DESCRIPTION AND PREPARATION OF THE CASE
In recent years, thermal efficiency in buildings has become one of the main concerns of architects and engineers when designing and constructing a building. According to the Spanish Institute for Diversification and Saving of Energy (IDEA), in Spanish households heating can account for up to 64% of the consumption in a single-family home on average. It is therefore interesting to bring about a reduction in expenditure, from an economic and environmental point of view.
Currently, most buildings and homes have water radiator heating systems. The positioning of these in the home is critical for energy efficiency and the tenants’ comfort. Normally, the radiators are located below the windows. It is often thought that this is because under the windows there is no furniture and therefore a good place to install them. However, they are put there for a reason, and that is to create a thermal curtain.
This concept will be explained below.
The case assigned to us is that of a single-family house remodeled by the company Quilding. Once the model and the distribution of the furniture were provided, the radiators were placed in the positions indicated above, under the windows.
In this way, by using computational fluid dynamics techniques (CFD), it is possible to observe in detail the physical phenomena that the air is subjected to when the heating is turned on.
As often happens in fluid simulations, the case should be simplified. This does not result in a loss of accuracy in the results, but certain objects may be insignificant for the movement of the air and, moreover, can greatly complicate the mesh; i.e. the discretization of the domain in finite volumes in which the Navier-Stokes equations (which in turn must be discretized numerically) will be solved.
The apartment has 3 bedrooms, a living room, a bathroom, and a kitchen. In all the rooms except the bathroom there are windows, so the radiators were fitted under them as mentioned above and can be seen in the following image of the floor plan.
The most important phenomena that occur in heating are natural convection and radiation:
Convection requires a material medium for it to happen since it is the movement of liquid molecules by advection processes (transport of the particles) and/or diffusion. The hot air rises above the cold air due to the difference in density and a flow is created by gravity through which hot air rises to the ceiling, cools down and descends, creating a constant circulation.
Radiation (in this case thermal) does not need a material medium. Electromagnetic waves and subatomic particles transport energy from one body to another. The equation that defines the power radiated by a body is the following:
Where ε s the emissivity of the body that radiates (1 in an ideal black body) and σ is the Stefan-Blotzmann constant: σ = 5,6703 e-8 W/m2K4.
Severe cold conditions were simulated which were: an outside temperature of around 0 degrees; standard single-pane windows (typical in an average Asturian house); and the temperature of the internal surface was 5 degrees higher than that of outside.
This very close value is due to the poor insulation of a typical window and the heat conduction from inside to outside. We started from this assumption, although in this simulation there wouldn’t be any conductive effects as even though they could be calculated (through “conjugated heat transfer”), this was not the objective.