Periodic solution of transient heat flow through multilayer walls and flat roofs by complex finite Fourier transform technique

An analytical solution method for the estimation of space heat gain through multilayer walls and flat roofs submitted to periodic boundary conditions is developed. Formulation of the transient heat transfer problem consisting of differential equation and the initial and boundary conditions is converted into dimensionless form and it is solved by the application of complex finite Fourier transform (CFFT) technique. This analytical solution is used to determine hourly variation of heat flow into the space through the walls and the temperature at the inner surface of the walls. A computer program is developed based on the analytical model to perform numerical calculations considering six different wall and two different roof constructions, characteristics to the buildings in Turkey. The CFFT technique provides itself as an alternative to other analytical and numerical methods and it appears to be useful in that it allows the calculations to be performed for various multilayer wall and roof constructions and for various climatological locations with varying ambient air temperatures and solar heat inputs.