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

Abstract

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.

Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties

“…However, it is well known that these properties may change with temperature, especially the thermal conductivity. Available literature on variable thermal conductivity [27][28][29][30][31] shows that the combined effects of variable thermal conductivity and thermal buoyancy has not been investigated for unsteady fluid flow and heat transfer over a porous stretching sheet.…”

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

“…The discussion on the new boundary condition ð1 þ eTðX; 0ÞÞ @T @Y ðX; 0Þ ¼ À1 arising due to variable thermal conductivity is given in Abel et al [2]. It is appropriate to mention here that T(X, 0) as seen in condition (13) (i.e., the thermal boundary condition in case of PHF) was inadvertently missed, while typing, in the paper by Abel et al [2].…”

“…It is appropriate to mention here that T(X, 0) as seen in condition (13) (i.e., the thermal boundary condition in case of PHF) was inadvertently missed, while typing, in the paper by Abel et al [2].…”

“…The stretching sheet problem involving a micropolar liquid is one of those problems in this class of formidable problems. The problem is a prototype of many practical problems like polymer-extrusion processes and such others (see [40,[1][2][3] and the references therein). In the problem a micropolar liquid is representative of the cooling liquid surrounding the stretching sheet that serves the purpose of a controlled cooling system in the presence of a magnetic field.…”

“…Generally the appropriate Maxwell equations are in this case combined into a single equation known as the magnetic induction equation. The Hartmann formulation is used when the liquid has weak electrical conductivity and in this case the Lorentz force gives rise to a linear drag similar to Darcy friction seen in porous media (see [40,2,3]). …”