# The Influence of the Initial Condition in the Transient Thermal Field Simulation Inside a Wall

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## Abstract

**:**

## 1. Introduction

## 2. Objectives and Methods

#### 2.1. Measurement Experimental Test Setup

^{2}K)). The composition of the envelope wall can be seen in Figure 2 and Table 1. Results related to similar issues have been published in recent years in [30,31,32,33].

#### 2.2. Applicability of the Measured Data

#### 2.3. Transient Numerical Simulation

#### 2.4. Methodology for Determining Initial Temperature Conditions

- In the second case: in time t = 0, the steady state temperature is calculated from the air temperatures: Exterior air is −13 °C, and interior air is 20 °C (BC −13 °C).
- In the third case: in time t = 0, the steady state temperature is calculated from the air temperatures: Exterior air is −3.42 °C, and interior air is 20 °C (BC −3.42 °C).
- In the fourth case: in time t = 0, the steady state temperature is calculated from the current ambient temperatures, without using start-up pre-calculation (BC without start-up).
- In the fifth case: start-up pre-calculation is used (calculation before t = 0 h, with a duration of one day), (BC start-up).

#### 2.5. Structure Specimens: Material Parameters

#### 2.6. Boundary Conditions

## 3. Results and Discussion

#### 3.1. Numerical Experiment Results

_{e}, as shown in Figure 6). The boundary condition of interior temperature is a constant value of 20° over the presented time period (θ

_{i}). Figure 9 shows sandstone; Figure 11 shows AAC; and Figure 14 shows AAC + EPS-simulated temperature profiles, after 0, 12 and 24 h. Temperature profiles are plotted to show their compliance with different IC considerations.

#### 3.2. Model Validation with a Full-Scale On-Site Experiment

#### 3.3. Discussion

## 4. Conclusions

- Building structures with a complicated geometry, e.g., analysis of thermal bridges (2D, 3D)
- Building structure made of different building materials (window/wall connection), e.g., protruding building structures (cornice, pilaster, balcony, etc.)
- Building structure containing innovative thermal insulations with small building thicknesses and low values of thermal conductivity (reflective and vacuum insulation).

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclatures

AAC | autoclaved aerated concrete |

EPS | expanded polystyrene |

HAM | heat-air-moisture |

ρ | bulk density, (kg/m^{3}) |

c | specific heat capacity J/(kg·K) |

λ | thermal conductivity W/(m·K) |

a | thermal diffusivity (m^{2}/s) |

q | heat flux (W/m^{2}) |

Zq | heat source (W/m^{3}) |

T | thermodynamic temperature (K) |

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**Figure 5.**Sample structures, according to Table 2 (inside left). (

**a**) An external test cell wall; and (

**b**) simple AAC and sandstone walls. The placement position for the plotted data are: the calculated temperatures in Figure 8 and Figure 10 in specimen S2/S3, in Figure 12 and Figure 13 in S1 and the measured temperatures in Figure 15, Figure 16 and Figure 17 in specimen S1.

**Figure 6.**Measured, sinusoidal and constant ambient air temperature over the selected time period as the boundary condition used to determine the initial temperature conditions, as according to Section 2.4.

**Figure 7.**The measured temperature values of the interior and exterior surfaces for the analyzed interval (14 February 2015 to 19 February 2015).

**Figure 9.**Temperature profile across the simple sandstone test wall at time t = 0 h, t = 12 h and t = 24 h for five cases under the initial condition. Abbreviations IC and BC refers to Section 2.4.

**Figure 11.**Temperature profile across the simple AAC test wall at time t = 0 h, t = 12 h and t = 24 h for five cases under the initial condition. Abbreviations IC and BC refers to Section 2.4.

**Figure 14.**Temperature profile across the outdoor test cell wall (AAC + EPS) at time t = 0 h, t = 12 h and t = 24 h for five cases under the initial condition. Abbreviations IC and BC refers to Section 2.4.

**Figure 15.**Plotted calculated and measured temperature courses in the outdoor test cell wall S1 in Position 1 during the chosen time period—with and without pre-calculation considerations.

**Figure 16.**Plotted calculated and measured temperature courses in the outdoor test cell wall S1 in Position 2 during the chosen time period—with and without pre-calculation considerations.

**Figure 17.**Temperature profile across the outdoor test cell wall S1 at t = 0 h, t = 24 h and t = 48—with and without pre-calculation considerations.

No. | Test-Wall Layer | d (m) | λ_{D} (W/(m·K)) | c (J/(kg·K)) | ρ (kg/m^{3}) |
---|---|---|---|---|---|

1 | AAC | 0.300 | 0.104 | 900 | 350 |

2 | Foam PUR | 0.010 | 0.040 | 800 | 35 |

3 | EPS polystyrene graphite | 0.170 | 0.033 | 920 | 16 |

4 | Adhesive mortar | 0.002 | 0.850 | 900 | 1300 |

5 | Primer basic paint | - | - | - | - |

6 | Silicone additive plaster | 0.002 | 0.700 | 900 | 1700 |

**Table 2.**Composition of the specimens (the layers are numbered from the inside in the direction of the heat flow) and physical properties of the material.

No. | Structure Specimens | Name of Layer | λ W/m·K | c J/kg·K | ρ kg/m ^{3} |
---|---|---|---|---|---|

S1 | Outdoor test cell wall (AAC + EPS) | AAC | 0.106 | 900 | 350 |

EPS | 0.035 | 920 | 16 | ||

S2 | Simple AAC wall | AAC | 0.106 | 900 | 350 |

S3 | Wall from sandstone | Sandstone | 1.700 | 840 | 2600 |

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**MDPI and ACS Style**

Zozulák, M.; Vertaľ, M.; Katunský, D.
The Influence of the Initial Condition in the Transient Thermal Field Simulation Inside a Wall. *Buildings* **2019**, *9*, 178.
https://doi.org/10.3390/buildings9080178

**AMA Style**

Zozulák M, Vertaľ M, Katunský D.
The Influence of the Initial Condition in the Transient Thermal Field Simulation Inside a Wall. *Buildings*. 2019; 9(8):178.
https://doi.org/10.3390/buildings9080178

**Chicago/Turabian Style**

Zozulák, Marek, Marián Vertaľ, and Dušan Katunský.
2019. "The Influence of the Initial Condition in the Transient Thermal Field Simulation Inside a Wall" *Buildings* 9, no. 8: 178.
https://doi.org/10.3390/buildings9080178