Heat transfer for turbulent flow with injection in a porous tube.

Abstract

The effect of injection on the eddy diffusivity of heat in the turbulent core region and the heat transfer rate in the thermally fully developed region was analyzed using a simple model. The analytical results were tested in experiments on the heat transfer of turbulent flows of water in a circular tube of porous wall through which heated water was injected. Measurements of heat transfer rate and temperature profile were made far downstream from the entrance. The experiments were performed for Reynolds numbers of the main flow ranging from 6, 000 to 34, 000 and for injection rates of m=-0.004 to -0.0004. It was found that the measured heat transfer rates and the eddy diffusivities of heat could be correlated well by the expressions obtained from the analysis. The j-factor of heat transfer divided by the dimensionless pressure gradient and the eddy diffusivity of heat normalized by Re(-dp*/dx*) were expressed as the sum of the linear function and the hyperbola of the injection rate parameter, m/(-dp*/dx*). In the range of 0>m/(-dp*/dx*)>-0.08 the Chilton-Colburn analogy was found to hold even in the presence of injection.