Thermal radiation heat transfer in one- and two-dimensional enclosures using the spectral collocation method with full spectrum k-distribution model

Abstract

Thermal radiation transfer in one-dimensional parallel plates and two-dimensional rectangle enclosures filled with non-gray gases, namely CO2, H2O, or their mixtures, is calculated using the spectral collocation method with full spectrum k-distribution model (SCM–FSK). The k-distribution model is a promising model for treating the spectral properties of an absorbing–emitting medium, representing an alternative to line-by-line calculations which reduces the number of radiative transfer equation (RTE) evaluations from the order of a million to the order of ten without any significant loss of accuracy. Moreover, the full spectrum k-distribution model, as a global model, can be easily combined with other numerical methods to solve the RTE. The spectral collocation method (SCM) which is used to solve partial differential equations is combined with FSK for the present problems. In order to test the accuracy and efficiency of SCM–FSK, several gas radiation transfer problems involving isothermal/non-isothermal and homogeneous/inhomogeneous non-gray gases are examined. The results obtained by SCM–FSK are assessed by comparing the predictions with line by line results. These comparisons indicate that SCM–FSK is sufficiently accurate and convenient for engineering calculations.