Pattern Selection in Double-Diffusive Ferro-Convection

Pattern formation due to double-diffusive convection in ferrofluids is investigated in the presence of an externally applied transverse magnetic field. The critical value of the Rayleigh number R for steady state bifurcation is found to be different from that for Hopf bifurcation in contrast to ordinary fluids where the two critical values are the same. The stability of steady state patterns}rolls, squares, and hexagons}has been discussed. For magnetic fluids, the rolls are found to be structurally stable on the square lattice, whereas on the hexagon lattice bifurcation may lead to either rolls or hexagons depending upon the value of the nondimensional magnetic parameter M.