MHD non-Darcian mixed convection heat and mass transfer over a non-linear stretching sheet with Soret-Dufour effects and chemical reaction

A study has been carried out to analyze the effects of variable thermal conductivity, Soret (thermal-diffusion) and Dufour (diffusion-thermo) on MHD non-Darcy mixed convection heat and mass transfer over a non-linear stretching sheet embedded in a saturated porous medium in the presence of thermal radiation, viscous dissipation, non-uniform heat source/sink and first-order chemical reaction. The governing differential equations transform into a set of non-linear coupled ordinary differential equations using similarity analysis. Similarity equations are then solved numerically using shooting algorithm with Runge-Kutta Fehlberg integration scheme over the entire range of physical parameters. A comparison with previously published work has been carried out and the results are found to be in good agreement. Graphical presentation of the local skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the temperature profiles show interesting features of the physical parameters.     

Chemical reaction,heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects

An analysis has been carried out to obtain the nonlinear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Boussinesq fluid on a vertical stretching surface with chemical reaction and thermal stratification effects. An approximate numerical solution for the flow problem has been obtained by solving the governing equations using numerical technique. A magnetic field is applied transversely to the direction of the flow. Adopting the similarity transformation, governing nonlinear partial differential equations of the problem are transformed to nonlinear ordinary differential equations. Then the numerical solution of the problem is derived using Gill method, for different values of the dimensionless parameters. The results obtained show that the flow field is influenced appreciably by the presence of thermal stratification, chemical reaction and magnetic field.     

MHD boundary‐layer flow over a stretching surface with internal heat generation or absorption

This article is concerned with the steady laminar magnetohydrodynamic boundary‐layer flow past a stretching surface with uniform free stream and internal heat generation or absorption in an electrically conducting fluid. A constant magnetic field is applied in the transverse direction. A uniform free stream of constant velocity and temperature is passed over the sheet. The effects of free convection and internal heat generation or absorption are also considered. The governing boundary layer and temperature equations for this problem are first transformed into a system of ordinary differential equations using similarity variables, and then solved by a new analytical method and numerical method, by using a fourth‐order Runge–Kutta and shooting method. Velocity and temperature profiles are shown graphically. It is shown that the differential transform method solutions are only valid for small values of independent variables but the results obtained by the DTM‐Padé are valid for the entire solution domain with high accuracy. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21054     

Unsteady MHD flow and heat transfer with viscous dissipation past a stretching sheet

In this paper a study is carried out to analyze the unsteady heat transfer effects of viscous dissipation on the steady boundary layer flow past a stretching sheet with prescribed constant surface temperature in the presence of a transverse magnetic field. The sheet is assumed to stretch linearly along the direction of the fluid flow. The assumed initial steady flow and temperature field neglecting dissipation effects becomes transient by accounting dissipation effects when time t′ > 0. The temperature and the Nusselt number are computed numerically using an implicit finite difference method. The obtained steady temperature field with dissipation is of practical importance.     

Unsteady boundary-layer flow and heat transfer of a nanofluid over a permeable stretching/shrinking sheet

The unsteady boundary layer flow of a nanofluid over a permeable stretching/shrinking sheet is theoretically studied. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. The results are obtained for the skin friction coefficient, the local Nusselt number and the local Sherwood number as well as the velocity, temperature and the nanoparticle fraction profiles for some values of the governing parameters, namely, the unsteadiness parameter, the mass suction parameter, the Brownian motion parameter, the thermophoresis parameter, Prandtl number, Lewis number and the stretching/shrinking parameter. It is found that dual solutions exist for both stretching and shrinking cases. The results also indicate that both unsteadiness and mass suction widen the range of the stretching/shrinking parameter for which the solution exists.     

Flow and heat transfer over an unsteady stretching surface with non-uniform heat source

The non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity is studied. The boundary layer equations are transformed by using similarity analysis to be a set of ordinary differential equations containing three parameters: unsteadiness parameter (S), space-dependent parameter (A?) and temperature-dependent parameter (B?) for heat source/sink. The velocity and temperature fields are solved using the Chebyshev finite difference method (ChFD). Results showed that the heat transfer rate, − θ′(0) and the skin friction, − f″(0) increase as the unsteadiness parameter increases whereas decrease as the space-dependent and temperature-dependent parameters for heat source/sink increase.     

Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet

This paper investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics in the presence of a uniform applied magnetic field. The boundary layer flow of a third-order fluid is induced due to linear stretching of a non-conducting sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is discussed. Velocity and temperature distributions are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Emphasis has been given to the variations of the emerging parameters such as third-order parameter, magnetic parameter, Prandtl number and the Eckert number. It is noted that the skin friction coefficient decreases as the magnetic parameter or the third grade parameter increases.     

Slip flow and heat transfer in microbearings with fractal surface topographies

The effects of random surface roughness on slip flow and heat transfer in microbearings are investigated. A three-dimensional random surface roughness model characterized by fractal geometry is used to describe the multiscale self-affine roughness, which is represented by the modified two-variable Weierstrass–Mandelbrot (W–M) functions, at micro-scale. Based on this fractal characterization, the roles of rarefaction and roughness on the thermal and flow properties in microbearings are predicted and evaluated using numerical analyses and simulations. The results show that the boundary conditions of velocity slip and temperature jump depend not only on the Knudsen number but also on the surface roughness. It is found that the effects of the gas rarefaction and surface roughness on flow behavior and heat transfer in the microbearing are strongly coupled. The negative influence of roughness on heat transfer found to be the Nusselt number reduction. In addition, the effects of temperature difference and relative roughness on the heat transfer in the bearing are also analyzed and discussed.     

Heat and mass transfer of thermophoretic MHD flow over an inclined radiate isothermal permeable surface in the presence of heat source/sink

In this paper, a free convection thermophoretic hydromagnetic flow over a radiate isothermal inclined plate with heat source/sink effect is considered. The shooting method is employed to yield the numerical solutions for the model. The effects of thermophoretic parameter and internal heat generation/absorption for both suction and injection cases are discussed and presented graphically. The values of skin friction, wall heat flux and wall deposition flux are also tabulated with the variation of thermophoresis, heat source/sink and suction/injection parameters.     

Three-dimensional viscous flow and heat transfer over a permeable shrinking sheet

This paper presents a numerical analysis of a steady three-dimensional fluid flow and heat transfer towards a permeable shrinking sheet. The governing nonlinear partial differential equations are transformed into a system of ordinary differential equations by a similarity transformation, which are then solved numerically by a shooting method. The effects of the governing parameters on the skin friction and heat transfer from the surface of the shrinking surface are illustrated graphically. It is found that dual solutions exist for the shrinking case. A comparison with known results from the open literature has been done and it is shown to be in excellent agreement.     

Viscoelastic boundary layer flow and heat transfer over an exponential stretching sheet

Viscoelastic boundary layer flow and heat transfer over an exponential stretching continuous sheet have been examined in this paper. Approximate analytical similarity solution of the highly non-linear momentum equation and confluent hypergeometric similarity solution of the heat transfer equation are obtained. Accuracy of the analytical solution for stream function is verified by numerical solutions obtained by employing Runge-Kutta fourth order method with shooting. These solutions involve an exponential dependent of stretching velocity, prescribed boundary temperature and prescribed boundary heat flux on the flow directional coordinate. The effects of various physical parameters like viscoelastic parameter, Prandtl number, Reynolds number, Nusselt number and Eckert number on various momentum and heat transfer characteristics are discussed in detail in this work.     

MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with non-uniform source/sink

The analysis includes a steady two-dimensional MHD flow of a dusty fluid near the stagnation point over a permeable stretching sheet with the effect of non-uniform source/sink. Two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The governing system of non-linear partial differential equations are transformed into ordinary differential equations using similarity transformations and which are then solved numerically using Runge Kutta Fehlberg fourth–fifth order method. Comparison of the numerical results is made with the existing literature and the results are found to be in good agreement. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed. It is found that velocity distribution for clean fluid decreases where as dust fluid increases with the increase of fluid particle interaction parameter when λ > 1 and λ < 1.     

Radiation effect on the flow and heat transfer over an unsteady stretching sheet

The effect of radiation on the heat and fluid flow over an unsteady stretching surface is analyzed. Using a similarity transformation the governing time dependent boundary layer equations for momentum and thermal energy are reduced to a set of ordinary differential equations. The resulting three-parameter problem is solved numerically for some representative values of the unsteadiness parameter A, the radiation parameter R and Prandtl number Pr. It is shown that the heat transfer rate is increased with increasing R, A and Pr. Also the effect of radiation parameter on the heat transfer rate is found to be more noticeable at larger values of A and Pr.     

Non-orthogonal stagnation-point flow towards a stretching surface in a non-Newtonian fluid with heat transfer

In the past, considerable attention has been given to the study of stagnation-point flows since they appear in many engineering and industrial applications. In some problems, flow is stagnated by a solid wall, while in others a free stagnation-point or line exists interior to the fluid domain. In this paper, the steady two-dimensional stagnation-point flow of a viscoelastic second-grade fluid over a stretching surface with heat transfer is examined. It is assumed that the fluid impinges on the wall obliquely. Using similarity variables, the governing partial differential equations are transformed into a set of three non-dimensional ordinary differential equations. These equations are then solved numerically using a quasi-linearization technique. It is shown that a boundary layer is formed when the stretching velocity of the surface is less that the inviscid free-stream velocity and velocity at a point increases with the increase in the elasticity of the fluid. It is also found that the temperature at a point decreases with increase in the elasticity of the fluid. The reported results are in good agreement with the available published work in the literature.     

Influence of chemical reaction and thermal radiation on the heat and mass transfer in MHD micropolar flow over a vertical moving porous plate in a porous medium with heat generation

An analysis is presented for the effects of chemical reaction and thermal radiation on hydromagnetic free convection heat and mass transfer for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of heat generation. The plate moves with a constant velocity in the longitudinal direction and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Analytical expressions are computed numerically. Numerical calculations are carried out the purpose of the discussion of the results which are shown on graphs and the effects of the various dimensionless parameters entering into the problem on the velocity, angular velocity, temperature, concentration. Also, the results of the skin-friction coefficient, the couple stress coefficient and the rates of the heat and mass transfers at the wall are prepared with various values of fluid properties and the flow conditions are studied.     

Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

The article examines the hydromagnetic laminar boundary layer flow and heat transfer in a power law fluid over a stretching surface. The flow is influenced by linear stretching of the sheet. Also the energy equation with temperature-dependent thermal conductivity, thermal radiation, work done by stress, viscous dissipation and internal heat generation is considered. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by Keller–Box method. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.     

Analytic solution of generalized three-dimensional flow and heat transfer over a stretching plane wall

This communication aims to investigate the incompressible generalized three-dimensional viscous flow with heat transfer analysis in the presence of viscous dissipation. The flow is generated due to uniform stretching of the plane wall. Complete analytic solutions for velocity and temperature are obtained by homotopy analysis method (HAM). Graphs are plotted to discuss the effects of different parameters.     

MHD flow and heat transfer in a backward-facing step

The laminar flow of a viscous incompressible electrically conducting fluid in a backward-facing step is investigated under the usual magnetohydrodynamic (MHD) hypothesis. Numerical simulations are performed for Reynolds numbers less then Re = 380 in the range of 0 ≤ N ≤ 0.2, where N is the Stuart number or interaction parameter which is the ratio of electromagnetic force to inertia force. Heat transfer is investigated for Prandtl number ranging from Pr = 0.02 corresponding to liquid metal, to Pr = 7 corresponding to water. It is found through the calculation of the reattachment length that external magnetic field acts to decrease the size of the recirculation zone. Velocity profiles show that, out of the recirculation zone, the basic flow is damped by the magnetic induced force, whereas flow near the walls channel is accelerated. Heat transfer is significantly enhanced by the magnetic field in the case of fluids of high Prandtl numbers.     

Effect of thermal radiation on unsteady mixed convection flow and heat transfer over a porous stretching surface in porous medium

An analysis is performed to investigate the effects of thermal radiation on unsteady boundary layer mixed convection heat transfer problem from a vertical porous stretching surface embedded in porous medium. The fluid is assumed to be viscous and incompressible. Numerical computations are carried out for different values of the parameters involved in this study and the analysis of the results obtained shows that the flow field is influenced appreciably by the unsteadiness parameter, mixed convection parameter, parameter of the porous medium and thermal radiation and suction at wall surface. With increasing values of the unsteadiness parameter, fluid velocity and temperature are found to decrease in both cases of porous and non-porous media. Fluid velocity decreases due to increasing values of the parameter of the porous medium resulting an increase in the temperature field in steady as well as unsteady case.