Page 302 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

SOME EXAMPLES OF FLUID FLOW AND HEAT TRANSFER PROBLEMS
294
Rows
Rows
Upper
Lateral
Upper
Lateral
6 8 100 Central Lower 8 6 100 Central Lower
Re = 200 Central Lower Re = 200 Central Lower
Lateral
Upper
Upper
Lateral
Central Lower Central Lower
300 Lateral Upper 300
Nu 4 Nu 4 Lateral Upper
2 2
0 0
1st 3rd 5th 7th 9th 1st 3rd 5th 7th 9th
Column Column
(a) q = 0°, staggered (b) q = 10°, staggered
8
Rows
Central Lower
100
6 Lateral Upper
Re = 200 Central Lower
Lateral Upper
Central Lower
300 Lateral Upper
Nu 4
2
0
1st 3rd 5th 7th 9th
Column
(c) q = 20°, staggered
Figure 9.36 Forced convection heat transfer from spherical heat sources mounted on the
wall. Average Nusselt number distribution for staggered arrangement at different inclination
angles and Reynolds numbers
9.6 Summary
In this chapter, the problem-solving capabilities of the finite element method have been
demonstrated. The emphasis of the chapter has been on the use of unstructured meshes
to prove the flexibility of the finite element method. Occasionally, structured meshes were
used for the purposes of comparison. The readers should use this chapter as a starting
point for problem-solving exercises, for which purpose several benchmark problems and
a few applications have been given. The CBS flow code may be used to further enhance
an understanding of the finite element method, heat transfer and fluid flow problems. This
chapter should form a basis for researchers and students who want to further explore
engineering heat transfer problems.

9.7 Exercise

Exercise 9.7.1 In this exercise, you are asked to make appropriate assumptions and model
flow past the heat exchanger tubes as shown in Figure 9.37.