Heat transfer through a homogeneous isotropic turbulent field

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Abstract
Because of the large scale of the motion responsible for mixing in turbulent fields, turbulent transport processes differ from molecular transport processes in that the mixing depends on the previous history of the diffusing material and turbulent fields are generally nonhomogeneous.The effect of the time dependency of the diffusion process is examined for the case of heat transfer from a hot wall to a cold wall through a turbulently flowing fluid. The fluid is assumed to have a uniform velocity and the turbulence is assumed to be homogeneous and isotropic. The calculations are carried out by assuming a distribution of heat sources along the hot wall and of heat sinks along the cold wall. G. I. Taylor's theory of turbulent diffusion for a homogeneous isotropic field is used to describe the properties of these sources and sinks. These calculations are compared with temperature profiles obtained as a solution to Fick's Law using a constant diffusion coefficient. A marked difference between the two sets of curves is obtained in the vicinity of the wall and in the beginning of the heat exchange section.A calculated profile on the basis of an idealized model of heat transfer in channel flow is compared with actual measurements made by Page, Corcoran, Schlinger, and Sage (7) at a distance far enough downstream so that the temperature profile had reached a steady condition.

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