Approximation errors in the heat flux integral of the discrete transfer method, part 1: transparent media

A method is presented to quantify truncation errors in the discrete transfer method due to discretization of the heat flux integral (hemisphere discretization error) and enclosure boundaries (surface discretization error) for radiation problems involving transparent media. The hemisphere discretization error is generally the larger of the two. Its rate of decay with increasing ray number NR depends strongly on the degree of continuity of the intensity field. For continuous intensity distributions the rate of error decay is proportional to 1/NR, but for piecewise-continuous fields the rate is proportional to 1/square root NR. The surface discretization error causes a small systematic error in the average surface heat flux in a finite-volume CFD/heat transfer calculations. The success of our theory has paved the way to economical error estimation in practically relevant cases.