Abstract :
If values of ambient temperature and room temperature are known at hourly intervals, the heat flow to or from the room at some specified time can be computed in terms of the values of recent temperatures and heat flows, weighted by values of a series of N wall transfer coefficients, bk, or ck, and dk, (k = 0 to N). These coefficients have hitherto been found by frequency domain methods. It is shown here that they can be evaluated using elementary time domain solutions for wall heat flow. A multi-layer wall with surface films representing radiant and convective exchange is discussed. Using suitable transmission matrices, solutions for the steady-progressive and transient temperature profiles through the wall are derived. The value of N and the wall dk values follow immediately from the wall decay times of the transient solution, together with the choice of 1 hour as time interval. Using a development of Fourier analysis, the steady-progressive and transient solutions are combined so as to provide the time-domain solution for the response to an imposed ramp in ambient or room temperature. Combination of three such ramps forms a triangular temperature pulse of excitation and the infinite series of wall response factors—hourly values of heat flow at and after the temperature peak—serve to describe the response of the wall when excited by such a pulse. The values of bk and ck follow from the response factors. The procedure is illustrated numerically.
