An assessment of discretization methods for computation of the radiation heat transfer in building enclosures

Abstract

Two different methods to compute local radiative heat flux and mean radiant temperatures inside transparent enclosures are discussed. Both of these methods: the Discrete Ordinates Method (DOM) and the Discrete Transfer Method (DTM) solve the equation of radiative transfer for a discrete number of angular directions. In the DOM a Cartesian grid is used to solve numerically the above equation. It is discovered that sharp intensity gradients rapidly degrade the performance of the DOM in such a way that its accuracy is poor in a room with more than one window or with more than one heat source. Furthermore, it is also discovered that the most common quadrature sets produce large errors in local heat flux calculations. This is due in part to the small number of angular directions available in these sets, and in part to the poor distribution of angular directions and weights that these quadratures present. The Thurgood quadrature family can have as many angular directions as desired and it also has a better distribution of weights and directions. It is recommended and used throughout this thesis. In contrast to the DOM, the DTM solves the equation of radiative transfer along the direction of the beams. A DTM, modified by the author to deal with transparent enclosures, is proposed as an alternative to the DOM. The method developed in this thesis works with short as well as with long wave radiation. Since the DTM does not have the problems of false scattering and false oscillations present in the DOM, it outperforms the DOM in heat flux as well as in mean radiant temperature calculations. In conclusion, it is shown that this novel version of the DTM is a valuable tool to calculate short and long wave radiant heat flux in an enclosure as well as mean radiant temperature in its interior. Therefore this version of the DTM, can be used to design radiant heat panels, to help in the evaluation of comfort conditions inside a building, or together with other models to compute the airflow inside a room.