There are many transient sequences in the energy industry where a hot or cold liquid enters a flow passage that is at a different temperature. Thermal energy is transferred by convection between the liquid and the boundary of the flow passage, causing both temperatures to change with time at all locations as the liquid column moves. This paper presents a theoretical analysis of transient heat transfer between an axial liquid flow at constant velocity V and the walls of the flow passage, which are in contact with constant temperature surroundings. A general nondimensional model that includes internal heat generation from the fluid flow is formulated and solved analytically for various cases such as obtaining the freezing point of a heated liquid material that solidifies after the flow passage extracts enough of its initial thermal energy. Analytical solutions for thin-walled pipes, temperature history at pipe entrance and temperature of the moving liquid front are also provided in this study. A simple numerical scheme is proposed in order to calculate liquid and passage wall temperatures at general points of the time-space domain where analytical solutions have not been obtained.

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