Axial conduction in a thick-wall matrix heat exchanger

Abstract

Solutions are developed for temperature distributions and ineffectiveness for a high Ntu matrix heat exchanger having simultaneous axial conduction in the single phase (matrix/fluid) flow channels and separating wall. A scale analysis of the governing equations shows a large disparity in length scales for the conduction and convection effects, thus indicating a singular perturbation problem. Solutions for both balanced and imbalanced flow are obtained by analytical methods with appropriate scaling so that all terms of the solution are well behaved in the limit of large Ntu. The limiting cases of only wall conduction and only matrix conduction are treated, the results from which are favourably compared with past works. Ineffectiveness resulting from simultaneous matrix and wall conduction from the present work is compared with a traditional heat exchanger model for axial conduction. Good agreement is found for only small ratios of axial and wall conductance to Ntu. Finally, the results are compared with earlier laboratory data. These data are found to be bracketed from below by the results of this work and, from above, by an earlier model for high Ntu performance which neglected axial conduction.