Page 231 - Fundamentals of The Finite Element Method for Heat and Fluid Flow

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CONVECTION HEAT TRANSFER
axis in the direction of the flow. Therefore, the temperature values close to the surface of
the sphere are near to unity, which reduce in value away from the sphere and finally reach
zero value in the free air stream. In the downstream direction, however, the temperatures are
greater than that of the free stream temperature all the way to the exit (see Figure 7.25). This
indicates that the cold air stream removes heat from the sphere, which is then transported
to the exit.
The values of drag coefficient and average Nusselt numbers are given in Tables 7.1
and 7.2 respectively. In Table 7.1, the quantity inside the brackets is the pressure drag
coefficient.

7.11.2 Buoyancy-driven convection heat transfer

Buoyancy-driven convection is created by the occurrence of local temperature differences
in a fluid. This type of convection can also be created by local concentration differences

Figure 7.25 Forced convection flow past a sphere. Temperature contours, Re = 100

Table 7.1 Comparison of coefficient of drag with existing literature
Author Re 100 200

Clift et al. (Clift et al. 1978) 1.087 —
S. Lee (Lee 2000) 1.096 (0.512) —
¸
G¨ ulcat and Aslan (G¨ ulc¸at ¨ and Aslan 1997) 1.07 0.78
Rimon and Cheng (Rimon and Cheng 1969) 1.014 0.727
Le Clair et al.(La Clair et al. 1970) 1.096 (0.590) 0.772 (0.372)
Magnaudet et al. (Magnaudet et al. 1995) 1.092 (0.584) 0.765 (0.368)
CBS 1.105 (0.564) 0.7708 (0.347)

Table 7.2 Comparison of average Nusselt number

Re (Yuge 1960) (Whitaker 1983) (Feng et al. 2000) CBS
50 5.4860 5.1764 5.4194 5.2176
100 6.9300 6.6151 6.9848 6.6589
200 8.9721 8.7219 9.1901 8.7599