Integral Transforms with Single Domain Formulation for Transient Three-Dimensional Conjugated Heat Transfer

Abstract

An analysis based on integral transforms is undertaken for transient three-dimensional conjugated conduction-convection heat transfer, with a focus on mini or micro channels-based devices. The numerical-analytical approach Generalized Integral Transform Technique (GITT) is combined with a single domain reformulation, providing accurate, robust, and cost-effective simulations for determining temperature distributions within the domain. The fluid and solid subdomains are represented as one single region, while the integral transformation is carried out using a three-dimensional eigenvalue problem encompassing the thermophysical properties and velocity field abrupt spatial variations. The steady state problem solution is employed as a filter and solved through an integral transformation based on the corresponding two-dimensional eigenvalue problem defined for the channel cross section. The transformed ordinary differential systems for both the steady and homogeneous transient problems are handled analytically, requiring only the numerical solution of the associated matrix eigensystem analysis. Converged numerical results for dimensionless temperature distributions are then critically compared with a finite element solution and a previously proposed GITT solution that implements a partial transformation scheme under a pseudo-transient formulation, both for the conjugated problem with thermally developing laminar flow in a rectangular channel.