Page 230 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

CONVECTION HEAT TRANSFER
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temperature of unity. All the side walls are subjected to a zero heat flux and a zero normal
velocity value. At the exit, only the boundary integrals are evaluated and prescribed.
It is obvious that a three-dimensional mesh is required, and for the problem under
consideration, linear tetrahedral elements were used. Three-dimensional meshes were gen-
erated using an efficient mesh generator as reported by Morgan et al. (1999). The total
number of elements used in the computation was approximately a million. The sphere and
a cross-sectional side view along the axis are shown in Figure 7.23.
The temperature contours near the vicinity of the sphere are shown in Figure 7.24
for inlet Reynolds numbers of 100 and 200 respectively. As mentioned previously, the
temperature on the surface of the sphere is unity. This diagram shows a cut view along the

(a) Sphere and two side boundaries (b) Cross-sectional view of the sphere
Figure 7.23 Forced convection heat transfer from a sphere. Three-dimensional mesh

(a) Re = 100 (b) Re = 200
Figure 7.24 Forced convection heat transfer from a sphere. Temperature distribution in
the vicinity of the sphere