A simple solution form for triple tube heat exchanger with non-adiabatic condition on the outer wall by analogy with moving bed heat exchanger

Triple tube heat exchangers (TTHEs) are suitable equipment for thick viscosity products, with or without particulates, with various applications in the food and pharmaceutical industries. Of less widespread use than double tube heat exchangers (DTHEs), they generally perform better when compared to the latter. However, in the case of thermal models of "TTHEs with heat loss to the surroundings" (TTHEs-HL), there is no analytical solution in which the character of the roots has been analyzed. - except for the analogous problem of a "tubular moving bed heat exchanger, indirectly heated and with heat loss to the surroundings " (MBHE-HL), but only for certain flow arrangements -. Thus, it is not certain that the known solutions are of general application. Furthermore, regarding the important design parameter for co-current flow TTHEs, the crossover point, very little is known for TTHEs-HL. Also, recently published analogies provide an opportunity to synergistically increase the knowledge of TTHEs and MBHEs, for the case of non-adiabatic external surface. Aware of these needs and opportunities, the present work starts from a known analytical solution for a MBHE-HL thermal model and, by analogy, develops a compact form of an analytical solution for TTHE-HL, suitable for co-current and counter-current flow arrangements. The character analysis of the roots - not trivial for this solution - is performed according to a methodology recently described in the literature, consisting of several mathematical techniques. Approximate expressions for crossover point and temperature equality point between streams are obtained. In the case studies, the values calculated by the analytical solution and by a numerical solution by the finite analytical method (FAM), were shown to be very close. For the flow arrangements analyzed, it was possible to conclude about the generality of the solutions, in addition, the analogies between MBHE and TTHE made it possible to advance in the understanding of the thermal operation of these equipments. For a better understanding of the underlying physics, a scale analysis was performed.