Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters.
Bhatta, Dambaru, "Linear Stability Analysis with Solution Patterns due to Varying Thermal Diffusivity for a Convective Flow in a Porous Medium" (2018). Mathematical and Statistical Sciences Faculty Publications and Presentations. 63.
Applications & Applied Mathematics