Transient conjugated heat transfer in microchannels: Integral transforms with single domain formulation

Abstract

The transient behaviour of conjugated heat transfer in laminar microchannel flow is investigated, taking into account the axial diffusion effects, which are often of relevance in microchannels, and including pre-heating or pre-cooling of the region upstream of the heat exchange section. The solution methodology is based on the Generalized Integral Transform Technique (GITT), as applied to a single domain formulation proposed for modelling the heat transfer phenomena at both the fluid stream and the channel wall regions. By making use of coefficients represented as space dependent functions with abrupt transitions occurring at the fluid–wall interfaces, the mathematical model carries the information concerning the transition of the two domains, unifying the model into a single domain formulation with variable coefficients. The proposed approach is illustrated for microchannels with polymeric walls of different thicknesses. The accuracy of approximate internal wall temperature estimates deduced from measurements of the external wall temperatures, accounting only for the thermal resistance across the wall thickness, is also analyzed.