Effects of rotation and temperature-dependent viscosity on thermal convection in Oldroydian fluid saturating porous media: A modified stability analysis

The onset of thermal convection in an incompressible Oldroydian fluid-saturating porous media is examined to study the combined impact of uniform rotation and temperature-dependent viscosity. A characteristic equation from the basic hydrodynamic equations governing the Brinkman–Oldroyd model is derived using linear stability theory and modified Boussinesq approximation. For various combinations of stress-free and slip-free boundaries, the expressions for the Darcy–Rayleigh numbers for both non-oscillatory as well as oscillatory convection with linear and exponential temperature-dependent viscosity are derived, using the “weighted residual method.” The effects of rotation, variable viscosity parameter, strain retardation and stress relaxation time parameters and other fluid parameters on non-oscillatory and oscillatory convection are investigated numerically and the results are presented graphically. From the analysis, it is found that overstability is the preferred mode of onset of convection. The rotation, the coefficient of specific heat variations (due to temperature variation), and the strain retardation time have a stabilizing influence on the stability of the system, whereas the stress relaxation imparts a destabilizing effect. Additionally, it is noticed that the variable viscosity parameter and Brinkman-Darcy number stabilize the system for each set of boundary conditions.