Marangoni Convection in a Fluid Saturated Porous Layer with a Prescribed Heat Flux at its Lower Boundary

Abstract

The onset of Marangoni convection in a horizontal porous layer heated from below with a constant heat flux is investigated. The Brinkman model is used and the Darcy law is employed to describe the flow in the porous medium heated from below. We obtain for the first time the closed form analytical solution for the onset of steady Marangoni convection in a fluid saturated porous layer with a prescribed heat flux at its lower boundary. Besides, the asymptotic solution of the long-wavelength is also obtained using regular perturbation technique with wave number as a perturbation parameter. The Marangoni numbers are found to depend on the Darcy number and Biot number. Predictions for the onset of convection are studied in detail.