Slip flow and heat transfer of nanofluids over a porous plate embedded in a porous medium with temperature dependent viscosity and thermal conductivity

It is well known that the best way of convective heat transfer is the flow of nanofluids through a porous medium. In this regard, a mathematical model is presented to study the effects of variable viscosity, thermal conductivity and slip conditions on the steady flow and heat transfer of nanofluids over a porous plate embedded in a porous medium. The nanofluid viscosity and thermal conductivity are assumed to be linear functions of temperature, and the wall slip conditions are employed in terms of shear stress. The similarity transformation technique is used to reduce the governing system of partial differential equations to a system of nonlinear ordinary differential equations (ODEs). The resulting system of ODEs is then solved numerically using the shooting technique. The numerical values obtained for the velocity and temperature profiles, skin friction coefficient and Nusselt's number are presented and discussed through graphs and tables. It is shown that the increase in the permeability of the porous medium, the viscosity of the nanofluid and the velocity slip parameter decrease the momentum and thermal boundary layer thickness and eventually increase the rate of heat transfer.