Heat transfer at small Grashof numbers

Abstract

Rough physical arguments suggest that the heat transfer from a body, immersed in a fluid, should be determined by the heat-conduction equation alone whenever the Grashof number, G , associated with the problem is small. However, heat-transfer rates predicted in this fashion are not always in accordance with the experimentally determined values. It is shown that, while convection is negligible in comparison with conduction near the body, it becomes as important at distances from the body of the order ( G ) -n , where n varies between 1/3 and ½ with the body shape. Whenever this distance is large in comparison with all the dimensions of the body the use of the conduction equation yields correct heat-transfer rates. If, however, this distance is small in comparison with the body length, the heat transfer may be calculated from the two-dimensional convection solution. An examination of the solutions in these two extreme cases reveals that the heat loss is the same as that by conduction to a certain surrounding surface maintained at ambient temperature. This interpretation enables certain qualitative deductions to be made for the case when the ratio of the lengths is neither large nor small. The agreement between theory and experiment is satisfactory.