Analytical periodic solution for the study of thermal performance and optimum insulation thickness of building walls in Tunisia

In Tunisia, the energy consumption in the building sector is rapidly increasing. Recently, very high electric energy consumption, used for air-conditioning loads, is reached during summer days. Insulation of building walls is recently applied with an insulation layer thickness typically ranging between 4 cm and 5 cm, regardless of the climatic conditions, type and cost of insulation material and other economic parameters. In the present study, an optimum insulation thickness is determined under steady periodic conditions. An analytical method, based on Complex Finite Fourier Transform (CFFT), is extended to rigorously estimate the yearly cooling transmission loads for two types of insulation materials and two typical wall structures. Estimated loads are used as inputs to a life-cycle cost analysis in order to determine the optimum thickness of the insulation layer. Results show that, the most profitable case is the stone/brick sandwich wall and expanded polystyrene for insulation, with an optimum thickness of 5.7 cm. In this case, energy savings up to 58% are achieved with a payback period of 3.11 years. The thermal performance of the walls under optimal conditions is also investigated. Then, comparison of the present study with the degree-days method is performed for different values of indoor design temperature.