Nonlinear Convection in a Horizontal Layer with an Internal Heat Source

Abstract

The problem of thermal convection is studied in a horizontal layer of fluid with an internal heat source which is restricted to vary linearly with the vertical variable. Square and hexagonal cells are found to be the only possible stable convection cells. Finite amplitude instability can occur for a range of the amplitude of convection. The presence of internal heating is found to be able to affect strongly the cell’s size, the critical Rayleigh number, the heat transported by convection, the stability of the convective motion and the internal motion of the hexagonal cells.