The group theoretic approach is applied for solving the problem of unsteady natural convection flow of micropolar fluid along a vertical flat plate in a thermally stratified medium. The application of two-parameter transformation group reduces the number of independent variables in the governing system consisting of partial differential equations and a set of auxiliary conditions from three to only one independent variable, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. Numerical solution of the velocity, microrotation and heat transfer have been obtained. The possible forms of the ambient temperature variation with position and time are derived.  2007 Elsevier Inc. All rights reserved.

The group theoretic approach is applied for solving the problem of unsteady natural convection flow of micropolar fluid along a vertical flat plate in a thermally stratified medium. The application of two-parameter transformation group reduces the number of independent variables in the governing system consisting of partial differential equations and a set of auxiliary conditions from three to only one independent variable, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions. Numerical solution of the velocity, microrotation and heat transfer have been obtained. The possible forms of the ambient temperature variation with position and time are derived.  2007 Elsevier Inc. All rights reserved.

This work presents a performance analysis of mixed convection boundary layer flow past a horizontal circular cylinder embedded in a fluid-saturated porous medium in a vertical stream flow using the Darcy-Brinkman model. The surface temperature is assumed to be constant. The fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. Both cases of a heated (assisting flow) and a cooled (opposing flow) cylinder are considered. The governing equations reduce to the similar Darcy's model, while it becomes nonsimilar for the Darcy-Brinkman model, and they are solved numerically employing the finite difference method. The effects of the Darcy-Brinkman parameter Γ, mixed convection parameter λ, viscosity parameter r, and thermal conductivity parameter ε are studied. It is found that cooling the cylinder (λ 0) brings the boundary layer separation point nearer to the lower stagnation point, and for sufficiently large negative values of the mixed convection parameter (in absolute sense) there is no boundary layer on the cylinder in the case of variable and constant fluid properties. Heating the cylinder (λ > 0) delays the separation of the boundary layer and can suppress it completely for large values (λ > 0). Results for the details of the velocity and temperature fields as well as skin friction and rate of heat transfer at the wall are presented. Results are compared with previously published work and are found to be in excellent agreement.

In this work, a numerical solution of flow and heat transfer of a micropolar fluid in a lid-driven cavity under different micro-gyration boundary conditions is presented. A finite difference method is employed to solve the governing system of partial differential equations. The cases of strong concentration of microelement and weak concentration of microelement are considered. The effects of the governing parameters, namely the dimensionless time parameter, micro-gyration boundary conditions parameter and vortex viscosity parameter on the streamlines contours and temperature contours as well as the velocity profiles at the enclosure mid-section, angular velocity profiles at the enclosure mid-section, Nusselt number and average Nusselt number at the bottom and top walls of the enclosure are investigated. The results for the Newtonian fluid condition are validated by favorable comparisons with previously published results. The numerically results are shown graphically to illustrate special features of the solutions. The values of the average Nusselt number at the bottom and top walls of the enclosure are presented in tables.