5.2.3 Natural convection around a horizontal flat surface
In the previous case of vertical flat surface, the principal body dimension was in-line with the gravity (i.e. vertical). Therefore, the flow produced by the free convection was parallel to the surface regardless of whether the surface was hotter or cooler compared to the bulk fluid around. However, in case of horizontal flat plate the flow pattern will be different and shown in fig. 5.3.
Fig. 5.3: A representative flow pattern (natural convection) for (a) hot surface down, (b) hot surface up, (c) cold surface down, and (d) cold surface up
Thus from fig. 5.3 it is understood that there are in fact two cases (i) when the heated plate facing up or cooled plate facing down, and (ii) heated plate facing down or cooled plate facing up.
| Case I: | Heated plate facing up, cooled plate facing down |
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(5.11) |
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(5.12) |
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| Case II: | Heated plate facing down, cooled plate facing up | |
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(5.13) |
where, Lc is characteristic length defined as below.
5.2.4 Natural convection around sphere
Churchill proposed,
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(5.14) |
Condition for applicability: Pr ≥ 0.7; Ra ≤ 1011