Response factor methods have been developed and recommended by ASHRAE for calculation of heat transfer through walls. These methods compute heat transfer fluxes based on the past history of wall surface temperatures. Subsequent developments such as conduction transfer functions (which are derived from response factors) and weighting factors offer shorter calculation sequences and require smaller storage of past temperature and heat flux values. But these methods are recursive in nature such that past calculated heat flux values are used to calculate a new value. When the energy balance procedure 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 calculated 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 when surface temperatures of the walls are given such as through the use of sol-air temperature. But when an energy balance is applied, there is an increased tendency for the recursive calculation to diverge. The divergence may be inferred from the stability property of an analogous dynamic system.

Reprinted from the International Journal of Heating, Ventilating, Air-Conditioning and Refrigerating Research, Vol. 7, No. 1, January 2001, pp. 15-30.

Units: SI