Conjugated heat transfer in circular microchannels with slip flow and axial diffusion effects

An integral transforms analysis is undertaken for conjugated heat transfer in circular microchannels with laminar gaseous flow in the slip flow regime. The solution methodology is based on the Generalized Integral Transform Technique applied to a single domain formulation that models the coupled heat transfer phenomena at the fluid stream and at the channel wall. The single domain formulation results in just one partial differential equation for the energy balance, making use of spatially variable coefficients with abrupt transitions, and accounting for the temperature jump at the interface due to the Knudsen numbers within the slip flow regime. This work extends the single domain formulation strategy, not a priori applicable to problems with discontinuities, by considering a very thin fictitious layer at the fluid-wall interface region, so as to mathematically represent an equivalence to the temperature jump. An integral balance technique for enhancing the convergence of the eigenfunctions is employed, so as to achieve more accurate results and improve convergence for the so derived multiscale problem. The results obtained are critically compared against a dedicated finite difference numerical solution for the original multi-region problem. Results for the Nusselt number are presented in order to investigate its behavior with respect to different Peclet and Knudsen numbers, and different wall thicknesses values, confirming the importance of the combined effects of slip flow, axial conduction and heat transfer conjugation in the analysis.