Linear Double Diffusive Convection In a Micropolar Liquid Occupying a Rectangular Box

Abstract

This paper is a Fourier-series assisted analytical study of two-dimensional steady finite amplitude double diffusive convection in micropolar liquids occupying a rectangular box. The horizontal walls of the cavity are uniformly heated and salted to establish linear temperature and concentration distributions in the vertical direction. The vertical walls are insulated and impermeable. The expression for the critical Rayleigh number is obtained in closed form as a function of aspect ratio, solutal Rayleigh number, micropolar liquids parameters and diffusivity ratio. The results of slender vertical, square and shallow boxes are obtained as limiting cases of the present study.