Effect of side wall conditions and aspect ratio on convective pattern formation in Rayleigh-Benard convection

Abstract

Effect of side wall boundary conditions and aspect ratio in very small boxes on patterns formed during Raleigh-Benard (RB) convection is studied using an indigenously developed flow solver based on the finite difference method. While keeping the bottom (hot) and top (cold) walls isothermal, the side wall thermal conditions are kept either constant heat flux or isothermal type. For constant heat flux side wall condition, the considered value of heat flux lies between 0 and maximum corresponding to conductive heat flux between top and bottom walls. For isothermal side wall condition, the chosen value of temperature is between the top and bottom wall temperatures. The computational domain is a cube or a square prism with aspect ratio in longitudinal direction (ARx) varied between 1.2 and 2 in steps of 0.2. For fixed value of ARx = 1.6, aspect ratio in transverse direction (ARz) has been varied for adiabatic side wall conditions. Effect of side wall condition on orientation of roll axis and the number of rolls has been investigated with observations well supported by stream traces and temperature contours. Moreover, for selected parameters, based on nature of pattern formation for steady flow, onset of oscillatory convection is explained.