On the stability of thermally driven shear flow of an Oldroyd-B fluid heated from below

The linear stability analysis of convection for Oldroyd-B fluid, in a shallow horizontal layer, with applied temperature gradient inclined to the vertical is presented. The flow is driven by a horizontal temperature gradient and the horizontal boundaries are taken to be rigid conducting. The eigenvalue problem is solved by the Chebyshev Tau–QZ method and results are presented in terms of horizontal and vertical Rayleigh numbers. It is found that consideration of lateral heating induces instabilities both in stationary and oscillatory rolls and also both as transverse and longitudinal modes and that presence of elasticity, in general, accelerates the destabilization.