Oscillatory Convection in Oldroyd‐B Fluid‐Saturated Porous Layers Under Variable Gravity and Temperature‐Dependent Internal Heating

ABSTRACT The present study investigates the onset of oscillatory convection in a porous layer saturated with an Oldroyd‐B viscoelastic fluid under non‐uniform gravitational fields and temperature‐dependent internal heat generation. A linear stability analysis is performed by considering three distinct gravity profiles—linear, parabolic, and exponential—and the Galerkin method is applied to determine the critical conditions corresponding to both stationary and oscillatory modes of convection. These results show that temperature‐dependent internal heat generation increases the critical Rayleigh number, thereby stabilizing the system by requiring stronger buoyancy forces to initiate motion. Viscoelastic effects exhibit a dual nature: the ratio of retardation to relaxation time enhances elastic resistance and stabilizes the flow, whereas the stress‐relaxation parameter weakens elasticity, promoting oscillatory instability. An increase in the Prandtl number elevates the oscillatory Rayleigh threshold, indicating enhanced damping of convective motion. The variable gravity parameter further strengthens buoyancy resistance and delays the onset of convection, with exponential gravity producing the highest stabilization, linear gravity showing moderate resistance, and parabolic gravity acting as the most destabilizing profile. These findings provide deeper physical insight into the interplay between thermal, elastic, and gravitational effects in thermoviscoelastic convection, with potential relevance to geothermal energy extraction, thermal insulation design, and subsurface heat transport processes.