Effect of rotation and internal heat generation on Darcy–Brinkman convection in Oldroyd-B liquid

Convection in an Oldroyd-B liquid saturated highly permeable porous medium is studied via both linear and nonlinear theories. Estimating a convection threshold is the objective of linear-stability analysis whereas convection amplitudes and heat transfer are elucidated by performing nonlinear-stability analysis. The eigenvalue problem is solved by the Galerkin method of weighted residuals. The oscillatory mode becomes dominant over the stationary mode. This is because of the race among diffusivity, viscoelasticity, internal-heat generation, and rotation. The increasing permeability, internal heat generation coefficient, and stress-relaxation parameter are liable to subcritical motions while the rotation, viscosities ratio, heat capacities ratio, and strain retardation parameter are responsible for the system attaining a supercritical state. The Runge–Kutta–Gill method presents the mechanism to evaluate the amount of heat transfer. The increasing Rayleigh number, internal Rayleigh number, Darcy number, Deborah number, Prandtl number, and the heat capacities ratio enhance the heat transfer. This offers a convenient mechanism for regulating convection. The results obtained in the present paper are expected to play a decisive role in some of the real-life applications such as oil-reservoir modeling, crude oil extraction, crystal growth, medicine industries, geothermal-energy utilization, and so on.