Forced convective heat transfer for Stokes flow including viscous dissipation in arbitrary corrugated channels

Abstract

The forced convective heat transfer for Stokes flow, including viscous dissipation in arbitrary corrugated channels, is studied using both an asymptotic method and a numerical solution. The aim is to specify the range of shape parameters for which the validity of the asymptotic approach is ensured, particularly regarding the characteristics of heat transfer. The axial velocity, transversal velocity, pressure, and temperature, for small corrugation's slope compared with unity, are sought as an asymptotic expansion in terms of a parameter that represents the corrugation's slope. The numerical solution is obtained by using ANSYS Fluent solver. Additionally, Python scripting is integrated to automate several parts of the simulations, including the creation of the geometry and a parametric study. Three different types of corrugations are investigated including zigzag, sinusoidal, and arbitrary corrugations defined using a function given by a particular case of the Fourier series. The Nusselt number is calculated to evaluate convective heat transfer. It is found that the asymptotic and numerical solutions for small corrugation's slope, are in good agreement with negligible quantitative differences. However, as the corrugation's slope increases (approaches unity), these quantitative differences increase up to cases where a change in the behavior of the local Nusselt number is observed. The results show that the local Nusselt number decreases in the channel's region with divergent walls due to the decrease in the average velocity. In contrast, it increases in the channel's region with convergent walls due to the increase in the average velocity.