“…The application of the recycle effect to increase the working fluid flowing velocity plays an important role in the strength of convective heat transfer coefficient resulting in improved device performance [11], and it is widely used in separation processes and chemical reactors, such as tubular reactor [12], gas scrubbers [13], gas absorbers [14], thermal diffusion [15], loop reactors [16], air-lift reactor [17], and draft-tube bubble column [18]. The purposes of this work are to develop the heat transfer model of the cool-thermal discharge systems with a moving boundary, to derive the equations of the temperature-time history in both ice and water layers, and to investigate recycle effect on the heat-transfer efficiency improvement of cool-thermal discharge systems.…”