DE-2548 -- Transfer Functions for Combined Walls and Pitched Roofs PDF

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)