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

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