Wall transient heat flow using time-domain analysis

If values of ambient temperature and room temperature are known at hourly intervals, the heat pow to or from the room at some specified rime can be computed in terms of the values of recent recent temperatures and heat flows, weighted by values of a sei ies of N wall transfer coefficients, b(k), or c(k), and d(k), (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 rime 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 d(k) 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 lime-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 POW at and after the temperature peak-serve to describe the response of the wall when excited by such a pulse. The values of b(k) and c(k) follow from the response factors. The procedure is illustrated numerically. (C) 1997 Elsevier Science Ltd.