THERMAL DIFFUSIVITY VARIATION EFFECT ON A HYDRO-THERMAL CONVECTIVE FLOW IN A POROUS MEDIUM

Abstract

We consider a hydrothermal convective flow in a porous medium to investigate the effect of the vertical rate of change in thermal diffusivity. Using a weakly nonlinear approach, we derive the linear and first-order systems assuming a no-flow basic state system. The solutions for the linear and first-order systems are computed numerically using both the fourth-order Runge-Kutta and shooting methods. Numerical results obtained in this study show a stabilizing effect on the dependent variables for the case of a positive vertical rate of change in diffusivity, whereas a destabilizing effect is noticed for the case of a negative vertical rate of change in diffusivity. The present results indicate that convective flow driven by the buoyancy force is more effective if thermal diffusivity is weaker, while the opposite result holds for a stronger diffusivity effect. In particular, both velocity and convective temperature decrease with increasing diffusivity, while they increase with decreasing diffusivity. At the middle of the layer (z = 0) for x = 0, the contribution of the linear and first-order solutions to the velocity component are 0.3345, 0.3031, and 0.3679 for the respective values 0.0, 0.6, and -0.4 of the diffusivity parameter. For temperature, these contributions are 0.0167, 0.0116, and 0.0229, respectively. Some other quantitative results are provided in tabular form.