Page 242 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

CONVECTION HEAT TRANSFER
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channel employed in this case is longer than that used for the laminar computation, that is,
40 times the height of the channel.
A structured mesh, with 12,000 elements and 6161 nodes, has been employed in the
turbulent flow calculations. The horizontal velocity distribution at the exit of the chan-
nel is compared with available experimental data and is shown in Figure 7.34. The inlet
Reynolds number is 24,600. The agreement between the experiments and the numerical
results is excellent away from the wall. More advanced turbulence models will result in
better accuracy of the results.

7.13 Extension to Axisymmetric Problems

The axisymmetric formulation of the heat conduction equations has been discussed in
many of the earlier chapters. Here, an extension of the plane formulation to axisymmetric
convection heat transfer problems will be discussed. The governing equations, in cylindrical
coordinates, are given with respect to Figure 7.35 as follows:
Conservation of Mass

1 ∂(ru r ) ∂u z
+ = 0 (7.206)
r ∂r ∂z

z

r

Figure 7.35 Coordinate system for axisymmetric geometries