Heat transfer from electrically heated cylinders

Abstract

The heat transfer from small electrically heated cylinders has been studied with particular reference to the performance of hot-wire anemometers. The thermal equilibrium for a cylinder normal to the flow was investigated in detail and the convective transfer to the fluid, conductive flow to the supports and the radiation losses were measured. A simple model of the heat transfer at the surface showed that the Nusselt number was proportional to the product of the skin friction coefficient, C f , and the Reynolds and Prandtl numbers, and was in good agreement with the measurements. At the same time it was argued that the skin friction coefficient was independent of the temperature of the cylinder, provided that the fluid properties are evaluated for the conditions at the surface in the absence of heat transfer. This is in general agreement with published results and the measurements described here. The same model showed that the coefficient of local heat transfer was expressed by h w = C f ρ V c v k w /π k 0 , where k w is the conductivity of air at the temperature of the wire surface. This expression was also in good agreement with the measurements which showed that the temperature dependence of the heat transfer coefficient can be expressed as h w = h 0 (1 + β T ), if it is assumed that k w = k 0 (1 + β T ). The measurements also showed that h 0 was proportional to the product of the mass flux and the skin friction coefficient, C f . The chief source of experimental error in the measurement of Nusselt number was found to be in the estimation of the surface temperature of the wire, the reason being that the hot wire itself was used as a resistance thermometer for this purpose. This difficulty is a major factor in the large scatter among Nusselt number measurements by different observers.