Radiosity Model and Compensation Theorem

Abstract

Abstract In the preceding conference contribution called “Radiative Heat Transfer in Buildings”, a general model for radiative heat transfer in inner spaces of buildings has been developed. The model is capable of determining radiosities, heat fluxes and heat flows with each surface of the interior. In closed spaces like interiors, the radiative energy should be conserved so that the total heat flow should be zero. This property may be formulated as the compensation theorem and should be mirrored in each reasonable model. Thus, it is desirable to verify whether our developed model satisfies such a property. The mathematical proof has been presented which has confirmed that the developed model obeys the compensation theorem. As a numerical illustration, radiative heat flows in a simple room have been computed and their total sum has been quantified and shown that this summation leads to zero value. The numerical illustrations start with formulating matrix of view factors that describe the ‘mutual visibility’ of interior surfaces and in this way they assist to redistribute radiative heat among the interior surfaces. As soon as the matrix of view factors is established, the system of algebraic equations is formed. These equations serve for computing surface radiosities. The radiosities enable estimating heat fluxes and heat flows occurring in the interior. Some of the heat flows are positive and some are negative. The positive value of heat flow means that the corresponding surface emits energy into the interior whereas the negative value indicates that the corresponding surface absorbs energy from the interior. By summing the positive and negative values of heat flows, the total heat flow can be obtained whose value is zero in agreement with the compensation theorem.