Estimation of total equivalent temperature difference values for multilayer walls and flat roofs by using periodic solution

A theoretical methodology was developed to find total equivalent temperature difference (TETD) values for multilayer flat roofs and walls of buildings. The TETD values based on time lag and decrement factor are estimated using measured hourly solar radiation on a horizontal surface and outside air temperatures. The time lag and decrement factor are obtained numerically using periodic solution of one-dimensional transient heat transfer problem for the building structures. The problem is initially formulated using a differential equation and the appropriate initial and boundary conditions. It is then converted into dimensionless form and solved by application of complex finite Fourier transform (CFFT). The solution is used to find hourly variation of temperature inside the structure, the heat gain to the building through the structure, the highest and lowest temperatures at the inner and outer surfaces of the roofs and walls, and the time periods involved in reaching these temperatures. Sol-air temperatures for different directions as well as time lag and decrement factor are obtained, and these are used to determine the TETD values of the structures.