The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below

Abstract

The effect of microstructure on the thermal convection in a rectangular box of fluid heated from below has been investigated by applying the micropolar fluid theory. The influence of lateral walls on the convection process in a rectangular box has been determined. The Galerkin method has been employed to get an approximate solution for the eigenvalue problem. The beam functions which satisfy two boundary conditions on each rigid surface have been used to construct the finite roll (cells with two nonzero velocity components depend on all three spatial variables) trial functions for the Galerkin method. The effect of variations of material parameters at the onset of convection has been presented graphically. It is observed that as the distance between the lateral walls increases the effect of one of the material parameters, characterizing the spin-gradient viscosity, at the onset of stability diminishes. A comparison has been made with the corresponding results for a Newtonian fluid.