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The utility of building heating and cooling load calculation methods depends on accurate and rapid determination of transient heat flows through walls, roofs, and floors. The transfer function approach is a recent advance which can replace toe direct, but time-consuming, numerDcal solution of the governing differential equations. In this approach, the heat flux through the surface is expressed algebraically as a function of previous values of heat fluxes and temperatures. The evolution of this method is described by Stephenson, Mitalas, Arseneault and Kusuda in a series of papers (1,2,3,4,5,6), and is incorporated in the recent edition of the ASHRAE Handbook of Fundamentals (7).

The equation for heat flux through any wall or roof to a room at constant temperatures is given by the finite series (7, page 25.28)