Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms

The present work advances a recently introduced approach based on combining the Generalized Integral Transform Technique (GITT) and a single domain reformulation strategy, aimed at providing hybrid numerical–analytical solutions to convection–diffusion problems in complex physical configurations and irregular geometries. The methodology has been previously considered in the analysis of conjugated conduction–convection heat transfer problems, simultaneously modeling the heat transfer phenomena at both the fluid streams and the channels walls, by making use of coefficients represented as space variable functions with abrupt transitions occurring at the fluid–wall interfaces. The present work is aimed at extending this methodology to deal with both fluid flow and conjugated heat transfer within arbitrarily shaped channels and complex multichannel configurations, so that the solution of a cumbersome system of coupled partial differential equations defined for each individual sub-domain of the problem is avoided, with the proposition of the single-domain formulation. The reformulated problem is integral transformed through the adoption of eigenvalue problems containing the space variable coefficients, which provide the basis of the eigenfunction expansions and are responsible for recovering the transitional behavior among the different regions in the original formulation. For demonstration purposes, an application is first considered consisting of a microchannel with an irregular cross-section shape, representing a typical channel micro-fabricated through laser ablation, in which heat and fluid flow are investigated, taking into account the conjugation with the polymeric substrate. Then, a complex configuration consisting of multiple irregularly shaped channels is more closely analyzed, in order to illustrate the flexibility and robustness of the advanced hybrid approach. In both cases, the convergence behavior of the proposed expansions is presented and critical comparisons against purely numerical approaches are provided.