MHD Double-Diffusive Carreau Fluid Flow through a Porous Medium with Variable Thermal Conductivity and Suction/Injection

In this article, we consider the effects of double diffusion on magnetohydrodynamics (MHD) Carreau fluid flow through a porous medium along a stretching sheet. Variable thermal conductivity and suction/injection parameter effects are also taken into the consideration. Similarity transformations are utilized to transform the equations governing the Carreau fluid flow model to dimensionless non-linear ordinary differential equations. Maple software is utilized for the numerical solution. These solutions are then presented through graphs. The velocity, concentration, temperature profile, skin friction coefficient, and the Nusselt and Sherwood numbers under the impact of different parameters are studied. The fluid flow is analyzed for both suction and injection cases. From the analysis carried out, it is observed that the velocity profile reduces by increasing the porosity parameter while it enhances both the temperature and concentration profile. The temperature field enhances with increasing the variable thermal conductivity and the Nusselt number exhibits opposite behavior.     

Mass transpiration on Newtonian flow over a porous stretching/shrinking sheet with slip

The motivation behind this article is to research the Newtonian liquid flow porous stretching/shrinking sheet utilizing a Brinkman model. The leading system of non-linear partial differential equations relating the article is mapped to standard ordinary differential equations via similarity transformations. Exact result is obtained for velocity. The effects of the Brinkman number or viscosity ratio, slip parameter, Darcy number, suction/injection (mass transpiration) parameter and the mass suction parameter on the velocity dispersion are introduced graphically and talked about. The outcomes have conceivable innovative applications in extrusion process and such other unified zones and in the fluid based frameworks including stretchable materials. Examination of fluid flow past a permeable stretching/shrinking sheet embedded in a non-Darcy permeable medium has been performed for a wide scope of various parameters. Exact solution has been obtained.     

Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet

This Letter endeavours to complete an earlier numerical analysis for flow and heat transfer in a viscous fluid over a sheet nonlinearly stretched by extending the investigation in two directions. On one side, the effects of thermal radiation are included in the energy equation, and, on the other hand, the prescribed wall heat flux case (PHF case) is also analyzed. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The variations of dimensionless surface temperature as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include a nonlinearly stretching sheet, thermal radiation, viscous dissipation and power-law index of the wall temperature parameters, are graphed and tabulated.     

Effects of variable properties on MHD heat and mass transfer flow near a stagnation point towards a stretching sheet in a porous medium with thermal radiation

The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic(MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented,taking into account thermal radiation and internal heat genberation/absorbtion.The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point.The Rosseland approximation is used to describe the radiative heat flux in the energy equation.The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung-Kutta method with the shooting technique.A comparison with previously published work has been carried out and the results are found to be in good agreement.The results are analyzed for the effect of different physical parameters,such as the variable viscosity and thermal conductivity,the ratio of free stream velocity to stretching velocity,the magnetic field,the porosity,the radiation and suction/injection on the flow,and the heat and mass transfer characteristics.The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1.In addition,the imposition of fluid suction increases both the rate of heat and mass transfer,whereas fluid injection shows the opposite effect.     

Magnetohydrodynamic tangent hyperbolic fluid flow past a stretching sheet

In this article, we investigate the MHD tangent hyperbolic fluid flow along a stretching sheet with suction/injection effect at the boundary. The governing nonlinear partial differential equations are transformed into a set of nonlinear ordinary differential equations using the similarity transformation developed by the Lie group analysis. The transformed non-dimensional ordinary differential equations are solved numerically by a shooting technique. The impacts of the governing parameters on the fluid flow and heat transfer characteristics are investigated and discussed, with the help of graphical representations.     

Convective heat transfer and MHD effects on Casson nanofluid flow over a shrinking sheet

Current study examines the magnetohydrodynamic (MHD) boundary layer flow of a Casson nanofluid over an exponentially permeable shrinking sheet with convective boundary condition. Moreover, we have considered the suction/injection effects on the wall. By applying the appropriate transformations, system of non-linear partial differential equation along with the boundary conditions are transformed to couple non-linear ordinary differential equations. The resulting systems of non-linear ordinary differential equations are solved numerically using Runge-Kutta method. Numerical results for velocity, temperature and nanoparticle volume concentration are presented through graphs for various values of dimensionless parameters. Effects of parameters for heat transfer at wall and nanoparticle volume concentration are also presented through graphs and tables. At the end, fluid flow behavior is examined through stream lines. Concluding remarks are provided for the whole analysis.     

Effects of radiation and thermal conductivity on MHD boundary layer flow with heat transfer along a vertical stretching sheet in a porous medium

A steady two-dimensional free convective flow of a viscous incompressible fluid along a vertical stretching sheet with the effect of magnetic field, radiation and variable thermal conductivity in porous media is analyzed. The nonlinear partial differential equations, governing the flow field under consideration, have been transformed by a similarity transformation into a systemof nonlinear ordinary differential equations and then solved numerically. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters. Finally, the effects of the pertinent parameters, which are of physical and engineering interest, are examined both in graphical and tabular form.     

Heat and mass transfer of MHD convective boundary layer flow past a stretching porous wall embedded in a porous medium

The hydromagnetic convective boundary layer flow past a stretching porous wall embedded in a porous medium with heat and mass transfer in the presence of a heat source and under the influence of a uniform magnetic field is studied. Exact solutions of the basic equations of motion, heat and mass transfer are obtained after reducing them to nonlinear ordinary differential equations. The reduced equations of heat and mass transfer are solved using a confluent hypergeometric function. The effects of the flow parameters such as a suction parameter (N), magnetic parameter (M), permeability parameter (K _p ), wall temperature parameter (r), wall concentration parameter (n), and heat source/sink parameter (Q) on the dynamics are discussed. It is observed that the suction parameter appears in the boundary condition ensuring the variable suction at the surface. Transverse component of the velocity increases only when magnetic field strength exceeds certain value, but the thermal boundary layer thickness and concentration distribution increase for all values. Results presented in this paper are in good agreement with the work of the previous author and also in conformity with the established theory.     

Temperature-Dependent Viscosity Effects on Non-Darcy Hydrodynamic Free Convection Heat Transfer from a Vertical Wedge in Porous Media

An analysis is presented to investigate the effect of temperature-dependent viscosity on free convection flow along a vertical wedge adjacent to a porous medium in the presence of heat generation or absorption. The governing fundamental equations are transformed into the system of ordinary differential equations using scaling group of transformations and are solved numerically by using the fifth-order Rung-Kutta method with shooting technique for various values of the physical parameters. The effects of variable viscosity parameter on the velocity, temperature and concentration are discussed. Numerical results for the problem considered are given and illustrated graphically.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter, thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

Effects of Thermal Radiation on a 3D Sisko Fluid over a Porous Medium Using Cattaneo-Christov Heat Flux Model

This paper investigates the three-dimensional flow of a Sisko fluid over a bidirectional stretching sheet, in a porous medium. By using the effect of Cattaneo-Christov heat flux model, heat transfer analysis is illustrated. Using similarity transformation the governing partial differential equations are transferred into a system of ordinary differential equations that are solved numerically by applying Nachtsheim-Swigert shooting iteration technique along with the 6-th order Runge-Kutta integration scheme. The effect of various physical parameters such as Sisko fluid, ratio parameter,thermal conductivity, porous medium, radiation parameter, Brownian motion, thermophoresis, Prandtl number, and Lewis number are graphically represented.     

Heat Transfer and Entropy in a Vertical Porous Plate Subjected to Suction Velocity and MHD

This article presents an investigation of heat transfer in a porous medium adjacent to a vertical plate. The porous medium is subjected to a magnetohydrodynamic effect and suction velocity. The governing equations are nondepersonalized and converted into ordinary differential equations. The resulting equations are solved with the help of the finite difference method. The impact of various parameters, such as the Prandtl number, Grashof number, permeability parameter, radiation parameter, Eckert number, viscous dissipation parameter, and magnetic parameter, on fluid flow characteristics inside the porous medium is discussed. Entropy generation in the medium is analyzed with respect to various parameters, including the Brinkman number and Reynolds number. It is noted that the velocity profile decreases in magnitude with respect to the Prandtl number, but increases with the radiation parameter. The Eckert number has a marginal effect on the velocity profile. An increased radiation effect leads to a reduced thermal gradient at the hot surface.     

Magnetohydrodynamic and radiation effects on the heat transfer of a continuously stretching/shrinking sheet with mass transpiration of the horizontal boundary

The aim of this paper is the investigation of heat transfer regarding the cases of both stretching and shrinking sheets with a sponge-like horizontal wall that allows for mass transpiration. The effects of Prandtl number, radiation and external magnetic field are extensively examined. The Navier-Stokes equations are reduced to partial differential equations, which are eventually become ordinary differential equations and solved analytically. Furthermore, the power-law wall temperature and heat flux boundary conditions are imposed on the boundary layer energy equation for obtaining exact analytical solutions. The results revealed that in both the stretching and shrinking sheet scenarios the thickness of the thermal boundary layer decreases with either increasing of transpiration as well as the Chandrasekhar and Prandtl number numbers or decreasing radiation number. Additionally, the characteristics of the heat transfer regarding a shrinking sheet and those of a stretching sheet are found not to be similar. In fact, a new solution branch appeared which indicates that multiple solutions may emerge under certain circumstances. Finally, by using the present analytical relationships, theoretical guidelines can be given for regulating the procedure.     

Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition

This paper presents a numerical solution for the steady mixed convection magnetohydrodynamic (MHD) flow of an electrically conducting micropolar fluid over a porous shrinking sheet. The velocity of shrinking sheet and magnetic field are assumed to vary as power functions of the distance from the origin. A convective boundary condition is used rather than the customary conditions for temperature, i.e., constant surface temperature or constant heat flux. With the aid of similarity transformations, the governing partial differential equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically, using the variational finite element method (FEM). The influence of various emerging thermophysical parameters, namely suction parameter, convective heat transfer parameter, magnetic parameter and power index on velocity, microrotation and temperature functions is studied extensively and is shown graphically. Additionally the skin friction and rate of heat transfer, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, have also been computed for these parameters. Under the limiting case an analytical solution of the flow velocity is compared with the present numerical results. An excellent agreement between the two sets of solutions is observed. Also, in order to check the convergence of numerical solution, the calculations are carried out by reducing the mesh size. The present study finds applications in materials processing and demonstrates excellent stability and convergence characteristics for the variational FEM code.     

Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation

An analytical study is presented for the problem of unsteady hydromagnetic heat and mass transfer for a micropolar fluid bounded by semi-infinite vertical permeable plate in the presence of first-order chemical reaction, thermal radiation and heat absorption. A uniform magnetic field acts perpendicularly to the porous surface which absorbs the micropolar fluid with a time-dependent suction velocity. The basic partial differential equations are reduced to a system of nonlinear ordinary differential equations which are solved analytically using perturbation technique. Numerical calculations for the analytical expressions are carried out and the results are shown graphically. The effects of the various dimensionless parameters related to the problem on the velocity, angular velocity, temperature and concentration fields are discussed in detail.     

Effect of radiation and chemical reaction on natural convective MHD flow through a porous medium with double diffusion

The influence of radiation and chemical reaction on a natural convective MHD flow through a porous medium bounded by a vertical infinite surface in the presence of transverse magnetic field is studied. The basic equations governing the flow, heat and mass transfer are reduced to a set of ordinary differential equations by appropriate transformations. Governing equations are solved by perturbation technique for velocity, temperature and concentration, and that has been presented graphically for different values of involved parameters. It is observed that effects of magnetic parameter and radiation parameter in the flow field affect the flow significantly.     

Thermal radiation and slip effects on MHD stagnation point flow of nanofluid over a stretching sheet

Present model is devoted for the stagnation point flow of nanofluid with magneto-hydrodynamics (MHD) and thermal radiation effects passed over a stretching sheet. Moreover, we have considered the combined effects of velocity and thermal slip. Condition of zero normal flux of nanoparticles at the wall for the stretched flow phenomena is yet to be explored in the literature. Convinced partial differential equations of the model are transformed into the system of coupled nonlinear differential equations and then solved numerically. Graphical results are plotted for velocity, temperature and nanoparticle concentration for various values of emerging parameters. Variation of stream lines, skin friction coefficient, local Nusselt and Sherwood number are displayed along with the effective parameters. Final conclusion has been drawn on the basis of both numerical and graphs results.     

Similarity solutions for boundary layer flow and heat transfer of a FENE-P fluid with thermal radiation

This Letter presents a numerical study of the flow and heat transfer of an incompressible FENE-P fluid over a non-isothermal surface. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of the thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient, as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) the sheet with prescribed surface temperature (PST case) and (ii) the sheet with prescribed heat flux (PHF case). Moreover, the mechanical characteristics of the corresponding flow are also presented.     

Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge

The candid intension of this article is to inspect the heat and mass transfer of a magnetohydrodynamic tangent hyperbolic nanofluid. The nanofluid flow has been assumed to be directed by a wedge on its way. In addition, the collective stimulus of the convective heating mode with thermal radiation is inspected. The governing set of PDEs is rendered into that of the coupled nonlinear ODEs. The resulting ordinary differential equations are then solved by the well known shooting technique for two different cases; the flow over a static wedge and flow over a stretching wedge. The impact of intricate physical parameters on the velocity, temperature and concentration profiles is analyzed graphically. It is noticed that the intensifying values of the generalized Biot number, Brownian motion parameter, thermophoresis parameter and Weissenberg number enhances the dimensionless temperature profile.     

MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation

This article numerically examines the boundary layer flow due to an exponentially stretching surface in the presence of an applied magnetic field. Casson fluid model is used to characterize the non-Newtonian fluid behavior. The flow is subjected to suction/blowing at the surface. Analysis is carded out in presence of thermal radiation and prescribed surface heat flux. In this study, an exponential order stretching velocity and prescribed exponential order surface heat flux are accorded with each other. The governing partial differential equations are first converted into nonlinear ordinary differential equations by using appropriate transformations and then solved numerically. The effect of increasing values of the Casson parameter is to suppress the velocity field. However the temperature is enhanced when Casson parameter increases. It is found that the skin-friction coefficient increases with increasing values of suction parameter. Temperature also increases for large values of power index n in both suction and blowing cases at the boundary. It is observed that the thermal radiation enhances the effective thermal diffusivity and hence the temperature rises.