Conjugated Heat Transfer With Slip Flow in Microchannels: Single Domain Integral Transforms With Enhanced Convergence

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

“…(8a)-(8b,c), which does not allow for a closed-form solution. Although the GITT itself can be readily employed to solve this eigenvalue problem [3,13,15], the convergence rates can become fairly slow, due to the multiscale behavior of the governing coefficients, requiring the implementation of a convergence enhancement technique for computational savings, such as the Integral Balance procedure [11,12], which can be employed to derive analytical expressions to accelerate the eigenfunctions expansion convergence [20,21].…”

“…Therefore, based on a very recent development regarding the convergence acceleration of eigenfunction expansions for Sturm-Liouville problems [20,21], employing an integral balance analytical procedure [11,12], the present work proposes the combination of the single domain formulation and the integral transforms method to accurately and efficiently handle the conjugated heat transfer problem within circular microchannels in the slip flow regime, including axial diffusion effects. For verification purposes, a steady or quasi-steady state test problem with hydrodynamically fully developed and thermally developing flow is addressed.…”