Finite element simulations for energy transfer in a lid-driven porous square container filled with micropolar fluid: Impact of thermal boundary conditions and Peclet number

Abstract

The phenomena of forced convection flow based on Peclet number in a porous square container filled with micropolar fluid is investigated here numerically with the help of powerful numerical technique. A penalty formulation based finite element method (FEM) is employed to simulate the developed flow equations. The present analysis is performed for dual cases based on different thermal boundary conditions. In the first case, the lower boundary is assumed to be constantly heated while in the second case it is considered that the lower boundary is maintained at a variable/sinusoidal temperature. In each case the rest of the boundaries of the container are cold and motionless except the top boundary which is sliding with uniform velocity. The above mentioned numerical technique is selected to get the solution for various values of Richardson number (10≤Ri≤104), Reynolds number (1≤Re≤102), Darcy number (10−5≤Da≤10−3), Peclet number (20≤Pe≤104) and micropolar parameter (0≤χ≤40). The present analysis can be helpful in engineering systems for examples, food and glass manufacturing, heat exchangers, solar ponds, lakes and reservoirs etc. It is also applicable in microfluidic devices and thin films. The present study can be extended for various geometrical shapes such as, rectangular or non-rectangular, triangular and curvilinear shapes enclosures.