MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip

In this paper we analyze the flow and heat transfer of an MHD fluid over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip. The governing partial differential equations of the problem are reduced to nonlinear ordinary differential equations by using a similarity transformation. The temperature boundary conditions are assumed to be linear functions of the distance from the origin. Analytical solutions of the energy equations for Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) cases are obtained in terms of a hypergeometric function, without applying the boundary-layer approximation. The effects of the governing parameters on the flow and heat transfer fields are presented through tables and graphs, and they are discussed. Furthermore, the obtained numerical results for the skin friction, wall-temperature gradient and wall temperature are analyzed and compared with the available results in the literature for special cases.     

Bio-fluid flow analysis based on heat transfer and variable viscosity

This study investigates the cilia transport phenomenon from the perspectives of the heat transfer and variable viscosity in a bending channel. The rightward wall is maintained at a temperature of T_0, and the leftward wall has a temperature of T_1. Each wall has a metachronal wave that travels along its wall. The structures of the ciliary assemblies are calculated by the well-known simplifying suppositions of the large wavelength and the small Reynolds number approximation. The flow phenomenon for the Newtonian fluid is described as a function of cilia and a metachronal wave velocity. The pressure rise is calculated with MATHEMATICA. The theme of the cilia beating flow is inspected with scheming plots, and its features are discussed at the end of the article.     

Boundary layer flow and heat transfer past a stretching plate with variable thermal conductivity

In the present paper, the boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the components of velocity have been obtained. Then, the heat flow problem has been considered in two ways: (i) prescribed surface temperature (PST), and (ii) prescribed stretching plate heat flux (PHF) in case of variable thermal conductivity. Due to variable thermal conductivity, temperature profile has its two part—one mean temperature and other temperature profile induced due to variable thermal conductivity. The related results have been discussed with the help of graphs.     

Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation

The flow and heat transfer of a non-Newtonian power-law fluid over a non-linearly stretching surface has been studied numerically under conditions of constant heat flux and thermal radiation and evaluated for the effect of wall slip. The governing partial differential equations are transformed into a set of coupled non-linear ordinary differential equations which are using appropriate boundary conditions for various physical parameters. The remaining set of ordinary differential equations is solved numerically by fourth-order Runge–Kutta method using the shooting technique. The effects of the viscosity, the slip velocity, the radiation parameter, power-law index, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin friction and Nusselt numbers are presented. Comparison of numerical results is made with the earlier published results under limiting cases.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness,variable thermal conductivity,and thermal radiation

This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations （PDEs） are transformed into a system of coupled non-linear ordinary differential equations （ODEs） with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method （DTM）. The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.     

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic (MHD) flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and Al₂O₃, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions are derived by the homotopy analysis method (HAM). The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.     

Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity

This paper deals with the study of boundary layer flow and heat transfer of a visco-elastic fluid immersed in a porous medium over a non-isothermal stretching sheet. The fluid viscosity is assumed to vary as a function of temperature. The presence of variable viscosity of the fluid leads to the coupling and the non-linearity in the boundary value problem. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge-Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. An analysis has been carried out for two different cases namely (1) prescribed surface temperature (PST), and (2) prescribed heat flux (PHF), to get the effect of fluid viscosity, permeability parameter and visco-elastic parameter for various situations. The important finding of our study is that the effect of fluid viscosity parameter is to decrease the wall temperature profile significantly when flow is through a porous medium. Further, the effect of permeability parameter is to decrease the skin friction on the sheet.     

Simultaneous radiative and convective heat transfer in a variable porosity medium

 The flow of an incompressible grey fluid through a horizontal channel filled with a saturated medium of variable viscosity has been considered in this paper. Such flows in porous media have several applications in industrial processes. For the radiative effects a two flux model has been used in order to simplify the governing integro-differential equations for which closed-form solutions are not obtainable. The problem has been solved by employing a highly successful tri-diagonal, implicit, iterative, finite difference method. The effects of the pertinent parameters on the velocity and temperature distributions have been shown in several figures. Received on 6 December 1999     

Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ _r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.     

Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation

The aim of the present paper is to study flow and heat transfer characteristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The resulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are made, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.     

Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions

The effect of flow slip on the nanofluid boundary layer over a stretching surface is studied. The present results provide a basic understanding on the effects of the slip boundary condition on heat and mass transfer of nanofluids past stretching sheets subject to a convective boundary condition from below. The results show that an increase of thermophoresis parameter or slip factor would decrease the reduced Nusselt number in some cases.     

Free convection effects on a vertical cone with variable viscosity and thermal conductivity

The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank–Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.     

Effect of temperature dependent viscosity on revolving axi-symmetric ferrofluid flow with heat transfer

The prime objective of the present study is to examine the effect of temperature dependent viscosity μ(T) on the revolving axi-symmetric laminar boundary layer flow of an incompressible, electrically non-conducting ferrofluid in the presence of a stationary plate subjected to a magnetic field and maintained at a uniform temperature. To serve this purpose, the non-linear coupled partial differential equations are firstly converted into the ordinary differential equations using well-known similarity transformations. The popular finite difference method is employed to discretize the non-linear coupled differential equations. These discretized equations are then solved using the Newton method in MATLAB, for which an initial guess is made with the help of the Flex PDE Solver. Along with the velocity profiles, the effects of temperature dependent viscosity are also examined on the skin friction, the heat transfer, and the boundary layer displacement thickness. The obtained results are presented numerically as well as graphically.     

Effects of thermal buoyancy and variable thermal conductivity on the MHD flow and heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a non-uniform heat source

The paper considers the flow of a power-law fluid past a vertical stretching sheet. Effects of variable thermal conductivity and non-uniform heat source/sink on the heat transfer are addressed. The thermal conductivity is assumed to vary linearly with temperature. Similarity transformation is used to convert the governing partial differential equations into a set of coupled, non-linear ordinary differential equations. Two different types of boundary heating are considered, namely Prescribed power-law Surface Temperature (PST) and Prescribed power-law Heat Flux (PHF). Shooting method is used to obtain the numerical solution for the resulting boundary value problems. The effects of Chandrasekhar number, Grashof number, Prandtl number, non-uniform heat source/sink parameters, wall temperature parameter and variable thermal conductivity parameter on the dynamics are shown graphically in several plots. The skin friction and heat transfer coefficients are tabulated for a range of values of the parameters. Present study reveals that in a gravity affected flow buoyancy effect has a significant say in the control of flow and heat transfer.     

Asymptotic analysis of convective flows in a rotating spheroid for vanishing viscosity and thermal conductivity

The six-dimensional model of viscous fluid thermal convection in a uniformly rotating ellipsoid [1] is studied. The limiting case in which the viscosity and thermal conductivity approach zero while the Prandtl number Pr remains finite is considered. Using both asymptotic and numerical methods, it is shown that for Pr > 2 the attractor is a two-dimensional invariant torus or a limit cycle; the corresponding convective flows are either quasiperiodic, with two basic frequencies, or periodic. It is also shown that resonances on the torus play a dominant role in the breakdown of two-dimensional toruses with increasing viscosity and thermal conductivity.Rostov-on-Don. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 35–38, September–October, 1995.     

Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction

An analysis is presented to investigate the effects of thermophoresis and variable viscosity on MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform porous medium in order to allow for possible fluid wall suction or injection. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the R.K. Gill and shooting methods. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.