Determination of the divergence of calculation methods for heat gain though walls

Response factor methods have been developed and recommended by ASHRAE for c alculation of heat transfer through walls. These methods compute heat trans fer fluxes based on the past history of wall surface temperatures. Subseque nt developments such as conduction transfer functions (which are derived fr om response factors) and weighting factors offer shorter calculation sequen ces and require smaller storage of past temperature and heat flux values. B ur these methods are recursive in nature such that past calculated heat flu : values are used to calculate a new value. When the energy balance procedu re is applied at the wall surfaces to further improve the vigor of the heat -transfer-calculation procedure, the new temperatures of the wall surfaces become additional unknowns. Both heat flux and temperature values are calcu lated recursively considering the energy balance at the surfaces. A systems approach is presented for examining such recursive calculation procedures. The results reveal that known recursive calculation procedures converge wh en surface temperatures of the walls are given such as through the use of s ol-air temperature. But when an energy balance is applied, there is an incr eased tendency for the recursive calculation to diverge. The divergence may be inferred from the stability property of an analogous dynamic system.