Darcy–Benard–Oldroyd convection in anisotropic porous layer subject to internal heat generation

Abstract

An anisotropic horizontal porous layer saturated with viscoelastic liquids of the Oldroyd-B type is explored to determine how the internal heat source affects thermal convection. As a momentum equation, a modified Darcy–Oldroyd model is used that takes into account the anisotropy of the porous layer. The energy equation is formulated in such a way that the influence of internal heat sources and anisotropy in thermal diffusivity on the stability criterion may be easily identified. The effects of anisotropy, viscoelasticity, and internal heat generation on the onset of thermal convection are investigated using linear stability analysis. It is understood that convection begins via an oscillatory mode instead of a stationary mode because viscous relaxation, thermal diffusions, and internal heat generation mechanisms compete with one another. Both steady and unsteady finite-amplitude convections are studied using nonlinear stability analysis with the truncated Fourier series method. The effect of different governing parameters on the system’s stability and on convective heat transfer is studied. The present investigation has been significantly validated by the recovery of several prior results as special situations. The findings presented in this work are anticipated to have significant implications for a number of real-world applications, including modeling of oil reservoirs, crude oil extraction, crystal growth, the pharmaceutical and medical industries, and the use of geothermal energy, among others.