Theoretical analysis of conjugated heat transfer with a single domain formulation and integral transforms

Abstract

The present work advances an analytical approach for conjugated conduction-convection heat transfer problems, by proposing a single domain formulation for modeling both the fluid stream and the channel wall regions. Making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid-wall interface, the mathematical model is fed with the information concerning the transition of the two domains, unifying the model into a single domain formulation with space variable coefficients. The Generalized Integral Transform Technique (GITT) is then employed in the hybrid numerical-analytical solution of the resulting convection-diffusion problem with variable coefficients, and critically compared for two alternative solution paths. A test problem is chosen that offers an exact solution for validation purposes, based on the extended Graetz problem including transversal conduction across the channel walls. The excellent agreement between approximate and exact solutions demonstrates the feasibility of the approach in handling more involved conjugated problems.