Numerical Analysis of Grashof and Darcy Number Effects on Dissipative Natural Convection Boundary Layers in a Micropolar Fluid-Saturated Geological Porous Medium

Abstract

The thermo-micropolar non-Newtonian theory is used to formulate a transport model for combined free convection heat and species transfer through a micropolar-fluid saturated Darcian porous medium. Temperatures in the medium are assumed to be high enough for viscous heating effects to be significant. The influence of thermal Grashof number, species Grashof number and Darcian porous number on the momentum, angular momentum, temperature and concentration flow fields are studied using the finite element method. Temperature is observed to be reduced with a rise in the thermal Grashof number. Species transfer is seen to be also decreased with increasing species Grashof number. Micro-rotation values are also decreased with both thermal and species Grashof numbers near the stretching surface and also depressed with a rise in the Darcy number in the near-field regime. The flow field is accelerated with a rise in Darcy number as indicated by the increase in translational velocities. Our computations are relevant to for example the diffusion of hydrogen gas in air-saturated porous materials, pollutant release in a geophysical regime etc.