Page 40 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

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A 2 SOME BASIC DISCRETE SYSTEMS
k 2
A 1 k 1

q h, T a
A 3 k 3

L 1 L 2

Figure 2.9 Heat transfer in a composite wall

h, T a
Insulation

r 2
Pipe r 3

Hot r
fluid 1
T h

Figure 2.10 Heat transfer through an insulating material

Exercise 2.5.4 A schematic diagram of a counterflow heat exchanger is shown in
Figure 2.12. The hot fluid enters the central, circular pipe from the left and exits at the
right. The cooling fluid is circulated around the inner tube to cool the hot fluid. Using the
principles of heat exchanger system discussed in this chapter, construct a discrete system to
determine the temperature distribution.

Exercise 2.5.5 A transient analysis is very important in the casting industry. In Figure 2.13,
a simplified casting arrangement is shown (without a runner or raiser). The molten metal is
poured into the mould and the metal loses heat to the mould and solidifies. It is often possible
to have a small air gap between the metal and the mould. The figure shows an idealized
system that has a uniform gap all around the metal. Assume that heat is transferred from the