Forced Convective Heat Transfer for Stokes Flow with Viscous Dissipation in Wavy Channels

Abstract

In this paper, an asymptotic solution of the forced convective heat transfer for Stokes flow including viscous dissipation in a two-dimensional sinusoidal wavy channel is presented. The velocity components, pressure, and temperature distributions are sought as an asymptotic expansion in terms of the amplitude to half-mean-height ratio up to the second order. The Nusselt number is calculated in terms of the amplitude to half-mean-height ratio, 𝛼𝛼, and the half-mean-height to wavelength ratio, 𝜀𝜀. In addition to that, a numerical solution, by using ANSYS Fluent solver and integrating Python scripting to automate several parts of the simulations, is presented to validate the asymptotic solution. It is found that the asymptotic and numerical solutions are in good agreement with slight quantitative differences for 𝛼𝛼 = 0.2 or 𝜀𝜀 = 0.5. However, as 𝛼𝛼 increases further, there is a change in the behavior of the Nusselt number defined at the wall due to the use of Taylor series expansions for the boundary conditions which induces an approximated corrugated channel that differ slightly from the exact sinusoidal channel as 𝛼𝛼 increases.