Stability of transient natural convection in impulsively heated inclined fluid layer

Abstract

The stability of the transient state of convection in an inclined fluid layer on heating one of the boundaries impulsively has been discussed. The closed form time dependent basic solutions for the velocity and the temperature are obtained. The non-linear stability of the transient state is investigated by using the energy method. The stability limit for the Rayleigh number Ra is found at different times. The competition between the buoyancy and the shear forces determines a value of the angle of inclination corresponding to which the layer is the least stable. The effect of the Prandtl number Pr on the stability boundary is investigated.