Applying recent efficient numerical methods for long-term simulations of heat transfer in walls to optimize thermal insulation

Abstract

Since transient simulations are quite resource intensive, the winter heat loss through building walls is often estimated by simple steady-state calculation based on e.g. the Degree-days method, which is often rather inaccurate. In this work, transient simulations are performed using the very recent leapfrog-hopscotch and modified Dufort-Frankel techniques, which are the most effective explicit and stable numerical algorithms to cope with heat transport issues, according to prior investigations. The optimum insulation thickness, energy savings, and payback time are determined using an economic model that takes into account the orientation of the outside walls, solar radiation, the cost of insulating material, the present cost of energy consumption, and the cost over the 25-year lifetime of a building in Miskolc City and a case is studied in the cold season. Three materials (Expanded Polystyrene (EPS), glass-wool, and rock-wool) and several thicknesses are examined. As a result, it was found that for the north-oriented wall, the optimum insulation thickness is (17, 22, and 12 cm) and the life cycle energy savings are (142.5, 153, and 132.12 kWh/m2) for the EPS, glass-wool, and rock-wool, respectively, while the payback time is (3.73, 3.14, and 4.33 years). According to the analysis of the life cycle energy savings, the optimal insulation properties can be achieved using 22 cm thick glass wool, which only slightly depends on the orientation of the wall.