The limiting solutions obtained in Sections 10.1.1 and 10.1.2 are equivalent to the "solution representation" for TTHE-A given by Bertoli et al. , thus showing consistency and providing alternative forms of the solution. ) or ( )-( ) cannot be used. For the TTHE-A with counter-current flow in the intermediate tube (fluid "1"), Bertoli et al. determined the conditions and solution for this special case, while Bertoli et al. carried out this analysis for the MBHE-A for all countercurrent flow arrangements. Thus, making use of the analogies between MBHE-A and TTHE-A ,