Finite Element Simulation of Nonlinear Convective Heat and Mass Transfer in a Micropolar Fluid-Filled Enclosure with Rayleigh Number Effects

Abstract

A mathematical model is presented to study the double-diffusive convective heat and mass transfer of a micropolar biofluid in a rectangular enclosure, as a model of transport phenomena in a bioreactor. The vertical walls of the enclosure are maintained at constant but different temperatures and concentrations. The conservation equations for linear momentum, angular momentum, energy and species concentration are formulated subject to appropriate boundary conditions and solved using both finite element and finite difference numerical techniques. Results are shown to be in excellent agreement between these methods. Several special cases of the flow regime are discussed. The distributions for streamline, isotemperature, isoconcentration and (isomicrorotation) are presented graphically for different Lewis number, buoyancy parameter, micropolar vortex viscosity parameter, gyration viscosity parameter, Rayleigh number, Prandtl number and micro-inertia parameter. Micropolar material parameters are shown to considerably influence the flow regime. The flow model has important applications in hybrid aerobic bioreactor systems exploiting rheological suspensions e.g. fermentation.