A Simple Solution for Triple Tube Heat Exchanger with Non-Adiabatic Outer Wall Condition 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. Although less commonly used than Double Tube Heat Exchangers (DTHEs), TTHEs often perform better than DTHEs. However, in the case of thermal models of TTHEs with Heat Loss (TTHEs-HL) to the surroundings, 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 with Heat Loss to the surroundings and indirectly heated (MBHE-HL), for specific flow configurations –. Thus, it is not certain that the known solutions are of general application. Furthermore, regarding the critical design parameter for co-current flow TTHEs – the crossover point – limited information is available about TTHEs-HL. Also, recently published analogies provide an opportunity to synergistically increase the knowledge of TTHEs and MBHEs, for the case of non-adiabatic outer wall. 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 of the roots is determined from literature results for the MBHE-HL, by analogy with the TTHE-HL. These results are based on parallel flow and counter-current flow of the fluid in the intermediate tube, for a wide range of parameters. From the solution obtained, it was possible to determine approximate expressions for crossover points. For the case studies analyzed, the values calculated by the analytical solution and the numerical solution using the compound method Trapezoidal Rule/Regressive Differentiation Formula (TR-BDF2) are almost identical. By comparison with other analytical solutions in the literature for thermal models of TTHE-HL, we have shown that the present solution is the first – to the best of our knowledge – that correctly represents the temperatures of the three fluids in co-current flow, and for a wide range of parameters in the counter-current flow of the fluid in the inner annular section. To better understand the underlying physics, a scale analysis is carried out.