The Effect of Liquid Solidification on Turbulent Flow Heat Transfer of a Heat Generating Fluid in a Cold Tube

A theoretical study has been conducted to investigate the effect of liquid solidification (freezing) on the heat transfer characteristics for the turbulent flow of a heat generating fluid in a cooled circular tube. Steady-state conditions and a uniform wall temperature, which is lower than the liquid freezing temperature, are assumed. The radius of the liquid-solid interface and the local Nusselt number are determined as a function of position along the tube for several different values of the Reynolds number and the Prandtl number. The thickness of the frozen shell increases with distance down the tube. It approaches its fully developed value, depending upon a single dimensionless freezing parameter which measures the relative rate of wall cooling and internal heating. The local Nusselt number, however, first decreases rapidly and then approaches its fully developed value, which depends on the Reynolds number and the Prandtl number