Convective Heat Transport in a Heat Generating Porous Layer Saturated by a Non-Newtonian Nanofluid

In this paper, the effect of temperature dependent internal source on the onset of convection and on the heat transfer in a porous layer saturated by a non-Newtonian nanofluid is examined. The Oldroyd-B type model incorporates the effects of Brownian motion and thermophoresis is used for the non-Newtonian nanofluid, while Darcy model is employed for porous medium. The flux of volumetric fraction of nanoparticles is considered to be zero on the boundaries. Linear and nonlinear stability analyses are used to examine onset and heat transfer in the system. The linear stability analysis is studied with the help of normal mode technique, and the nonlinear stability analysis is made using truncated representation of Fourier series. The effects of the internal heat source parameter, the stress relaxation parameter, the strain retardation parameter, the heat capacity ratio, and the nanoparticle parameters on the onset of convection and on the heat transfer are obtained and depicted graphically. It is observed that the effects of increasing internal heat source parameter, the stress relaxation parameter, and the nanoparticles parameters have a destabilizing effect on the stability of the system and also increase the heat transfer across the porous layer, whereas an opposite trend is noticed with increasing the strain retardation parameter and the heat capacity ratio.