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.

In this study, we numerically investigated the transient steady state for the problem of double-diffusive convection in porous triangular enclosures with the effects of thin fin, various thermal and concentration boundary conditions in the presence of heat source. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely heat generation parameter, buoyancy parameter and Lewis number on the streamlines, temperature and concentration contours as well as selected velocity component in the x-direction, Nusselt and Sherwood numbers and average Nusselt and Sherwood numbers at the enclosure bottom wall in the case of fixed boundary conditions and the case various boundary conditions were considered. The present results are validated by favorable comparisons with previously published results. All the results are presented in graphical and tabular forms and discussed.

A numerical investigation of unsteady magnetohydrodynamic free convection in an inclined square cavity filled with a fluid-saturated porous medium and with internal heat generation has been performed. A uniform magnetic field inclined with the same angle of the inclination of the cavity is applied. The governing equations are formulated and solved by a direct explicit finite-difference method subject to appropriate initial and boundary conditions. A parametric study illustrating the influence of the Hartmann number, Rayliegh number and the inclination angle of the cavity on the flow and heat transfer characteristics such as the streamlines, isotherms and the Nusselt number is performed. The velocity components at mid section of the cavity as well as the temperature profiles are reported graphically. The values of Nusselt number for various parametric conditions are presented in tabular form.

The problem of double-diffusive convection in inclined finned triangular porous enclosures for various thermal and concentration boundary conditions and in the presence of heat source or sink was studied. The finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of the governing parameters, namely the dimensionless time parameter, the inclination angle, Darcy number, heat generation/absorption parameter, the buoyancy parameter and the Rayleigh number on the streamlines, temperature and concentration contours as well as selected velocity component in the x-direction, local and average Nusselt numbers and local and average Sherwood number at the heated and concentrated wall for various values of the aspect ratio and the position of the fin were considered. The present results are validated by favorable comparisons with previously published results. All the results of the problem were presented in graphical and tabular forms and discussed.

Continuum equations governing thermal non-equilibrium modeling of steady natural convection inside wavy enclosures with the effect of thermal radiation are developed. These equations account for such effects as the inter-phase heat transfer coefficient effect, the thermal radiation effect, the modified conductivity ratio effect and the Rayleigh number effect. Finite difference method is employed to solve these equations and comparisons between previous published works are presented. Numerical results for the flow and heat transfer for the fluid and solid phases are obtained for various combinations of the physical parameters. Graphical and tabular results illustrating interesting features of the physics of the problem are presented and discussed.

Bulk chalcogenide Ge20Se80−xTex (where x = 0, 10, 20 and 30 at.%) glasses were prepared using the meltquench technique. The total structure factors of these alloys are obtained from the X-ray scattering data in the momentum transfer interval 0.61≤K≤16.45 ˚A−1. From reverse Monte Carlo (RMC) simulations of the X-ray scattering data, the short and intermediate-range order parameters are obtained. The simulations are useful to compute the partial pair distribution functions, gij(r), and the partial structure factors, Sij(K). In Te-rich glass, the first sharp diffraction peak (FSDP) appears as a shoulder, instead of a peak for others, confirms that Se–Se bonds in addition to Ge–Ge bonds are responsible for the intermediate-range order inside these glasses. The partial coordination numbers and the bond angle distributions within the first coordination shell have been calculated. The ratio of the first to second peak positions (r1/r2) and the corresponding bond angle (theta) have confirmed that the Ge(Se1/2)4 tetrahedra, connected by Se–Se chains, can be considered as the main building units inside the investigated glasses.

Bulk chalcogenide Ge20Se80−xTex (where x = 0, 10, 20 and 30 at.%) glasses were prepared using the meltquench technique. The total structure factors of these alloys are obtained from the X-ray scattering data in the momentum transfer interval 0.61≤K≤16.45 ˚A−1. From reverse Monte Carlo (RMC) simulations of the X-ray scattering data, the short and intermediate-range order parameters are obtained. The simulations are useful to compute the partial pair distribution functions, gij(r), and the partial structure factors, Sij(K). In Te-rich glass, the first sharp diffraction peak (FSDP) appears as a shoulder, instead of a peak for others, confirms that Se–Se bonds in addition to Ge–Ge bonds are responsible for the intermediate-range order inside these glasses. The partial coordination numbers and the bond angle distributions within the first coordination shell have been calculated. The ratio of the first to second peak positions (r1/r2) and the corresponding bond angle (theta) have confirmed that the Ge(Se1/2)4 tetrahedra, connected by Se–Se chains, can be considered as the main building units inside the investigated glasses.