Influence of temperature dependent viscosity and internal heating on the onset of convection in porous enclosures saturated with viscoelastic fluid

Abstract

AbstractThe combined influence of temperature dependent viscosity and internal heat source on the onset of convection in porous enclosures saturated by a viscoelastic fluid is studied using linear and weak nonlinear stability theories. The enclosures are taken to be rectangular, square, and slender. For the viscoelastic fluid, the Oldroyd‐B type model is used, whereas the Darcy's model is taken for porous medium. The linear theory based on normal mode technique is used to find the criteria for the onset of marginal and oscillatory convections, and weakly nonlinear analysis based on minimal representation of truncated Fourier series is considered to discuss the convective heat transport in the system. It is observed that the beginning of convection will be oscillatory only if the strain retardation parameter is not greater than the stress relaxation parameter. The influence of raising the viscosity variation parameter, the internal heating parameter, and the stress relaxation parameter is to fast the onset of convection and also boost the heat transmission through the porous enclosures, but an opposite tendency is identified by raising the strain retardation parameter and the heat capacity ratio. The heat transmission decreases with the aspect ratio for rectangular enclosure, whereas this outcome is revered for the slender enclosure.