Finite-difference prediction of transient indoor temperature and related correlation based on the building time constant

A numerical procedure for the calculation of the transient indoor temperature in buildings is developed. The procedure is based on an implicit finite-difference solution of a closed set of differential equations, which express the indoor energy balance and the transient heat conduction in all elements of the building envelope. Using the above procedure, calculations are carried out for 21 types of buildings with 18 and 10 different kinds of wall and roof constructions, respectively, i.e. the total number of building cases examined is 21 x 18 x 10 = 3780 with floor areas ranging from 30 m(2) to 3000 m(2). It is found that buildings of different construction characteristics and sizes but with the same time constant, respond in a similar way under the same outdoor temperature variation. Based on this similarity, a correlation is developed which expresses, under periodic conditions, the indoor temperature variation in terms of the building time constant and the outdoor temperature characteristics. The correlation contains nine coefficients, the values of which are different for different ranges of the building time constant.