Conjugate Heat Transfer Within a Heterogeneous Hierarchical Structure

Optimization of heat exchangers (HE), compact heat exchangers (CHE) and micro-heat exchangers by design of their basic structure is the focus of this work. Consistant models are developed to describe transport phenomena in a porous medium that take into account the scales and other characteristics of the medium morphology. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. The description of the structural morphology determines the importance of these terms and the range of application of the closure schemes. A natural way to transfer from transport equations in a porous media with integral terms to differential equations with coefficients that could be experimentally or numerically evaluated and determined is described. The relationship between CFD, experiment and closure needed for the volume averaged equations is discussed. Mathematical models for modeling momentum and heat transport based on well established averaging theorems are developed. Use of a ‘porous media’ length scale is shown to be very beneficial in collapsing complex data onto a single curve yielding simple heat transfer and friction factor correlations. The general transport equations developed for a single phase fluid in a heat exchange medium have many more integral and differential terms than the homogenized or classical continuum mechanics equations. Once these terms are dealt with by closure, the resulting equation set is relatively simple and their solution is obtained using simple numerical methods quickly enough for multiple parameter optimization using Design of Experiment (DOE) or Genetic Algorithms (GA). Current efforts to significantly improve the performance of a HE for electronic cooling, a two temperature problem, and of a finned tube heat exchanger, a three temperature problem, are described.