Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Analysis of Energy and Exergy for Mixed Convection Flow in Microstructure Filled Vented Enclosures

Abstract: Understanding heat transfer through saturated porous media is of great importance to many engineering and geophysical systems such as cooling the electronic devices and solar power collectors, and post-accidental heat removal in nuclear reactors. Large numbers of research studies have been and are conducted on the expanding field of porous media due to the high rate of heat transfer in these systems. Despite the efforts made towards the study of the mechanics of fluid flow through porous media, little is studied the rate of exergy which is the only factor presenting the rate of reusable energy potentially produced by a heat generating body. The objective of this study is to develop a design of experiment to carry out a numerical analysis of heat transfer in a rectangular enclosure filled with a saturated porous medium. The optimum heat transfer rate will be obtained for various configuration-related parameters, namely different inlet to outlet ratios and different inlet width to cavity width ratios. These parameters will be optimized to achieve maximum rate of heat transfer and minimum rate of entropy generation. The results of this study will also help to determine relationships for predicting the heat transfer characteristics of the enclosure.Copyright © 2011 by ASME

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Boundary and inertia effects on flow and heat transfer in porous media

Abstract: The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.

Effects of thermal boundary conditions on natural convection flows within a square cavity

Abstract: A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 103 ⩽ Ra ⩽ 105 and Prandtl number Pr, 0.7 ⩽ Pr ⩽ 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.

Natural convection in rectangular enclosures heated from below and symmetrically cooled from the sides

Abstract: Steady natural convection in an enclosure heated from below and symmetrically cooled from the sides is studied numerically, using a streamfunction-vorticity formulation. The Allen discretization scheme is adopted and the discretized equations were solved in a line by line basis. The Rayleigh number based on the cavity height is varied from 103 to 107. Values of 0.7 and 7.0 for the Prandtl number are considered. The aspect ratio L H (length to height of the enclosure) is varied from 1 to 9. Boundary conditions are uniform wall temperature and uniform heat flux. For the range of the parameters studied, a single cell is observed to represent the flow pattern. Numerical values of the Nusselt number as a function of the Rayleigh number are reported, and the Prandtl number is found to have little influence on the Nusselt number. A scale analysis is presented in order to better understand the phenomenon.