Combined impact of variable internal heat source and variable viscosity on the onset of convective motion in a porous layer

Abstract

The qualitative effect of variable internal heat source and temperature dependence of fluid viscosity on the onset of convection in a horizontal fluid saturated porous layer is investigated using linear stability analysis. The temperature-dependence of viscosity is considered to be exponential. A parametric study is performed out by varying the following parameters: viscosity parameter \((\mathrm{B})\) and internal heat source parameter \((N s)\). We addressed four cases of variance in the internal heat source : (i) \(N(z)=z\), (ii) \(N(z)=z^2\), (iii) \(N(z)=z^3\) and (iv) \(N(z)=e^z\). Results indicate that for both parameters of the factor viscosity and heat source variance are to delay the beginning of convective moment. It seen that the system is to be more unstable for case (iii), while more stable for case (iv).