Determination of wall decay times by use of a polynomial equation

The determination of the thermal decay times of the wall of a building is an essential step in calculating the wall’s thermal transfer coefficients. The series of decay times zj is normally found by varying time z and searching for zeros of e12, one of the four elements of the wall transmission matrix. It is demonstrated here that they can be efficiently found by expressing e12 as a polynomial as a function of time z and then solving the polynomial for e12 = 0. The method is illustrated by wall examples whose decay times are known by other means. A simple procedure is demonstrated to check whether any solutions have been missed. The article summarises an existing procedure to check for missing roots of e12 by also finding solutions to e11 = 0 and in an appendix shows the structure of the solutions which are found when all four values of eik of the transmission matrix are set equal to zero.