Darcy–Benard–Oldroyd convection in anisotropic porous layer subject to internal heat generation - Swamy, Mahantesh S.; Hanumagowda, B. N.; Khan, Umair; Vidyashree, K.; Hassan, Ahmed M.; Mohammed Saeed, Abdulkafi; Kumar, Ranvijay (Frontiers in Materials, 2023)
Influence of internal heat source on thermal convection in viscoelastic liquid of Oldroyd-B type drenched within anisotropic horizontal porous layer is studied. A modified Darcy-Oldroyd model which takes into account the anisotropy of the porous layer is employed as momentum equation. Equation of energy is so taken that the effect of internal heat sources and anisotropy in thermal diffusivity, on the stability criteria could be easily revealed. Linear stability analysis is implemented to explore how the anisotropy, viscoelasticity and the internal heat generation affect the onset of thermal convection. It is established that due to the competition between the mechanisms of viscous relaxation, thermal diffusions and internal heat generation the convection sets in via oscillatory mode instead of stationary one. Nonlinear stability analysis equipped with truncated Fourier series method provides the information of both steady and unsteady finite amplitude convections. The effect of various governing parameters on the stability of the system and also on the convective heat transfer is investigated. Some of the earlier results are recovered as the special cases which strongly validate the present investigation. 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, extraction of crude oil, crystal growth, medicine industries, geothermal energy utilization and so on.