Civil Engineering Reference
In-Depth Information
7
CHAPTER
Applications in
Heat Transfer
7.1 INTRODUCTION
In this chapter, the Galerkin method introduced in Chapter 5 and the interpola-
tion function concepts of Chapter 6 are applied to several heat transfer
situations. Conduction with convection is discussed for one-, two-, and three-
dimensional problems. Boundary conditions and forcing functions include
prescribed heat flux, insulated surfaces, prescribed temperatures, and convec-
tion. The one-dimensional case of heat transfer with mass transport is also
developed. The three-dimensional case of axial symmetry is developed in detail
using appropriately modified two-dimensional elements and interpolation
functions. Heat transfer by radiation is not discussed, owing to the nonlinear
nature of radiation effects. However, we examine transient heat transfer and
include an introduction to finite difference techniques for solution of transient
problems.
7.2 ONE-DIMENSIONAL CONDUCTION:
QUADRATIC ELEMENT
Chapter 5 introduced the concept of one-dimensional heat conduction via the
Galerkin finite element method. In the examples of Chapter 5, linear, two-node
finite elements are used to illustrate the concepts involved. Given the develop-
ment of the general interpolation concepts in Chapter 6, we now apply a higher-
order (quadratic) element to a previous example to demonstrate that (1) the basic
procedure of element formulation is unchanged, (2) the system assembly proce-
dure is unchanged, and (3) the results are quite similar.
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