On the thermal and hydrodynamic stability of a fluid in a vertical slot

This investigation is devoted to studying the thermal and hydrodynamic stability of the conduction regime of natural convection of a fluid with a nonlinear density temperature relationship in a slender slot with different, but constant, temperature walls. Linear perturbation techniques are applied for the transverse two dimensional disturbances to derive a set of two coupled twelfth order partial differential equations; the Galerkin method was used to solve the eigenvalue problem. The results of this analysis indicate that this flow is much more susceptible to thermal stability than to hydrodynamic stability for Prandtl number, Pr greater than 3.2. On the other hand for Pr less than 3.2 the reverse is true. Furthermore, both shear and bouyant mode characteristics are determined for a wide range of Pr.