A Coupled Approach to Predict Microscopic Temperature Distribution Inside a Unit Cell of Nonisothermal Laminar Flow in Periodic Porous Media
Kuang‐Ting Hsiao, Suresh G. Advani · Journal of Porous Media · 2002
A method to compute the microscopic temperature distribution inside a unit cell for a laminar flow of an incompressible fluid in periodic porous media is presented in this paper. Previous approaches have only exploited the similarity of the periodic unit cells to assume the microscopic unit cell problem regardless of its comformity with the macroscopic energy balance. In this article, we consider both the similarity and compatibility with the macroscopic temperature distribution to pose the nonisothermal unit cell problem. The natural mode temperature solution of the macroscopic energy balance equation is used as the macroscopic solution to derive the unit cell problem. Aperiodic unit cell problem with arbitrary structures has been formulated. Its consistency with energy conservation at both the microscopic and macroscopic levels has been examined. Taylor's dispersion solution is found to be a special case of this unit cell solutions. The potential of this method is demonstrated by performing a numerical simulation of nonisothermal laminar Incompressible flow through a two-dimensional in-line cylindrical unit cell. From simulation results, the total effective thermal conductivity of the unit cell is calculated and compared with reported experimental results. The good agreement confirms the validity of this approach. This inverse unit cell approach makes it possible to evaluate the influence of the heat capacity ratio of the fluid and the solid which was not possible to study with previous numerical unit cell approaches.