Effect of Oldroyd-B fluid on thermal convection stability in a bidispersive porous media with relatively large macropores

Abstract

This study investigates the effect of Oldroyd-B fluids on the thermal convection instability in a bi-disperse porous medium with relatively large macropores. The modified momentum equation of Oldroyd-B fluid in the macro- and micropores is first derived, assuming local thermal equilibrium. The Orr–Sommerfeld (O–S) equation is derived using the new modified incompressible Navier–Stokes equations of Oldroyd-B fluid. The Chebyshev collocation method is employed to solve the generalized eigenvalue problem, and the neutral stability curves and temporal growth rates are obtained. The results demonstrate that the relaxation time enhances the convective instability, while the retardation time suppresses it. Furthermore, the effect of relaxation time is generally small for smaller wave number, but the effect of relaxation time is significant for large wave number, and this effect becomes accentuated as the wave number increases. The retardation time does not have any influence when the wavenumber is small, and the influence of retardation time becomes small with the large relaxation time. Moreover, the convection instability is enhanced with the higher micropermeability and a higher ratio of momentum transfer coefficient between the macro- and microphases will suppress the instability.