Stability of a fluid-saturated porous medium heated from below by forced convection

Abstract

A linear stability analysis determining the onset of convection in a bounded rectangular cavity containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top wall, and bottom wall heated by forced convection. The nature of the bottom wall heating necessarily involves the Biot number, Bi. Numerical calculations of the critical Rayleigh number, R c made over the range of Biot numbers 10 −4⩽ Bi⩽10 4 for cavity aspect ratios 0⩽( a, b)⩽5 cover all effective bottom heating conditions from the constant heat flux global limit, R c=27.096 found as Bi→0 to the isothermal global limit, R c=4 π 2 found as Bi→∞. Marginal stability boundaries, preferred cellular modes and disturbance temperature contours are displayed graphically.