Numerical Study of Thermal Convection in Boussinesq-Stokes Suspension Occupying a Rectangular Box

This paper is a Fourier–series assisted numerical study of two-dimensional thermal convection in Boussinesq–Stokes suspensions occupying a cavity. The suspension is modeled as a couple stress liquid. The horizontal walls of the cavity are assumed to be perfectly heat conducting and the vertical walls are non-uniformly heated to establish a linear temperature in the vertical direction. The critical Rayleigh number is obtained numerically as a function of couple stress parameter and aspect ratio, and the same is plotted graphically. The results of slender vertical cavity, classical Rayleigh-Be´nard convection, rectangular and square cavities of finite aspect-ratio heated from below are obtained as limiting cases of the study.