Buoyancy Driven Instability Due to Internal Heat Sources in a Horizontal Layer of Binary Fluid Mixture

Abstract

This paper is concerned with the problem of the onset of buoyancy driven instability in a horizontal layer of binary fluid mixture which is heated internally by a uniform distribution of heat sources. The layer is bounded below by a thermal insulator and above by a rigid wall of constant temperature. Linear stability theory is applied to derive an eigenvalue system of eighth order which is then solved by the power series method. In order to reduce the amount of numerical work, Galerkin's method is also used. For wide ranges of various parameters, the conditions under which instability sets in are determined in detail.