An Analytical Study of Weakly Nonlinear Convection in a Horizontal Mushy Layer

Abstract: The present analytical study deals with the problem of weakly nonlinear convective instability in a horizontal mushy layer under suitable assumptions and approximations. By applying a modified perturbation technique, the basic state solutions, solutions to the first and the second orders are determined. The influence of the governing parameters on the profiles of total Rayleigh number, velocity and local solid-fraction are studied. The computations are done for a feasible set of values of the parameters. An excellent correlation is obtained between the present and the available results for the limiting cases