Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method

Mohsen Sheikholeslami, Davood Domairry Ganji

• Publisher: Academic Press
• Year: 2015
• Print ISBN: 9780128029503
• eBook ISBN: 9780081003619
• Topic: Physical Sciences
• Subtopic: Thermodynamics

Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems), hydro-magnetic techniques in materials and bioengineering, and convective flow in fluid-saturated porous media. The topics are of practical interest to engineering, geothermal science, and medical and biomedical sciences.- Introduces a detailed explanation of Control Volume Finite Element Method (CVFEM) to provide for a complete understanding of the fundamentals- Demonstrates applications of this method in various fields, such as nanofluid flow and heat transfer, MHD, FHD, and porous media- Offers complete familiarity with the governing equations in which nanofluid is used as a working fluid- Discusses the governing equations of MHD and FHD- Provides a number of extensive examples throughout the book- Bonus appendix with sample computer code

Chapter 1

Control volume finite element method (CVFEM)

Abstract

There are several methods that can be used to solve the governing equations of fluid flow and heat transfer, such as the finite difference method, the finite volume method (FVM), and the finite element method (FEM). The control volume finite element method (CVFEM) comprises interesting characteristics from both the FVM and FEM. The CVFEM combines the flexibility of the FEMs to discretize complex geometry with conservative formulation of the FVMs, in which the variables can be easily interpreted physically in terms of fluxes, forces, and sources. This chapter highlights the basic concept of CVFEM. The necessary ingredients in numerical solutions are discussed.

Keywords

CVFEM

Grid

Mesh

Cloud

Shape functions

Advection-diffusion

Unsteady

Source term

1.1 Introduction

Fluid flow has several applications in engineering and nature. Mathematically, real flows are governed by a set of nonlinear partial differential equations in complex geometry. So, suitable solutions can be obtained through numerical techniques such as the finite difference method, the finite volume method (FVM), and the finite element method (FEM). In the past decade the FEM has been developed for use in the area of computational fluid dynamics; this method ha...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Nomenclature
• Preface
• Chapter 1: Control volume finite element method (CVFEM)
• Chapter 2: CVFEM stream function-vorticity solution
• Chapter 3: Nanofluid flow and heat transfer in an enclosure
• Chapter 4: Flow heat transfer in the presence of a magnetic field
• Chapter 5: Flow and heat transfer in porous media
• Appendix: A CVFEM code for lid driven cavity
• Index