High accuracy heat flow calculation: a method to calculate the heat flow for an arbitrary wall with constant material properties in a natural climate.

The paper describes a method to calculate the heat flow through a multiple layer wall in a natural climate. The thermal properties needed for the calculation are the thermal resistance and the heat capacity of each layer, and they are assumed to be independent of the temperature. The natural climate can be measured temperatures, either surface temperatures or temperatures of the surrounding air. The method is based on well-known equations for calculating the heat flow due to a sinusoidal temperature variation. The natural climate is first transformed to a sum of periodical variations by using Fourier analysis. The heat flow is then obtained as the sum of the heat flows caused by the individual temperature components. In the paper, there is a comparison between the heat flows calculated with an analytical, exact solution and the heat flows calculated with the suggested method for a single layer wall exposed to a sudden external temperature step. The proposed method gives results close to the exact solution. There is also a comparison of the thermal performance of three walls, a light wooden stud wall, a gas concrete wall and a heavy concrete sandwich wall. All three are exposed to a temperature step on the external side and the heat flows on the internal side are calculated. The suggested method to calculate the heat flow through a wall in a natural climate is a good alternative to existing finite difference and finite element methods. The only approximation needed is to describe the boundary temperatures with Fourier series. After this approximation, all remaining calculations are exact.