Page 273 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

9

Some Examples of Fluid Flow

and Heat Transfer Problems

9.1 Introduction

In this chapter, we discuss some solved examples of fluid flow and heat transfer problems.
First, the readers are made aware of the benchmark problems available to test their codes.
The second objective is to provide more experience to the readers in tackling problems
of their own interest. In addition to discussing the benchmark problems, we also provide
a few application problems in heat transfer. Only a brief discussion of the solution will
be provided for most of the problems considered. Isothermal flow (no heat transfer), non-
isothermal problems and a transient solution are included in this chapter.

9.2 Isothermal Flow Problems

Isothermal flow problems obviously do not involve heat transfer but are quite important in
testing and validating the fluid dynamics part of an algorithm or a developed code. Both
steady and unsteady isothermal flow problems are considered in the following subsections.

9.2.1 Steady state problems
Steady state problems are problems that are independent of time, and a solution to such
problems can be obtained using either the steady Navier–Stokes equations, along with an
appropriate implicit fluid dynamics solver (Taylor and Hughes 1981), or the unsteady state
Navier–Stokes equations and the appropriate time marching procedure (Donea and Huerta
2003; Gresho and Sani 2000; L¨ ohner 2001; Zienkiewicz and Taylor 2000). Solutions to
all the fluid flow problems presented in this chapter are produced using the characteristic-
based-split (CBS) scheme, which is a time marching algorithm. Details of the CBS scheme
Fundamentals of the Finite Element Method for Heat and Fluid Flow R. W. Lewis, P. Nithiarasu and K. N. Seetharamu
 2004 John Wiley & Sons, Ltd ISBNs: 0-470-84788-3 (HB); 0-470-84789-1 (PB)