# Application Method of a Simplified Heat and Moisture Transfer Model of Building Construction in Residential Buildings

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## Abstract

**:**

## 1. Introduction

^{2}–10

^{4}times over in a single-zone building. This shows that for complex buildings, more calculation time is required.

## 2. Computational Methods for Coupled Heat and Moisture Transfer

#### 2.1. Mass Balance Equation

^{3}; ${R}_{v}$ is the gas constant for water vapor, J/kg K; ${T}_{z}$ is the zone air temperature, K; ${V}_{z}/\left({R}_{v}\text{}{T}_{z}\right)$ is the moisture capacity of the zone air; ${p}_{v,z}$ is the partial vapor pressure of the zone air, Pa; $\tau $ is time, s; ${\dot{M}}_{i}$ is the internal gain moisture in the zone, kg/s; ${\dot{M}}_{sys}$ is the moisture addition (or removal) by the HVAC system, kg/s; ${A}_{j}$ is the inside wall surface, j, m

^{2}; ${\dot{V}}_{inf}$ is the volume flow rate of infiltration, m

^{3}/s; ${p}_{v,amb}$ is the partial vapor pressure of outdoor air, Pa; ${p}_{v,surf}$ is the partial vapor pressure of the inside wall surface, Pa; and ${\beta}_{j}$ is the water vapor transfer coefficient, kg/m

^{2}s Pa.

#### 2.2. Simplified Model—Effective Moisture Penetration Model

#### 2.3. Detailed Model—Heat and Moisture Transfer Model

^{®}[23], ESP-r [24,25], and EnergyPlus [26] simulation programs. This model is based on the hygrothermal building component calculation model, and is a one-dimensional, finite-element, heat, and moisture transfer model [27,28]. This model uses a heat balance equation and a moisture balance equation, both of which are linked with each other through the moisture dependence of thermal conductivity, the heat source term, and the total enthalpy, as well as through the temperature dependence of the moisture flows:

## 3. Steady-State Moisture Flux Model

_{h,Ttl}, total sensible heat resistance). The steady-state latent heat flux can be calculated based on the vapor pressure difference between the outdoor and indoor air and the moisture resistance (R

_{v,Ttl}, total latent heat resistance) [17,29]. Therefore, the total sensible heat resistance and total latent heat resistance of the wall are shown in Figure 1, and can be expressed as follows:

## 4. Evaluation of Alternatives for Heat and Moisture Transfer Model for Residential Buildings

#### 4.1. Simulation Models

#### 4.2. Simulation Conditions

#### 4.2.1. Climate Conditions

#### 4.2.2. Building Descriptions

## 5. Results

#### 5.1. Very Hot and Humid Climate

#### 5.2. Mixed and Humid Climate

#### 5.3. Cool and Humid Climate

## 6. Conclusions

- (1)
- In Miami, from May to September, the percent difference between the HAMT model and the EMPD+SSMF model was less than 5%. As for the deviation of annual total heat transfer between the HAMT model and the analyzed model, the CTF model coupled with the SSMF model reduced the deviation in the annual total heat transfer from −24% to 2%, compared to the CTF model alone. The SSMF model also decreased the error of the EMPD model from −26% to −10%; cooling coil loads were also reduced.
- (2)
- In Atlanta, the monthly deviations between the HAMT model and the EMPD+SSMF model were the lowest, at 5%, among the analyzed cases. For the CTF model, when coupled with the SSMF model, the deviation in the positive annual total heat transfer decreased from −13% to 3% and that in the negative annual total heat transfer increased from 9 to 11%. For the EMPD model, the error of the positive value was cut down from −13% to −1% by applying the SSMF model, while that of the negative value increased from 10% to 11% by applying the SSMF model.
- (3)
- In Chicago, compared to the monthly total heat transfer calculated by the HAMT model, the SSMF model effectively reduced the errors of the CTF and EMPD models during June to September. The deviation between the HAMT model and the EMPD+SSMF model was less than ±5% in July and August. However, the SSMF model actually increased the error in the overall cooling coil load.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**Total sensible and latent heat resistance of the wall (the symbol EXT represents outdoor, and the symbol INT represents indoor).

**Figure 2.**Simulation process of the steady-state moisture flux model for moisture transfer with the model.

**Figure 4.**Daily heat transfer of all surfaces in Miami (July): (

**a**) sensible heat transfer from all inside surfaces and surface temperature, (

**b**) latent heat transfer from all inside surfaces, and (

**c**) total heat transfer from all inside surfaces.

**Figure 5.**Monthly total heat transfer from surfaces and the monthly percentage difference between models in Miami.

**Figure 6.**Daily heat transfer of all surfaces in Atlanta (July): (

**a**) sensible heat transfer from all inside surfaces and surface temperature, (

**b**) latent heat transfer from all inside surfaces, and (

**c**) total heat transfer from all inside surfaces.

**Figure 7.**Monthly total heat transfer from surfaces and the monthly percentage difference between models in Atlanta.

**Figure 8.**Daily heat transfer of all surfaces in Chicago (July): (

**a**) sensible heat transfer from all inside surfaces and surface temperature, (

**b**) latent heat transfer from all inside surfaces, and (

**c**) total heat transfer from all inside surfaces.

**Figure 9.**Monthly total heat transfer from surfaces and the monthly percentage difference between models in Chicago.

Model | Description | |
---|---|---|

Case1 | CTF | Conduction transfer functions |

Case2 | CTF+SSMF | Steady-state moisture flux with CTF model |

Case3 | EMPD | Effective moisture penetration depth with CTF |

Case4 | EMPD+SSMF | Steady-state moisture flux with EMPD model |

Case5 | HAMT | Combined heat and moisture transfer |

Model | Simulation Run Time (Seconds) | |
---|---|---|

Case 1 | CTF | 700 |

Case 2 | CTF+SSMF | 1080 |

Case 3 | EMPD | 720 |

Case 4 | EMPD+SSMF | 1140 |

Case 5 | HAMT | 6800 |

Location | Latitude | Longitude | Degree Days | Annual Average | Climate Zone | |||
---|---|---|---|---|---|---|---|---|

City | HDD | CDD | Temp (°C) | RH (%) | W (kg/kg′) | |||

Miami, FL | 25°46′27″ N | 80°11′37″ W | 130 | 4458 | 24.5 | 72.6 | 0.0143 | 1A: very hot and humid |

Atlanta, GA | 33°44′56″ N | 84°23′16″ W | 2694 | 1841 | 16.6 | 65.7 | 0.0090 | 3A: mixed and humid |

Chicago, IL | 41°51′00″ N | 87°39′00″ W | 6311 | 842 | 9.9 | 70.3 | 0.0067 | 5A: cool and humid |

Building type | Residential building (two stories) | ||

Building area | 111.53 m^{2} (1200.55 ft^{2}) | ||

Building shape | Prototype building. | ||

Architecture | Exterior wall | Acrylic Stucco + building paper felt + plywood + OSB + fiberglass + dry wall | 0.517 W/m^{2}K (0.091 Btu/h·ft ^{2}·°F) |

Exterior roof | Plywood + OSB | 2.674 W/m^{2}K (0.471 Btu/h·ft ^{2}·°F) | |

Gable | Acrylic Stucco + building paper felt + plywood + OSB + dry wall | 2.727 W/m^{2}K (0.480 Btu/h·ft ^{2}·°F) | |

Ceiling | Fiberglass + drywall | 0.229 W/m^{2}K (0.040 Btu/h·ft ^{2}·°F) | |

Floor | Plywood + concrete | 3.33 W/m^{2}K (0.586 Btu/h·ft ^{2}·°F) | |

Window | Window fraction: North/South (13.14%) and East/West (15.23%) | 2.845 W/m^{2}K (0.501 Btu/h·ft ^{2}·°F) | |

Infiltration | 24 h (effective leakage area method) | 600 cm^{2} (Living) and 370 cm^{2} (Attic) | |

Internal mass | Interior furnishing and lumber truss | 9.99 m^{2} (living) and 35 m^{2} (Attic) | |

HVAC | System | Central electric air conditioning and gas furnace | DX cooling coil and gas heating coil |

Thermostat set-point | 24 h | 23.88 °C (75 °F) Cooling/ 22.22 °C (72 °F) Heating | |

Ventilation | 24 h | 0.151 ACH | |

Internal loads and schedules | Lighting | Internal load schedule. | 1.698 W/m^{2} |

Plug | 2.46 W/m^{2} | ||

People | 117.28 W/person (3 persons) |

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**MDPI and ACS Style**

Kim, J.; Brandemuehl, M.J.
Application Method of a Simplified Heat and Moisture Transfer Model of Building Construction in Residential Buildings. *Energies* **2021**, *14*, 4180.
https://doi.org/10.3390/en14144180

**AMA Style**

Kim J, Brandemuehl MJ.
Application Method of a Simplified Heat and Moisture Transfer Model of Building Construction in Residential Buildings. *Energies*. 2021; 14(14):4180.
https://doi.org/10.3390/en14144180

**Chicago/Turabian Style**

Kim, Joowook, and Michael J. Brandemuehl.
2021. "Application Method of a Simplified Heat and Moisture Transfer Model of Building Construction in Residential Buildings" *Energies* 14, no. 14: 4180.
https://doi.org/10.3390/en14144180