via uniform free-stream (Blasius flow). The variable conductivity and viscosity ratio parameters and non-linear chemical reaction are employed in the mathematical equations. Similarity variables are employed in the governing transport expressions to convert into the ordinary differential system. The transformed system is computed numerically by employing Runge-Kutta scheme via shooting criteria. Results of concentration, velocity and temperature distributions are studied through plots. Moreover, mass and heat transfer rates and friction factor have been discussed in detail. The constraint of chemical reaction slow down the friction-factors and heat transportation rates for the Sakiadis-Blasius flow situations and enhances the mass transportation rate in both cases. Rate of mass transportation is smaller in Sakiadis flow as comparative to Blasius flow. The present results of the heat transfer rate are matched with the literature and excellent agreement is noticed.

The objective of this research is to study the combined influences of applied electric and magnetic fields on the two-phase peristaltic motion of nanofluid through a curved channel. A two-phase model of a nanofluid, Maxwell’s model of thermal conductivity [1], and no-slip velocity and thermal boundary conditions have been used in this study. Hall effects, Joule heating (due to magnetic and electric fields), and viscous heating aspects are under consideration. Governing equations for the present flow configuration have been modeled and simplified by enforcing the lubrication scheme. Debye-Huckel approximation is used to obtain the analytical solution of the electric potential function (Poisson-Boltzmann equation). Resulting expressions are solved numerically through the NDSolve command in Mathematica and plotted in order to understand the effects of different dimensionless parameters on the temperature, stress, heat transmission rate, and fluid’s velocity. Graphical results demonstrated that the thermal transmission rate is augmented by increasing the Hartmann number, Brinkman number, and Debye-Huckel parameter while decreases for zeta potential ratio, Joule dissipation parameter, and electro-osmotic velocity. A decrease in axial velocity is noted near the lower wall for higher values of $${m}^{\ast}$$ .

The combined effects of nonlinear thermal convection and radiation in 3D boundary layer flow of non-Newtonian nanofluid are scrutinized numerically. The flow is induced by the stretching of a flat plate in two lateral directions. The mechanism of heat and mass transport under thermophoretic and Brownian motion is elaborated via implementation of the thermal convective condition. The prevailing two-point nonlinear boundary value problem is reduced to a two-point ordinary differential problem by employing suitable similarity transformations. The solutions are computed by the implementation of homotopic scheme. At the end, a comprehensive parametric study has been conducted to analyze the typical trend of the solutions. It is found that the nanoparticle volume fraction and temperature profiles are stronger for the case of solar radiation in comparison with problem without radiation. Keywords: Non-linear convection, Nonlinear density temperature (NDT), Nonlinear thermal radiation, Three dimensional flow, Maxwell fluid, Nanoparticles

Lattice Boltzmann Method (LBM) is utilized to simulate the magnetohydrodynamic (MHD) nanofluid forced convective heat transfer inside a porous three dimensional enclosure with hot cubic obstacle. Impact of Hartmann number H a , Darcy number D a and Reynolds number Re on nanofluid treatment were depicted. Al2O3- H 2 O nanofluid has been utilized considering single phase model. Results are demonstrated in forms of isokinetic, isotherms , streamlines, Nusselt number and velocity contours. Results show that temperature boundary layer becomes thinner with augment of D a and Re . Convective heat transfer reduces with rise of Hartmann number while it improves with rise of Darcy number.

In this research, nanofluid thermal behavior in an energy storage system is illustrated by means of FEM. CuO nanoparticles have been dispersed into the water to overcome the poor thermal conductivity. Role of Brownian motion is included for estimating characteristics of nanofluid. Results are shown as solid fraction, isotherm contours, average temperature and total energy profiles. Results showed that dispersing nanoparticles to pure PCM have important impact on heat transfer rate. As A and N enhances, total energy and solidification time decrease. Furthermore, in order to reach greatest solidification rate, nanoparticles with dp = 40 nm should be used.

A numerical study of hydromagnetic radiative stagnation point flow of micropolar nanofluid passed through a shrinking sheet is reported. Magnetic field is utilized in transverse direction. Nonlinear system of partial differential equations is converted into system of nonlinear ordinary ones by applying similarity transformations. Convective types of boundary conditions are applied on temperature and concentration. RKF45 technique is applied to investigate the numerical results of different dimensionless physical parameters in graphical and tabular forms. It is visualized that the increasing values of Biot numbers correspond to enhancement in temperature and nanoparticle volume distributions. Further, we observed that the increasing values of thermophoretic and Brownian motion parameters have reverse effects on nanoparticle volume fraction. Keywords: Micropolar nanofluid, MHD, Shrinking sheet, Brownian motion, Thermophoresis

Current study provides a comprehensive numerical investigation of the peristaltic transport of boron nitride-ethylene glycol nanofluid through a symmetric channel in presence of magnetic field. Significant effects of Brownian motion and thermophoresis have been included in the energy equation. Hall and Ohmic heating effects are also taken into consideration. Resulting system of non-linear equations is solved numerically using NDSolve in Mathematica. Expressions for velocity, temperature, concentration and streamlines are derived and plotted under the assumption of long wavelength and low Reynolds number. Influence of various parameters on heat and mass transfer rates have been discussed with the help of bar charts.

The present communication investigates flow of Carreau-Yasuda nanofluid in presence of mixed convection and Hall current. Effects of viscous dissipation, Ohmic heating and convective conditions are addressed. In addition zero nanoparticle mass flux condition is imposed. Wave frame analysis is carried out. Coupled differential systems after long wavelength and low Reynolds number are numerically solved. Effects of different parameters on velocity, temperature and concentration are studied. Heat and mass transfer rates are analyzed through tabular values. It is observed that concentration for thermophoresis and Brownian motion parameters has opposite effect. Further heat and mass transfer rates at the upper wall enhances significantly when Hartman number increases and reverse situation is noticed for Hall parameter. Keywords: Peristalsis, Carreau-Yasuda nanofluid, Magnetic field, Mixed convection, Numerical solution

The nonlinear convective flow of kerosene-Alumina nanoliquid subjected to an exponential space dependent heat source and temperature dependent viscosity is investigated here. This study is focuses on augmentation of heat transport rate in liquid propellant rocket engine. The kerosene-Alumina nanoliquid is considered as the regenerative coolant. Aspects of radiation and viscous dissipation are also covered. Relevant nonlinear system is solved numerically via RK based shooting scheme. Diverse flow fields are computed and examined for distinct governing variables. We figured out that the nanoliquid’s temperature increased due to space dependent heat source and radiation aspects. The heat transfer rate is higher in case of changeable viscosity than constant viscosity.

Peristalsis of fluids through curved geometries is widely encountered in several industrial and domestic pumping devices. Keeping this fact in mind, effects of variable magnetic field on peristalsis of Carreau-Yasuda (C-Y) fluid through a curved channel with velocity and thermal slip boundary conditions are studied. Heat transfer analysis has been carried out by considering the Joule heating and viscous dissipation effects. The long wavelength and small Reynolds number assumptions are adopted in mathematical modeling of the problem. Resulting non-linear system of differential equations has been solved numerically. Graphical results for axial velocity, temperature, heat transfer rate and stresses at the walls for the different flow parameters are discussed. It is reported that the radially varying magnetic field decreases velocity and increases the temperature of the fluid. Such magnetic field also enhances the heat transfer rate and stresses at the boundaries.

Entropy generation is one of the key features in the analysis as it exhibits irreversibility of the system. Therefore, present study investigates entropy generation rate in a mixed convective peristaltic motion of a reactive nanofluid through an asymmetrical divergent channel with heat and mass transfer characteristics. Endorsed nanofluid model holds thermophoresis and Brownian diffusions. Mathematical modeling is configured under the effects of mixed convection, heat generation/absorption and viscous dissipation. Chemical reaction is also introduced for the description of mass transportation. Resulting system of differential equations is numerically tackled by employing the Shooting method. Findings reveal that entropy generation rises by improving Brownian motion and thermophoresis parameters. Temperature of nanofluid decreases by rising buoyancy forces caused by concentration gradient. Concentration profile increases by increasing chemical reaction parameter. Velocity increases by enhancing Brownian motion parameter.

This article highlights the influence of mixed convection, Hall current and magnetic field on peristaltic motion of Powell-Eyring nanofluid in the symmetric channel. Energy equation include the viscous dissipation, Ohmic heating and thermal radiation effects. Brownian motion and thermophoresis are considered to explore the nanofluid characteristics. Velocity slip, thermal jump and zero mass flux conditions are considered on the boundary wall. Further temperature dependent viscosity is taken into account. Lubrication approach is used to simplify the dimensionless form of governing equations. Final form of equations are solved numerically. Velocity, temperature, concentration and entropy generation behaviors are studied with the help of graphs. Temperature depicts increasing behavior for higher magnetic field whereas the opposite trend is noticed for Hall effects.

Time-dependent and incompressible squeezing flow of Casson and micropolar nanofluids is analyzed. The non-Newtonian liquids are confined through parallel disks. The bottom disk is saturated in the plane z = 0 and the fluid is squeezed by the movement of the upper disk along axial direction. Nanofluid theory (Buongiorno model) is accomplished in the flow phenomenon. A uniform injection/suction is act upon at the lower disk. Velocity, thermal and concentration slip effects are also incorporated at the bottom fixed disk. The similarity functions are first accomplished in order to achieve the governing system of ordinary differential equations and then the system is solved in numerical manner using Runge-Kutta-Fehlberg fourth fifth (RKF-45) order numerical procedure. Results are disclosed in tabular and graphical forms against the various physical quantities. For the validation of our numerical technique, the results are compared well with the literature work under limiting case. It is perceived that increased squeezing Reynolds number pushed the radial velocity profiles towards the upper disk. The micropolar parameter tends to the fluid rotation in opposite way due to which microrotational field first enhanced and then reduced by the vortex viscosity parameter.

The temperature-dependent heat source/sink in Maxwell nanoliquid flow towards a riga plate is investigated. In this model, we incorporated convective heat and mass boundary conditions. Similarity transformations are applied to convert the governing dimensional expressions into non-dimensional forms. Finite difference method along with Richardson extrapolation technique is utilized to elaborate the numerical solutions of physical phenomenon. Effects of different values of governing parameters on velocity, temperature and concentration profiles are evaluated via graphs. The quantities of interest like Nusselt and Sherwood numbers are discussed in detail through numerical data.

Purpose The aim of this works is to characterize the role of Cattaneo?Christov heat flux in two-dimensional flows of second-grade and Walter’s liquid B fluid models. Design/methodology/approach In this study similarity transformations have been used to transform the system into ordinary ones. Numerical and analytical solutions are computed through homotopic algorithm and shooting technique. Findings The numerical values of temperature gradient are tabulated, and the temperature gradient reduces rapidly with enhancing values of the Darcy parameter, but this reduction is very slow for Forchheimer parameter. Originality/value No such analyses have been reported in the literature.

Efficient heat transfer characteristics of carbon nanotubes (CNTs) extend the applications of nanofluids in various engineering and biomedical processes. Model for the peristaltic transport of nanofluid through an asymmetric channel is presented here. Analysis is carried out in the presence of viscous dissipation, mixed convection, and heat generation/absorption parameter. Convective heat transfer at the boundaries is also accounted by making use of the effective thermal conductivity of nanofluid. Mathematical modelling has been carried out in view of long wavelength and low Reynolds number approximations. Resulting nonlinear equations are solved for the development of series solutions. Series solutions for small Brinkman number are computed. Effects of sundry parameters on the axial velocity, pressure gradient, pressure rise per wavelength, temperature, streamlines, and heat transfer rate at the boundary are studied through their respective plots. Comparison between single-walled CNTs and multi-walled CNTs is also presented. Results indicate that by adding CNTs to the water, the velocity and temperature are decreased. Further, the heat transfer rate at the boundaries enhances with an increase in the CNT volume fraction. Also, the single-wall carbon nanotubes (SWCNTs) show larger heat transfer rate at the boundary when compared with the multiple-wall carbon nanotubes (MWCNTs).

Variation in effective viscosity of nanofluids with temperature is well admitted now. Peristalsis of nanofluid with temperature dependent viscosity is investigated here. Distinct nanoparticles i.e. Copper (Cu), Silver (Ag), Gold (Au) and iron oxide (Fe 2 O 3 ) along with two models for effective thermal conductivity of nanofluids are used in the analysis. Effects of the Hall and Ohmic heating are also accounted. Resulting nonlinear equations are solved numerically. Physical interpretation of the results is presented. Comparison of results is made for constant and variable viscosity, for different thermal conductivity models and for various nanoparticles. It is reported that the values of velocity, temperature and heat transfer rate reported through Maxwell's model are large when compared with the Hamilton-Crosser's thermal conductivity model. Results indicate that enhanced values of variable viscosity parameter decrease the effective viscosity of nanofluid and hence fluid flows freely. Velocity and temperature of nanofluid increases when variable viscosity parameter is allocated larger values. Further, heat transfer rate at the boundary is large when nanofluid is composed of gold nanoparticles.

The effect of non-linear convection in a laminar three-dimensional Oldroyd-B fluid flow is addressed. The heat transfer phenomenon is explored by considering the non-linear thermal radiation and heat generation/absorption. The boundary layer assumptions are taken into account to govern the mathematical model of the flow analysis. Some suitable similarity variables are introduced to transform the partial differential equations into ordinary differential systems. The Runge-Kutta-Fehlberg fourth- and fifth-order techniques with the shooting method are used to obtain the solutions of the dimensionless velocities and temperature. The effects of various physical parameters on the fluid velocities and temperature are plotted and examined. A comparison with the exact and homotopy perturbation solutions is made for the viscous fluid case, and an excellent match is noted. The numerical values of the wall shear stresses and the heat transfer rate at the wall are tabulated and investigated. The enhancement in the values of the Deborah number shows a reverse behavior on the liquid velocities. The results show that the temperature and the thermal boundary layer are reduced when the non-linear convection parameter increases. The values of the Nusselt number are higher in the non-linear radiation situation than those in the linear radiation situation.

This article concerned with the three-dimensional flow fills the porous space bounded by a bidirectional stretching sheet with non-linear thermal radiation and heat source/sink. Maxwell fluid model is accounted as a working liquid. The imposed conditions for temperature and nanoparticle concentration are convective type. The self-similar forms of equations are obtained by the implementation of similarity variables. The solutions are computed via shooting algorithm with fourth-fifth-order Runge-Kutta-Fehlberg procedure. Comparison of obtained results with the known numerical solution is made and examined an excellent agreement. It is noted that the role of Brownian motion in temperature and heat transfer rate is significant. The results reveal that concentration of nanoparticles and temperature are decreased with an enhancement in Deborah number.

The role of the Cattaneo-Christov heat flux theory in the two-dimensional laminar flow of the Jeffrey liquid is discussed with a vertical sheet. The salient feature in the energy equation is accounted due to the implementation of the Cattaneo-Christov heat flux. A liquid with variable thermal conductivity is considered in the Darcy-Forchheimer porous space. The mathematical expressions of momentum and energy are coupled due to the presence of mixed convection. A highly nonlinear coupled system of equations is tackled with the homotopic algorithm. The convergence of the homotopy expressions is calculated graphically and numerically. The solutions of the velocity and temperature are expressed for various values of the Deborah number, the ratio of the relaxation time to the retardation time, the porosity parameter, the mixed convective parameter, the Darcy-Forchheimer parameter, and the conductivity parameter. The results show that the velocity and temperature are higher in Fourier’s law of heat conduction cases in comparison with the Cattaneo-Christov heat flux model.