# Dynamic Heat Transfer Calculation for Ground-Coupled Floor in Emergency Temporary Housing
## 1 Introduction  
Building simulation tools are often used to evaluate the indoor thermal environment and energy demand of buildings. Because of the lack of straightforward mathematical expressions, calculating fast and accurately the ground-coupled heat transfer is a difficult task [1]. Heating losses to the ground could be around 50% of annual building energy consumption, particularly for low-rise buildings [2]. The interest and importance of ground-coupled floor heat transfer attract researchers to develop various calculation methods. These methods could be categorized into five groups: simplified method, analytical solution, numerical modeling, response factor method, and artificial intelligence-based method [3, 4]. Simplified methods, such as the ASHRAE slab-on-grade heat transfer calculation method [5] and the ISO 13370 simplified method [6], could provide quick calculations of stead-state or long-time heat transfer, which are derived from analytical or empirical results. The DOE-2.1e building simulation software uses a one-dimensional approximation methodto calculate the transient ground heat transfer. However, a higher and delayed peak heat flux was reported when it was compared with numerical results [7]. In fact, there was no success in finding three-dimensional transient analytical solutions, even for a simple slab-on-grade problem [1]. Only if a harmonic time-dependence heat transfer was assumed could long-time solutions be expressed as a function of a steady-state solution and an angular frequency. In 1983, [PERSON] et al. [8] derived a two-dimensional and a three-dimensional steady-state solution for rectangular floors. That could be used when temperature or heat flux is specified at the floor surface. As for mixed temperature-flux conditions, an approximation approach was also presented by [PERSON] [9]. Then, [PERSON] [10] developed a three-dimensional approximation solution based on [PERSON]'s two-dimensional solution, and other researchers extended it to a calculation for arbitrary floor shapes [11]. A numerical method is also an option in building simulation software such as EnergyPlus and TRNSYS. In EnergyPlus, a finite-difference processor module is used to calculate the monthly average temperature under a concrete slab [12]. Varieties of parameters, including climate, floor shape, soil condition, and building shading, can be inputted into the module. Similarly, ground contact slab temperature is calculated at every time step through a three-dimensional finite-difference slab model in TRNSYS [2]. Obviously, it costs a longer computation time. The thermal response factor method, presented by [PERSON] and [PERSON] [13,14], describes the heat transfer characteristics of building components as a series of response factors or transfer functions. It involves less arithmetic than finite-difference calculation, which means a higher computational efficiency [15]. However, its use on three-dimensional problems seems to be difficult. In general, a one-dimensional approximation model combining numerical or empirical values is necessary [16]. Although there might be large inaccuracy, it is still a workable approach for dealing with complex floor configuration situations [7,17]. Artificial intelligence-based methods predict building heat loads according to variables such as climate conditions and building characteristics. Compared with the complex models built in building simulation tools, artificial intelligence models have the advantages of model simplicity, fast calculation speed, and high accuracy. On the other hand, the models require historical data to train the model and require to be re-trained for different buildings [4]. Differently from conventional buildings, temporary housing usually is constructed directly on the ground and has a shorter life cycle [18, 19, 20, 21, 22]. Thus, the ground-coupled heat transfer could not reach an annual periodic state [23]. The annual periodic assumption would cause an underestimation of ground-coupled floor heat losses in temporary housing.