A thermal model for energy loss through walls behind radiators

A one-dimensional thermal network model is developed for the purpose of predicting the heat transfer behaviour between wall-mounted domestic radiators and outdoor-facing walls. Importantly, the model includes radiation heat transfer between the rear of the radiator and the wall and is able to estimate the resulting heat losses to the outdoors for different thermal loading conditions, such as radiator and outdoor temperatures and wall U-values. To contextualize the problem, a model of a conventional single panel domestic radiator is included so that the energy losses through the wall can be evaluated in terms of the influence on the overall efficiency of the radiator thermal system. Depending on the outdoor condition, the heat losses can be in the region of 5% for poorly insulated walls, highlighting an opportunity for small, yet non-negligible, energy savings if cost effective technologies are deployed to reduce these losses. To this end, the influence of wall-mounted reflector panels, aimed to reduce the heat losses, is evaluated. The reflector panels have two influences: they reduce the overall heat losses thus improving the overall efficiency of the radiator system, and they reduce the total thermal output of the radiator; the magnitude of each depending strongly on the U-value of the wall structure. Finally, two radiation shield concepts are evaluated; one with reflecting surfaces on both sides and one with a highly emissive surface facing the radiator and a low emissivity surface facing the wall. The latter is found to be the best performing radiation barrier as it can increase the total heat transfer into the room whilst significantly reducing the heat losses, whereas the former causes a reduction in the total thermal power of the radiator and lower heat transfer to the room for a commensurate reduction in heat losses.