Conjugated heat transfer in complex channel-substrate configurations: Hybrid solution with total integral transformation and single domain formulation

Integral transforms have been extensively employed in the analysis of linear and nonlinear convection-diffusion problems, in light of the robust, precise and cost-effective hybrid numerical-analytical solutions that can be achieved in several different classes of problems in heat and fluid flow. In recent years, a single domain reformulation strategy has been introduced which, in combination with the Generalized Integral Transform Technique (GITT), allows for the straightforward handling of complex geometries, rewritten with space variable equation coefficients such as in heterogeneous media. This work further advances the solution of conjugated heat transfer problems for complex channel-substrate geometrical configurations through the GITT approach, here combining a single domain formulation and a total integral transformation scheme based on a multidimensional eigenvalue problem. An application is considered more closely to illustrate the approach for a two-dimensional geometry, consisting of a horseshoe-like microchannel within a rectangular substrate. The results presented demonstrate the adequacy of the solution methodology for the thermal analysis and design of thermal microsystems with complex shapes.