On the convected linear stability of a viscoelastic Oldroyd B fluid heated from below

Abstract

We investigate the linear stability problem of convection by the general Oldroyd B fluid and its Maxwell limit in the presence of rigid or free boundaries and fixed temperature or fixed flux. Comparison with recent results by Rosenblat [9] for the analytically accessible case of free boundary conditions shows a qualitative similarity in the shape of the neutral stability curves. But while Newtonian and Jeffreys (general Oldroyd B) fluids are sharply stabilized by the presence of rigid boundaries, the Maxwell fluid is largely unaffected at even moderately large Prandtl number. The reasons for this are discussed. Also, a discrepancy between the earlier works by Vest and Arpaci [3], and Sokolov and Tanner [4], which treat the case of a Maxwell fluid, is found to be due to algebraic error, and not multivaluedness of the stress-strain rate relation as earlier suggested by Eltayeb [6].