An analytical model of view factors for radiation heat transfer in planar and tubular solid oxide fuel cells

Abstract

Radiant heat transfer plays an important role in the distribution of cell temperature and current density in solid oxide fuel cells (SOFC). The objective of this paper is to introduce a mathematical model of view factors for radiation heat exchange in an in-house longitudinally distributed SOFC model. A differential view factor model is first developed for planar and tubular SOFC configurations, but is found invalid when the infinitesimal element size is comparable to the characteristic size. Then, a finite-difference view factor model is developed to solve the problem of discontinuities in the differential view factor model. Starting from a classical problem of convective and radiant heat transfer for a transparent gas flow in a gray-wall tube, a fast and accurate computation is available for the finite-difference view factor model without extra mathematical derivations of the governing equations. Compared to the simple modeling which only takes into account the surface-to-surface radiation exchange between two directly opposed elements, the detailed radiation model based on analytical view factors predicts more uniform distribution of cell temperature and current density in the overall SOFC modeling.