This paper proposes and implements a new methodology for optimizing Finned-Tube Heat Exchangers (FTHEs) using a Volume Averaging Theory (VAT) physical model and a Genetic Algorithm (GA) optimizer. This method allows for multiple-parameter constrained optimization of FTHEs by design of their basic morphological structures.  A consistent model is used to describe transport phenomena in a FTHE based on VAT, which allows for the volume averaged conservation of mass, momentum, and energy equations to be solved point by point, with the morphology of the structure directly incorporated into the field equations and full conjugate effects included. The equations differ from those often presented and are developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in every pore space. These averaged equations have additional integral and differential terms that must be dealt with in order for the equation set to be closed, and recent work has provided this closure for FTHEs.  The resulting governing equation set is relatively simple and is discretized and quickly solved numerically. Such a computational algorithm is fast running, but still able to present a detailed picture of the temperature fields in both of the fluid flows as well as in the solid structure of the heat exchanger. A GA is integrated with the VAT-based solver to carry out the FTHE numerical optimization, which is a ten parameter problem, and the FTHE is optimized subject to imposed constraints. This method of using the VAT-based solver fully integrated with a GA optimizer results in a new all-in-one tool for performing multiple-parameter constrained optimization on FTHEs.

The present paper describes an effort to obtain closure for a Volume Averaging Theory (VAT) based model of a plane fin heat sink (PFHS) with scale-roughened surfaces by evaluating the closure terms for the model using Computer Fluid Dynamics (CFD). Modeling a PFHS as porous media based on VAT, specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts and the VAT based governing equations can be efficiently solved for a wide range of parameters. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a Representative Elementary Volume (REV). The terms in the closure expressions are complex and sometimes relating experimental data to the closure terms is difficult. In this work we use CFD to obtain detailed solutions of flow and heat transfer through an element of the scale-roughened heat sink and use these results to evaluate the closure terms needed for a fast running VAT based code, which can then be used to solve the heat transfer characteristics of a higher level heat sink. The objective is to show how heat sinks can be modeled as a porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort to obtain closure for a VAT based model.