Thermal Convection of Plane Couette Flow in a Fluid Overlying a Highly Porous Medium

The present article deals with the temporal linear stability analysis of plane Couette flow (PCF) in a horizontal fluid layer of depth d that overlies a porous layer of depth \(d_m\) . The maintenance of constant temperature difference between the upper and lower plates \((T_L>T_U )\) along with the uniform movement of the upper plate with velocity U (in other words, Couette flow) introduces the mixed convection in the system. The Darcy-Brinkman model governs the flow of the Newtonian and incompressible fluid in the highly porous layer. The Chebyshev spectral collocation method aids in solving the generalized eigenvalue problem, which in turn helps to analyse the impact of the depth ratio \((\hat{d})\) , the Reynolds number (Re) and the Prandlt number (Pr) on the instability of the system. The fluid overlying porous geometry introduces more than a single lobe along the neutral stability curves plotted for porous Rayleigh number \((Ra_m)\) versus porous wavenumber \((a_m)\) , which gives rise to the unimodal and bimodal nature along the curves. The porous (fluid) mode correlates with the lobe of neutral curves with low (high) oscillatory frequency and causes instability therein. Consideration of two different values of porosity \((\phi )\) 0.3 and 0.78 for the Darcy and Darcy-Brinkman model assist to compare the stability results between the two models. The analysis indicates substantial differences between the models in terms of early/later appearance of instability as well as the modal behavior of the neutral stability curves.