# Effects of Different Surface Heat Transfer Coefficients on Predicted Heating and Cooling Loads towards Sustainable Building Design

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## Abstract

**:**

## 1. Introduction

^{2}K in 1995 to 0.35 W/m

^{2}K in 2000 [5]. Recent investigations have aimed to further promote building energy efficiency. In particular, Delgarm et al. [6,7] studied a set of building energy efficiency and indoor thermal comfort solutions using a multi-objective optimization approach, where the predicted percentage dissatisfied decreased by 49.1–56.8% and the total energy consumption only increased by 2.9–11.3%. Liu et al. [4] also proposed a building energy efficiency evaluation index to represent the energy-saving performance of buildings. Degree days obtained with the average daily indoor and outdoor air temperatures were used to eliminate the effects of envelopes on the building energy efficiency. However, it was difficult to represent the relationship between the thermal performance of envelopes and the energy consumption of the whole building based on degree days. Hence, the building energy consumption and building energy efficiency evaluation index were no longer suitable for representing the energy efficiency performance of building envelopes during the early stages of office building design.

^{−2}·°C

^{−1}for the SHTC, radiative heat transfer coefficient, and CHTC, respectively. For phase change envelopes [19], the heat flux was assigned to different stages according to the phase change process, thereby leading to segmented SHTCs. To obtain SHTC measurements, Anderson. Ref. [20] illustrates the impact of building envelope on the optimal use of energy. Rui et al. [21] constructed a validated dynamic model for a heated gradient sensor to solve the problem caused by an unsteady-state convective airflow. Thus, experimental methods were established in these previous studies, and constant and dynamically changing values were obtained for building envelopes. In addition to experiments, numerical simulation investigations have been conducted. In particular, Liu et al. [22] investigated CHTCs for the external windward, leeward, lateral, and top surfaces of building arrays and found that large eddy simulation-based CHTCs were more accurate than those obtained by solving Reynolds-averaged Navier–Stokes equations. Kahsay et al. [23] used rectangular floor-plan building models with heights of 3, 10, 15, and 20–30 stories to derive the CHTC correlations based on the Reynolds numbers and building height. Blocken et al. [24] obtained the correlations between CHTCs with the wind speed and direction based on three-dimensional CFD simulations of a low-rise cubic building. Other studies investigated CHTCs according to the effects of the building geometry [25], by deriving new generalized expressions based on analytical formulas [26], by utilizing non-conformal grids [27], and the influence of oblique wind directions [28]. Costanzo et al. [29] found that the DOE-2 algorithm was much less accurate than the adaptive model for cool roofs when the solar reflectivity of the roof was low. Selçuk et al. [30] three building types are analyzed with a novel optimization approach, optimal results are produced for different goals in terms of energy-saving targets. These previous numerical and experimental investigations of SHTCs (CHTCs) have contributed significantly to our understanding of the heat transfer mechanism. However, these studies focused on the correlations with SHTCs under conventional or specific conditions, whereas the effects of different methods or algorithms for selecting SHTCs based on building loads have not been adequately assessed. Thus, the relationship between fundamental research and building energy efficiency design can be improved, and this was the focus of the present study.

- The hourly load behavior on a typical day in winter and summer was studied with different SHTCs.
- The daily cumulative load behavior on a typical day in winter and summer was investigated with different SHTCs.
- The annual cumulative heating and cooling load behavior were examined with different SHTCs.
- Finally, the annual cumulative loads were corrected based on the Thermal Analysis Research Program (TARP) model and compared with those using constant SHTCs.

## 2. Methodology

#### 2.1. Representative Building

#### 2.2. Simulation Process

_{in}and h

_{out}are the SHTCs at the internal and external surfaces, respectively, W·m

^{−2}·°C

^{−1}; h

_{in,c}and h

_{in,r}are the convection and radiation components of h

_{in}; and h

_{out,c}and h

_{out,r}are the convection and radiation components of h

_{out}[38].

_{in,n}was only considered for h

_{in,c}. For the external side, both the natural h

_{out,n}and forced convection components h

_{out,f}were considered for h

_{out,c}, which are given as follows.

_{in&out,n}of TARP-based CHTCs were determined using the temperature difference and direction of the facing surface, as follows:

_{f}is the fitting coefficient, i.e., 1.0 for windward surfaces and 0.5 for leeward surfaces; P is the perimeter of the surface, m; V

_{z}is the local wind speed calculated at the height above ground of the surface centroid, m·s

^{−1}; A is the surface area of the surface, m

^{2}; and R

_{f}is the surface roughness multiplier, which is based on the ASHRAE graph of surface conductance, as shown in Table 3.

_{in,s}and T

_{in,air}are the internal wall surface temperature and air temperature; T

_{out,s}and T

_{out,air}are the external wall surface temperature and air temperature. For comparative studies on a typical day with constant SHTCs, the values at the external surface were 23 W·m

^{−2}·°C

^{−1}in winter and 19 W·m

^{−2}·°C

^{−1}in summer. The value at the internal surface was set at 8.7 W·m

^{−2}·°C

^{−1}for both typical days. For annual cumulative heating and cooling load comparisons with constant SHTCs, the values at the external surface were 23 and 19 W·m

^{−2}·°C

^{−1}, respectively. The value at the internal surface was set at 8.7 W·m

^{−2}·°C

^{−1}all year-round. All of the settings above were selected according to the Code for thermal design of the civil building (GB 50176-2016). The conduction transfer function (CTF) algorithm was employed to solve the heat transfer in building envelopes, as defined in GB 50176-2016. According to the engineering reference for EnergyPlus [39], the time step was selected as 1 h. Weather data comprised the typical meteorological year (TMY) integrated with EnergyPlus [40]. The typical day was 21 January in winter (the indoor temperature was 18 °C for calculations) and 21 July in summer (the indoor temperature was 26 °C for calculations). For the annual cumulative heating and cooling load comparisons, the indoor temperatures for calculations were 18 °C and 26 °C, respectively. The hourly occupancy rate, lighting power density, and equipment power density were 15 W/m

^{2}, air change rate were 0.7 ach, according to related standards.

_{VHTC}, U

_{CHTC,W}and U

_{CHTC,S}are the envelope U-values in the variable HTC model, constant HTC model in winter and constant HTC model in summer respectively; d is the thickness of the corresponding building material, λ is the thermal conductivity.

#### 2.3. Climate Analysis

## 3. Results and Discussion

#### 3.1. Hourly Load Behavior on a Typical Day

#### 3.2. Daily Cumulative Load Behavior on a Typical Day

#### 3.3. Correction of Annual Cumulative Load

#### 3.4. Correction of Annual Cumulative Load

## 4. Conclusions

- (1)
- The hourly building loads on a typical day determined with the TARP model clearly differed from those obtained with the traditional approach. In most conditions, the relative deviation increased as the shape factor increased.
- (2)
- Corrections were obtained for the annual cumulative loads based on the relative deviations between the results produced by the TARP model and with the traditional constant SHTCs. The correction factors were determined as 67.5% and 25.3% for Lhasa with φ = 0.49 and 0.29, respectively. In Xi’an and Beijing, the correction factors determined with φ = 0.49 were 13.3% and 12.0%, respectively. The correction factors were lower than 5.0% for other conditions, thereby indicating that no corrections are required.
- (3)
- The SHTCs and shape factors are readily available types of information that can be used for decision making in the early stages of building design, and they will clearly influence the energy performance of a building through the design stage.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Comparisons between different surface heat transfer coefficients (SHTCs) (convective heat transfer coefficients, CHTCs).

**Figure 3.**Building models and floor plans for the selected office buildings: (

**a**) Building model with φ = 0.49; (

**b**) Floor plan with φ = 0.49; (

**c**) Building model with φ = 0.29; (

**d**) Floor plan with φ = 0.29.

**Figure 4.**Comparison between the estimations of the BLAST and Thermal Analysis Research Program (TARP) programs for an office space on summer design day.

**Figure 5.**Climate characteristics of the five selected cities: (

**a**) Locations of five selected cities; (

**b**) Average temperature and humidity values in TMY.

**Figure 6.**Comparisons of hourly loads with different internal SHTCs on a typical day: (

**a**) Hourly heating load on a typical day in winter; (

**b**) Hourly cooling load on a typical day in summer.

**Figure 7.**Comparisons of hourly loads with different external SHTCs on a typical day: (

**a**) Hourly heating load on a typical day in winter; (

**b**) Hourly cooling load on a typical day in summer.

**Figure 8.**Comparisons of hourly loads with different internal and external SHTCs on a typical day: (

**a**) Hourly heating load on a typical day in winter; (

**b**) Hourly cooling load on a typical day in summer.

**Figure 9.**Comparisons of daily cumulative loads with different SHTCs on a typical day: (

**a**) Indoor side with the TARP model; (

**b**) Outdoor side with the TARP model; (

**c**) Both sides with the TARP model.

**Figure 10.**Boxplots showing the relative deviations in the daily cumulative load on a typical day with different SHTCs: (

**a**) Daily cumulative load on a typical day in winter; (

**b**) Daily cumulative load on a typical day in summer.

**Figure 11.**Comparisons of annual cumulative loads with different internal and external SHTCs: (

**a**) Indoor side with the TARP model; (

**b**) Outdoor side with the TARP model; (

**c**) Both sides with the TARP model.

**Figure 12.**Boxplots showing the relative deviations in the annual cumulative heating and cooling loads with different SHTCs: (

**a**) Annual cumulative heating loads; (

**b**) Annual cumulative cooling loads.

Material | Thermal Conductivity λ (W·m ^{−1}·°C^{−1}) | Density ρ (kg·m ^{−3}) | Specific Heat Capacity c (J·kg ^{−1}·°C^{−1}) |
---|---|---|---|

Cement mortar | 0.930 | 1800 | 1050 |

Rigid polyurethane foam insulation board | 0.022 | 30 | 1380 |

Steam pressurized concrete blocks | 0.200 | 500 | 1005 |

Reinforced concrete | 1.740 | 2500 | 920 |

Lime–sand brick | 1.100 | 1900 | 1050 |

Polyurethane insulation board | 0.030 | 30 | 1380 |

Expanded polystyrene board | 0.049 | 20 | 1400 |

City | Shape Factor | Structure | Construction (from Outside to Inside) |
---|---|---|---|

Xi’an | 0.49 | External wall | 20 mm cement mortar, 100 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 65 mm polyurethane insulation board, 30 mm reinforced concrete | ||

0.29 | External wall | 20 mm cement mortar, 90 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar | |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 45 mm polyurethane insulation board, 30 mm reinforced concrete | ||

Beijing | 0.49 | External wall | 20 mm cement mortar, 100 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 65 mm polyurethane insulation board, 30 mm reinforced concrete | ||

0.29 | External wall | 20 mm cement mortar, 90 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar | |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 45 mm polyurethane insulation board, 30 mm reinforced concrete | ||

Urumqi | 0.49 | External wall | 20 mm cement mortar, 70 mm rigid polyurethane foam insulation board, 180 mm reinforced concrete, 15 mm cement mortar |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 90 mm polyurethane insulation board, 30 mm reinforced concrete | ||

0.29 | External wall | 20 mm cement mortar, 100 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar | |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 65 mm polyurethane insulation board, 30 mm reinforced concrete | ||

Lhasa | 0.49 | External wall | |

Roof | |||

0.29 | External wall | 20 mm cement mortar, 90 mm expanded polystyrene board, 180 mm reinforced concrete, 15 mm cement mortar | |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 45 mm polyurethane insulation board, 30 mm reinforced concrete | ||

Mohe | 0.49 | External wall | 20 mm cement mortar, 75 mm rigid polyurethane foam insulation board, 180 mm reinforced concrete, 15 mm cement mortar |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 100 mm polyurethane insulation board, 30 mm reinforced concrete | ||

0.29 | External wall | 20 mm cement mortar, 70 mm rigid polyurethane foam insulation board, 180 mm reinforced concrete, 15 mm cement mortar | |

Roof | 20 mm cement mortar, 30 mm reinforced concrete, 100 mm steam pressurized concrete block, 90 mm polyurethane insulation board, 30 mm reinforced concrete | ||

All cities | All shape factors | Internal wall | 20 mm cement mortar, 240 mm lime–sand brick, 20 mm cement mortar |

Floor slab | 5 mm cement mortar, 100 mm reinforced concrete, 5 mm cement mortar | ||

Floor | 20 mm cement mortar, 50 mm expanded polystyrene board, 120 mm reinforced concrete |

Roughness | R_{f} | Example |
---|---|---|

Very rough | 2.17 | Stucco |

Rough | 1.67 | Brick |

Medium rough | 1.52 | Concrete |

Medium smooth | 1.13 | Clean pine |

Smooth | 1.11 | Smooth plaster |

Very smooth | 1.00 | Glass |

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**MDPI and ACS Style**

Wu, Y.; Jian, W.; Yang, L.; Zhang, T.; Liu, Y.
Effects of Different Surface Heat Transfer Coefficients on Predicted Heating and Cooling Loads towards Sustainable Building Design. *Buildings* **2021**, *11*, 609.
https://doi.org/10.3390/buildings11120609

**AMA Style**

Wu Y, Jian W, Yang L, Zhang T, Liu Y.
Effects of Different Surface Heat Transfer Coefficients on Predicted Heating and Cooling Loads towards Sustainable Building Design. *Buildings*. 2021; 11(12):609.
https://doi.org/10.3390/buildings11120609

**Chicago/Turabian Style**

Wu, Yanwen, Wenna Jian, Liu Yang, Tengyue Zhang, and Yan Liu.
2021. "Effects of Different Surface Heat Transfer Coefficients on Predicted Heating and Cooling Loads towards Sustainable Building Design" *Buildings* 11, no. 12: 609.
https://doi.org/10.3390/buildings11120609