Analysis of conjugated heat transfer in micro-heat exchangers via integral transforms and non-intrusive optical techniques

Abstract

The purpose of this paper is to employ the Generalized Integral Transform Technique in the analysis of conjugated heat transfer in micro-heat exchangers, by combining this hybrid numerical-analytical approach with a reformulation strategy into a single domain that envelopes all of the physical and geometric sub-regions in the original problem. The solution methodology advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures, and fluid temperature measurements obtained through micro Laser Induced Fluorescence. The methodology is applied in the hybrid numerical-analytical treatment of a multi-stream micro-heat exchanger application, involving a three-dimensional configuration with triangular cross-section micro-channels. Space variable coefficients and source terms with abrupt transitions among the various sub-regions interfaces are then defined and incorporated into this single domain representation for the governing convection-diffusion equations. The application here considered for analysis is a multi-stream micro-heat exchanger designed for waste heat recovery and built on a PMMA substrate to allow for flow visualization. The methodology here advanced is carefully validated against experimental results from non-intrusive techniques, namely, infrared thermography measurements of the substrate external surface temperatures and fluid temperature measurements obtained through Laser Induced Fluorescence. A very good agreement among the proposed hybrid methodology predictions, a finite elements solution from the COMSOL code, and the experimental findings has been achieved. The proposed methodology has been demonstrated to be quite flexible, robust, and accurate. The hybrid nature of the approach, providing analytical expressions in all but one independent variable, and requiring numerical treatment at most in one single independent variable, makes it particularly well suited for computationally intensive tasks such as in optimization, inverse problem analysis, and simulation under uncertainty.