OHAM simulation of 3D transverse magnetic field in rotating flow of Maxwell nanofluid over a stretching sheet with chemical reaction and heat source/sink

In this article, we investigate the heat transfer characteristics of a Maxwell nanofluid along a stretching sheet with transverse magnetic field, considering the presence of heat source/sink and chemical reaction. We consider appropriate similarity transformation for transforming the governing nonlinear equations into nondimensional highly nonlinear coupled ordinary differential equations. The optimal homotopy analysis method is utilized for solving the resultant-coupled equations. The impact of all sundry parameters, like, Deborah number, Prandtl number, magnetic parameter, thermophoresis, rotation parameter, chemical reaction, velocity slip, Schmidt number, Brownian motion parameter, heat sources per sink, Biot number, and Eckert number, on the temperature, velocity, and concentration fields is reported, analyzed, and described through graphs and tables. It is noticed that higher values of magnetic parameter and Deborah number reduce the horizontal velocity field. Furthermore, it is observed that the Biot number and heat source/sink parameter enhance the temperature distribution.     

Numerical study of chemical reaction and heat transfer of MHD slip flow with Joule heating and Soret–Dufour effect over an exponentially stretching sheet

A study of Soret–Dufour effects along with chemical reaction, viscous dissipation combining on MHD Joule heating for viscous incompressible flow is presented. It is assumed that fluid is flowing past an angled stretching sheet saturated in porous means. The slip conditions of velocity, concentration, and temperature are accounted for at the boundary. The mathematical expression of the problem contains highly nonlinear interconnected partial differential equations. To convert governing equations into ordinary differential equations, appropriate similarity transformations were utilized. These differential equations with boundary constraints are resolved by homotopy analysis method. Expression for velocity, concentration, and temperature are derived in the form of series. Effects of numerous physical parameters, for example, Schmidt number, Soret number, buoyancy ratio parameter, slip parameter, and so forth, on various flow characteristics are presented through graphs. Numerous values of velocity, concentration, and temperature gradient are tabulated against different parameters. Results show that the fluid velocity increases by enhancing the Soret number, Dufour number, or permeability parameter. The fluid's concentration rises as the Soret number increases, while it falls as the Dufour number, chemical reaction parameter, or permeability parameter increases.     

Heat transfer and hydromagnetic electroosmotic Von Kármán swirling flow from a rotating porous disc to a permeable medium with viscous heating and Joule dissipation

Magnetohydrodynamic flow and heat transfer in an ionic viscous fluid in a porous medium induced by a stretching spinning disc and modulated by electroosmosis under an axial magnetic field and radial electrical field is presented in this study. The effects of convective wall boundary conditions, Joule heating and viscous dissipation are incorporated. The governing partial differential conservation equations are transformed into a system of self-similar coupled, nonlinear ordinary differential equations with associated boundary conditions. The Matlab bvp4c solver featuring a shooting technique and the fourth-order Runge–Kutta–Fehlberg method are used to numerically solve the governing dimensionless boundary value problem. Multivariate analysis is also performed to examine the thermal characteristics. An increase in rotation parameter induces a reduction in the radial velocity, whereas it elevates the tangential velocity. Greater electrical field parameter strongly damps the radial velocity whereas it slightly decreases the tangential velocity. Increasing magnetic parameter also damps both the radial and tangential velocities. An increment in electroosmotic parameter substantially decelerates the radial flow but has a weak effect on the tangential velocity field. Increasing permeability parameter (inversely proportional to permeability) markedly damps both radial and tangential velocities. The pressure gradient is initially enhanced near the disk surface but reduced further from the disk surface with increasing magnetic parameter and electrical field parameter, whereas the opposite effect is produced with increasing Joule dissipation. Increasing magnetic and rotational parameters generate a strong heating effect and boost temperature and thermal boundary layer thickness. Nusselt number is boosted with increasing Brinkman number (viscous heating effect) and Reynolds number. The simulations are relevant to electromagnetic coating flows, bioreactors and electrochemical sensing technologies in medicine.     

Thermophoretic hydromagnetic dissipative heat and mass transfer with lateral mass flux,heat source,Ohmic heating and thermal conductivity effects: Network simulation numerical study

A two-dimensional mathematical model is presented for the laminar heat and mass transfer of an electrically-conducting, heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule (Ohmic) heating. The Talbot–Cheng–Scheffer–Willis formulation (1980) is used to introduce a thermophoretic coefficient into the concentration boundary layer equation. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable, η. The resulting coupled, nonlinear equations are solved under appropriate transformed boundary conditions using the Network Simulation Method. Computations are performed for a wide range of the governing flow parameters, viz Prandtl number, thermophoretic coefficient (a function of Knudsen number), Eckert number (viscous heating effect), thermal conductivity parameter, heat absorption/generation parameter, wall transpiration parameter, Hartmann number and Schmidt number. The numerical details are discussed with relevant applications. Excellent correlation is achieved with earlier studies due to White (1974) and Chamkha and Issa (2000). The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and nuclear hazards.     

Effect of Prandtl number on leading edge accretion and ablation: A numerical study of unsteady boundary layer flow over a flat plate

An efficient numerical method, namely, the Runge‐Kutta fourth order integration scheme with shooting technique is employed to give a suitable solution for the unsteady magnetohydrodynamic boundary layer flow of viscous incompressible fluid with accretion or ablation effects over a flat plate under the influence of homogenous first order chemical reaction. When compared to the other numerical techniques such as perturbation methods, this approach provides the accurate numerical results valid uniformly for all nondimensional time. The unsteady behavior of chemically reacting magnetohydrodynamic boundary layer flow is investigated by analyzing the nature of buoyancy and magnetic parameters in the momentum equation. Also, results are extended to the energy and concentration equations by considering the viscous dissipation, Joule heating and chemical reaction effects. With the help of suitable similarity transformations, the highly nonlinear, coupled, time‐dependent partial differential equations are reduced to ordinary differential equations. Furthermore, the numerical solutions in terms of velocity, temperature and concentration profiles within the boundary layer are presented for the various values of control parameters. Also, the impact of physical parameters on the flow, heat and mass transfer characteristics are examined thoroughly. The present investigation reports that, the increasing magnetic parameter increases the temperature field and decreases the velocity field. Also, Eckert number enhance the thermal field whereas, the chemical reaction parameter decays the concentration field. Before concluding the considered problem, present results are validated with the previous results and are found to be in good agreement.     

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge–Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A¹ and the temperature dependent heat source parameter B¹) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet.     

Thermal analysis of buoyancy-motivated Casson fluid flow with time-independent chemical reaction under Lorentz forces

The present research study examines the magneto-hydrodynamic natural convection visco-elastic boundary layer of Casson fluid past a nonlinear stretching sheet with Joule and viscous dissipation effects under the influence of chemical reaction. To differentiate the visco-elastic nature of Casson fluid with Newtonian fluids, an established Casson model is considered. The present physical problem is modeled by utilizing the considered geometry. The resulting system of coupled nonlinear partial differential equations is reduced to a system of nonlinear ordinary differential equations by applying suitable similarity transformations. Numerical solutions of these reduced nondimensional governing flow field equations are obtained by applying the Runge-Kutta integration scheme with the shooting method (RK-4). The physical behavior of different control parameters is described through graphs and tables. The present study describes that the velocity and temperature profiles decreased for increasing values of Casson fluid parameter. Velocity field diminished for the increasing nonlinear parameter whereas velocity profile magnified for increasing free convection parameter. Thermal field enhanced with increasing magnetic parameter in the flow regime. The concentration profile decreased for the rising values of the chemical reaction parameter. The magnitude of the skin-friction coefficient enhanced with increasing magnetic parameter. Increasing Eckert number increases the heat transfer rate and increasing chemical reaction parameter magnifies the mass transfer rate. Finally, the similarity results presented in this article are excellently matched with previously available solutions in the literature.     

Thermochemistry and viscous heat dissipative effects on unsteady upper-convected Maxwell fluid flow past a stretching vertical plate with thermophysical variables

In this paper, unsteady upper-convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature-dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature-dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence.     

Significance of thermal radiation on dusty fluid flow over a stretching rotating disk with convective boundary condition

This paper explores the flow of dusty fluid over a stretching rotating disk with thermal radiation. Further, the convective boundary condition is considered in this modeling. The described governing equations are reduced to ordinary differential equations by using apt similarity transformations and then they are numerically solved using Runge–Kutta–Fehlberg-45 scheme. To gain a clear understanding of the current boundary layer flow problem, the graphical results of the velocity and thermal profiles, shear stresses at the disk, and Nusselt number are drawn. Results reveal that the increase in the value of the porosity parameter reduces the velocity of both particle and fluid phases. The increase in the value of the Biot number improves the temperature gradient of both particle and fluid phases. The rise in the value of the radiation parameter advances the heat transference of both phases. The rise in the value of the Biot number improves the rate of heat transfer. Finally, increasing the value of the radiation parameter improves the rate of heat transfer.     

Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.     

Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Flow and heat transfer of a third grade fluid past an exponentially stretching sheet with partial slip boundary condition

Non-Newtonian boundary layer flow and heat transfer over an exponentially stretching sheet with partial slip boundary condition has been studied in this paper. The flow is subject to a uniform transverse magnetic field. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST), and (ii) prescribed heat flux (PHF). Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. An effective second order numerical scheme has been adopted to solve the obtained differential equations. The important finding in this communication is the combined effects of the partial slip and the third grade fluid parameters on the velocity, skin-friction coefficient and the temperature boundary layer. It is found that the third grade fluid parameter β increases the momentum boundary layer thickness and decreases the thermal boundary layer thickness.     

Simulation of fourth-grade magnetized fluid flow due to motile cilia in a heated curved channel

This research aims to investigate the main features of the ciliary flow of fourth-grade fluid in a curved channel. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the addition of viscous dissipation and thermal radiation. The governing system of coupled partial differential equations with extremely nonlinear expressions is simplified using the long wavelength and low Reynolds number approximations. The numerical outcomes of simplified normalized equations are obtained using the finite difference method incorporating the relaxation algorithm. The numerical outcomes regarding the influences of several physical parameters on the temperature, velocity, pumping characteristics, and stream function are examined through graphs. The outcomes reveal that fluid velocity diminishes by enhancing the magnetic parameter. Also, the temperature is enhanced by enhancing the values of the Brickman number. The current model has been used in bioengineering processes, microfluidics, and drug delivery systems.     

Heat transport on steady MHD flow of copper and alumina nanofluids past a stretching porous surface

An attempt is made to investigate the steady magnetohydrodynamic convective flow of the viscous nanofluid due to a permeable exponentially stretching porous surface. Water is used as a traditional fluid while nanoparticles include copper and alumina. The fluid is electrically conducting, subject to an applied magnetic field with a constant strength. Convective type boundary conditions are employed in modeling the heat transfer process. The nonlinear partial differential equations governing the flow are reduced to an ordinary differential equation by similarity transformations and then solved using the Runge‐Kutta fourth‐order method. A parametric study of the physical parameters is made, and a representative set of numerical results for the velocity and temperature, as well as local shear stress and local Nusselt number, is presented graphically. Hartman number increase diminishes the velocity and has the contrary result in the subjective sense for the mass transfer parameter. An increase in the Prandtl number Pr lessens the temperature and thickness of the thermal boundary layer. The main conclusions have been indicated.     

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

The present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.     

Lie symmetry analysis and numerical solutions for thermosolutal chemically reacting radiative micropolar flow from an inclined porous surface

Steady, laminar, incompressible thermosolutal natural convection flow of micropolar fluid from an inclined perforated surface with convective boundary conditions is studied. Thermal radiative flux and chemical reaction effects are included to represent phenomena encountered in high-temperature materials synthesis operations. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Lie scaling group transformation is implemented to derive a self-similar form of the partial differential conservation equations. The resulting coupled nonlinear boundary value problem is solved with Runge-Kutta fourth order numerical quadrature (shooting technique). Validation of solutions with an optimized Adomian decomposition method algorithm is included. Verification of the accuracy of shooting is also conducted as a particular case of nonreactive micropolar flow from a vertical permeable surface. The evolution of velocity, angular velocity (microrotation component), temperature, and concentration are examined for a variety of parameters including coupling number, plate inclination angle, suction/injection parameter, radiation-conduction parameter, Biot number, and reaction parameter. Numerical results for steady-state skin friction coefficient, couple stress coefficient, Nusselt number, and Sherwood number are tabulated and discussed. Interesting features of the hydrodynamic, heat and mass transfer characteristics are examined.     

Numerical study of heat and mass transfer in MHD flow of nanofluid in a porous medium with Soret and Dufour effects

This article models the transport mechanism of mass and heat energy under temperature and concentration gradients. Mathematical models in the form of partial differential equations based on conservation laws for fluid flow and transfer of heat and mass subjected to thermal diffusion and diffusion thermos, heat generation porous medium, and buoyancy forces are developed under boundary layer approximations. These models along with models of nanostructures are solved numerically using the shooting method with the Runge–Kutta method of order five. Convergent solutions are obtained and are used for parametric analysis regarding thermal enhancement of a working fluid having nanoparticles of CuO, Al₂O₃, and TiO₂. Numerical experiments are performed and it is observed that the transport of heat is accelerated when the compositional gradient is increased. Similarly, a significant rise in the transport across concentration is noted when the temperature gradient is increased. The magnetohydrodynamic flow experienced retardation when the porous medium parameter and Hartmann number are increased. The temperature increased when the friction force produced heat and that heat is distributed to the particles of the fluid. Hence, viscous dissipation is responsible for widening the thermal boundary layer region.     

Features of Cattaneo‐Christov heat flux model for Stagnation point flow of a Jeffrey fluid impinging over a stretching sheet: A numerical study

The present work focuses on a two‐dimensional steady incompressible stagnation point flow of a Jeffery fluid over a stretching sheet. The Cattaneo‐Christov heat flux model is incorporated into this study. Simulation is conducted via the Runge‐Kutta fourth‐order cum shooting method for the transformed system of nonlinear equations. The influence of the governing parameters on the dimensionless velocity, temperature, skin friction, streamlines, and isotherms is incorporated. A significant outcome of the current investigation is that an increase in the relaxation time parameter uplifts temperature; however, a gradual decrease is observed in the velocity field. Another important outcome of the present analysis is that the momentum boundary layer augments due to an increase in the Deborah number; however, a decrease is observed in the temperature. Furthermore, it is also observed that the skin friction coefficient escalates with an increase in the relaxation time parameter for the assisting flow, but a reverse trend is observed for the opposing flow.     

Effects of nonlinear thermal radiation over magnetized stagnation point flow of Williamson fluid in porous media driven by stretching sheet

In this study, the stagnation point flow of a magnetized Williamson fluid past a stretching sheet in the presence of nonlinear thermal radiation and buoyancy effect is studied. The present situation is remodeled using similarity transformation that transforms the flow model of partial differential equations into the set of nonlinear ordinary differential equations. The fourth-order Runge-Kutta scheme and shooting method are employed to solve these reduced equations. The effects of various associated parameters over the velocity and temperature profiles are plotted and the outcome of each associated parameter is discussed through graphs. The key findings are noted as follows: the velocity profile declines with an increase in the magnetic force number, and an increment in buoyancy parameter leads to the increase in the boundary layer thickness and decrease in the thickness of the thermal boundary layer.     

Flow and heat transfer analysis of MHD third-grade fluid flow through a vertical microchannel subjected to entropy generation

This paper analyses the generation of entropy in an electrically conducting third-grade fluid through a vertical channel considering the variable thermal conductivity. Aspects of radiation, viscous dissipation, porous medium, Joule heating, convective boundary condition, and heat generation are studied. Nonlinear systems of ordinary differential equations are obtained via applying suitable dimensionless variables. After that, the system is solved with the aid of using the Runge–Kutta–Fehlberg method. The numerical solutions are used to characterize the irreversibility and irreversibility ratio. It is established that the entropy is enhanced with accelerating estimations of the third-grade material parameter, Brinkman number, magnetism, Biot number, porous parameter, and the impact is decelerated with elevating values of the radiation. The rate of heat transfer is higher for the Brinkman number, and a similar impact on drag force is noticed for magnetic and Grashof numbers. All the parameters on flow, temperature, fluid irreversibility and irreversibility ratio are discussed through graphical illustration.