Dynamic characteristics of convection heat and radiation heat on building surfaces under cyclic heat flow

Abstract

The dynamic heat transfer of building surfaces has thermal conduction, convection and radiation at the same time. It is the basis of building thermal environment simulation, air conditioning load calculation, building energy analysis and air conditioning system conservation operation. Under cyclic heat flow, the convection and radiation separating method was used to calculate the radiation heat and convection heat of building surfaces, and dynamic characteristics of convection heat and radiation heat on building surfaces was provided in this paper. For the dynamic heat transfer of building surfaces under cyclic heat flow, three indexes of peak error, mean error and average relative error were used to analyze dynamic heat transfer. The temperature distribution and dynamic heat transfer of convection heat and radiation heat of building surfaces were studied systematically. The separating cooling load and the room cooling load were basically consistent with each other, the convection and radiation separating method was reliable and available. The peak value of convection heat corresponded to the foot value of the radiation heat, and the relative error of them was 1.9%-2.2%. The dynamic characteristics of radiation heat and convection heat had important reference for the study of dynamic heat transfer of building surfaces under cyclic heat flow.

Keywords

Dynamic heat transfer on surfaces convection heat radiation heat convection and radiation separating method cyclic analysis

Introduction

In recent decades, with development of building industry, the building sector accounts for 20%-40% of initial energy consumption. In order to reduce building energy consumption, the research on building thermal environment and heat transfer is becoming more and more important and prominent.^1,2 The heat transfer characteristics of building surfaces have great value and it provides energy saving significance to the optimal control of air conditioning system. The heat transfer of building surfaces is a composite heat transfer process including thermal conduction, convection and radiation. Accurately calculating heat transfer of building surfaces is foundation of building thermal environment simulation, air conditioning load calculation, building energy analysis, and air conditioning system conservation operation.^3–5 The heat entering indoor through enclosures includes two parts of convection heat and radiation heat, and the heat transfer analysis is the basis of calculating convection heat and radiation heat.^6,7

The study on the convection heat and radiation heat of building surfaces has attracted the attention of many researchers. Lu⁸ conducted a measured analysis of thermal conduction, convection and radiation for the radiant floor under radiant floor single operation, fan coil single operation and combined operation. Zhang⁹ carried out a comparative performance test on supply air system combined with dry and wet radiant floor, and compared the radiation heat and convection heat of the two floors. Zhang¹⁰ conducted a measured study on the cooling capacity of suspended metal radiation cooling plates, and analyzed the thermal conduction, convection heat and radiation heat of the radiation plates. Based on the analysis of convection heat transfer and radiation heat transfer on building surfaces, the Radiation Time Series Method (RTSM) is proposed to calculate the room air conditioning load based on the Transfer Function Method (TFM), and it has been widely recognized and applied.^6,11 Ning^12,13 proposed a radiation and convection time series method for heat transfer analysis of radiant cooling room, which applied RTSM to air conditioning load calculation of radiant roof system. The above studies are based on the dynamic simulation and analysis of convection heat transfer and radiation heat transfer on building surfaces.

The heat transfer of the building surfaces is affected by many external factors, such as outdoor temperature, outdoor humidity, solar radiation intensity and outdoor wind speed. Outdoor air temperature and solar radiation change regularly every day. Outdoor air humidity and wind speed are in a state of random variation. Under unsteady condition, the convection heat and radiation heat of the building surfaces are dynamically changing. It has more practical significance to study the dynamic heat transfer characteristics and mechanisms of radiation heat and convection heat under the cyclic heat flow.^14–18

Although on-site measurement has more significance, it is difficult to intervene or control outdoor environment artificially. And it is also complicated to conduct a separated experiment for a certain factor since there are complex coupling relationships among various factors, which brings some difficulties to analyze the effect on final results.^19–21 As a research method, the model experiment can control the main variables of test object, and the external or natural conditions can be realized by experimental simulation variables, such as the power of heating film on the surfaces. By strictly controlling the main variables of the object, it is conducive to highlight the main contradictions in the complicated experiment.^22–24

Some researchers studied the thermal environment and heat transfer of the building surfaces by model experiments. Lin²⁵ studied the flow law of supply air under large space stratified airflow, and established a mathematical model of airflow motions and verified it. The salt water model experiment has superiority in simulating airflow motion. Wang²⁶ conducted an experimental study on the ventilation effects for interior source of the building, heat transfer of the building surfaces and solar radiation. The single space natural ventilation driven by hot pressing was studied based on the model experiment and natural ventilation model experimental similarity law was also analyzed.

For offices, shopping malls, hotels, gyms, etc., considering the activities of personnel, it is necessary to set up the necessary air conditioning system to meet the needs of people's comfort. The heat transfer of building surfaces is the basis of air conditioning system selection and energy saving operation analysis. The convection heat and radiation heat of building surfaces were studied respectably on thermal environment analysis. But, there are the following deficiencies and defects:

At present, the researches are mostly under steady-state condition. The convection heat and radiation heat on building surfaces under dynamic condition are insufficient, especially the actual cyclic heat flow conditions.

Under steady-state condition, the convection heat and radiation heat on building surfaces is the focus of many researchers, but verification of the convection heat and radiation heat has not been reported. The analysis of the heat transfer process under cyclic heat flow is also rarely reported.

In summary, the research on dynamic heat transfer of building surfaces has more practical significance for air conditioning load calculation, thermal comfort analysis, and energy conservation operation. In this paper, firstly the convection heat transfer and radiation heat transfer of building surfaces were calculated by using the convection and radiation separating method based on indoor air temperature and surface temperature. Secondly, verification of room cooling load and separating cooling load were carried out and the peak error, mean error and average relative error were used to analyze the heat transfer process under cyclic heat flow. Finally, the dynamic characteristics of building surfaces temperature evolution, radiation heat and convection heat of building surfaces were obtained, which benefited to the study on dynamic heat transfer process of building surfaces. Research results provide important information for the optimization of air conditioning system, and then have a great role and significance on building energy efficiency.

Analysis method of dynamic convection heat and radiation heat

Convection and radiation separating method

To obtain the data of convection heat and radiation heat of building surfaces in a cycle, it is necessary to separate the convection heat and radiation heat for the composite process on the building surfaces. As shown in Figure 1, the convection and radiation separating method is: according to the relationship among thermal conduction, convection and radiation on the internal surfaces of building envelope, thermal conduction is measured in experiment, the radiation heat of each internal surface is calculate by the internal surface temperature, and the convection heat of each internal surface is calculated by Eq. (1) or Eq. (2) or Eq. (3).^6,27

Figure 1.

The diagram of convection and radiation separating method. (a) Internal heat gain, (b) Envelope heat storage, (c) Envelope heat release.

In a cyclic heat gain process, the composite heat transfer process of the internal surfaces for the high temperature surface is shown in Figure 1(a)). When the thermal conduction enters the room, the radiation heat and convection heat also flow into the room. At this time, the heat conduction is equal to the sum of radiation heat and convection heat, and which is described using by the following equation:

q_{λ} = q_{R} + q_{d}

(1)

Where q_λ is surface thermal conduction, W·m⁻²; q_R is surface radiation heat, W·m⁻²; q_d is surface convection heat, W·m⁻².

When the radiation heat from high temperature surface is increasing, the composite heat transfer process of the internal surface is shown in Figure 1(b)). Part of heat is stored in the envelope, the internal surface radiation heat is performed as heat gain, the internal surface convection heat is characterized as heat loss, and convection heat is less than radiation heat. At this time, the radiation heat is equal to the sum of thermal conduction and convection heat. And it is illustrated by Eq. (2):

q_{R} = q_{λ} + q_{d}

(2)

When the radiation heat from high temperature surface is decreasing, the composite heat transfer process of the internal surface is shown in Figure 1(c)). The heat stored in the envelope is released, the internal surface radiation heat is performed as heat gain, the internal surface convection heat transfer is characterized as heat loss, and convection heat is more than radiation heat. At this time, the convection heat is equal to the sum of thermal conduction and radiation heat. Their relationship is illustrated by Eq.(3):

q_{d} = q_{λ} + q_{R}

(3)

According to the convection and radiation separating method, the composite heat transfer process of each surface can be analyzed to calculate various heat gain and cooling load. The thermal conduction q_λ is obtained by measured, and the surface radiation heat is written as follows:²⁸

Q_{i R} = \frac{ε_{i} A_{i}}{1 - ε_{i}} (σ θ_{i}^{4} - J_{i})

(4)

J_{i} - (1 - ε_{i}) \sum_{j = 1}^{n} J_{j} X_{i j} = ε_{i} σ θ_{i}^{4}

(5)

Where Q_iR is surface i radiation heat, W; ε_i is surface i radiation coefficient; A_i is surface i area, m²; σ is Stefan-Boltzmann constant = 5.67 × 10⁻⁸, W·m⁻²K⁻⁴ ; θ_i is surface i temperature, K; J_i is surface i effective radiation; X_ij is angle coefficient from surface i to surface j.

Air conditioning cooling load and separating cooling load

Based on the convection and radiation separating method, the heat gain and cooling load of the room are analyzed. The heat gain involves room heat gain and radiation heat gain, and the cooling load involves room cooling load and separating cooling load.^6,17,28 (1)

Room heat gain Q_t: As shown in Figure 1(a)), room heat gain of the environmental chamber is obtained from thermal conduction measurement by heat flow meters. Two heat flow meters are mounted on the south surface and room heat gain is:

Q_{t} = q_{λ k} \cdot S_{k}

(6)

Where Q_t is the room heat gain, W; q_λk is the thermal conduction of the heating surface, W·m⁻²; S_k is the heating surface area, m²;

(2)

Radiation heat gain Q_R: the sum of net radiation heat of each surface except heating surface (the south surface). The radiation heat of each surface can be calculated by Eq.(4) and Eq. (5), and it is also equal to the net radiant heat loss of the heating surface, which is:

Q_{R} = \sum_{i = 1}^{n} S_{i} q_{i R} = - Q_{k}, i \neq k

(7)

Where Q_R is the radiation heat gain of the room, W; S_i is the other surfaces area except heating surface, m²; q_iR is the radiation heat flow of other surfaces except the heating surface, W·m⁻²; Q_k is the net radiation heat loss of heating surface, W.

(3)

Room cooling load q_t: for room heat gain, room cooling load is calculated by parameters such as supply air temperature, return air temperature and air volume. The room cooling load is given as the following:

q_{t} = C_{p} L ρ_{s} (t_{h} - t_{s}) / 3.6

(8)

Where q_t is the room cooling load, W; C_p is the air specific heat, W·kg⁻¹·°C⁻¹; L is the supply air volume, m³·h; ρ_s is the supply air density, kg·m⁻³; t_s is supply air temperature, °C; t_h is return air temperature, °C.

(4)

Separating cooling load q_s: the convection heat is separated by convection and radiation separating method for each surface, which can be calculated by the heat balance equation involved in Figure 1. The sum of convection heat separated from all the surfaces is the separating cooling load.

q_{s} = \sum_{i = 1}^{n} S_{i} q_{i d}

(9)

Where q_id is the convection heat flow of surface i, W.

Analysis indexes of dynamic convection heat and radiation heat

The calculation value and measured value of the room cooling load are both periodic data in the experiment. In order to compare and analyze the results, this paper use the peak error (Eq.(10)), the mean error (Eq.(11)) and the average relative error (Eq.(12)) to manage the experimental results. The three indexes are defined as follows:^15,27

δ_{1} = \frac{max ({q^{'}}_{f \cdot τ}) - max (q_{f \cdot τ})}{max (q_{f \cdot τ})}

(10)

δ_{2} = \frac{(1 / 24) \sum_{τ = 1}^{24} {q^{'}}_{f \cdot τ} - (1 / 24) \sum_{τ = 1}^{24} q_{f \cdot τ}}{(1 / 24) \sum_{τ = 1}^{24} q_{f \cdot τ}} = \frac{\sum_{τ = 1}^{24} ({q^{'}}_{f \cdot τ} - q_{f \cdot τ})}{\sum_{τ = 1}^{24} q_{f \cdot τ}}

(11)

δ_{3} = \frac{1}{24} \sum_{τ = 1}^{24} \frac{| {q^{'}}_{f \cdot τ} - q_{f \cdot τ} |}{q_{f \cdot τ}}

(12)

Where $q_{f \cdot τ}^{'}$ is the calculation value of the room cooling load at τ hour, W; q_f·τ is the measured value of the room cooling load at τ hour, W.

Among them, the peak value of room cooling load is the basis of air conditioning equipment selection, and the peak error can reflect the difference between the maximum values of the calculation value and measured value of the room cooling load. The mean error can reflect the difference between the calculation value and measured value in the whole 24 h cycle. The average relative error can reflect the deviation of the calculation value relative to the measured value.

Based on the above research, the research content and calculation process of this study are as follows in Figure 2.

Figure 2.

Flow chart of research and analysis.

Experimental system and experimental method

Experimental system

The testing counter consists of an environmental chamber, a cold and heat source system, an air handling system and an electric control and test system, as showed in Figure 3. The environmental chamber, which dimension is 2.5 m(L) × 2.1 m(W) × 2.5 m(H), is in a suit room whose ambient temperature can be controlled. The enclosure structure adopts 100 mm thick polyurethane insulation board, and the heating films are mounted on internal surfaces of chamber, which could simulate the thermal conduction. The thermal conductivity coefficient of the chamber envelope is 0.611W·m⁻²·K⁻¹. During the experiment, heating film on south surface was heated periodically as designed power with the principle of controlling return air. The water chiller provided the cooling and supply air entered indoor at a lower temperature. Under the cyclic disturbance, return air temperature was controlled unchanging.

Figure 3.

Brief figure of testing counter. 1-expansion tank, 2-three-way valve, 3-chilled pump, 4-refrigeration machine, 5-cooling pump, 6-cooling tower, 7-filter, 8-surface cooler, 9-electrical heater, 10-nozzle, and 11- fan. (a) Inner scene, (b) system diagram.

Under the cyclic disturbance, the dynamic heat transfer experiment needed to be carried out on unstable conditions. The heating film on south surface was loaded with cyclic heat flow to simulate the thermal conduction. In the whole experiment, electric control cabinet of heating film was periodically heated under the set power (it concluded 24 h to simulate the hourly heat gain). For the cyclic dynamic heat transfer experiment, it was necessary to maintain a certain indoor air temperature. In the experiment, adopting return air controlling, we adjusted the supply air temperature through the electric control cabinet to adapt to cyclic disturbance. According to the measured supply air temperature and return air temperature, supply air volume, internal surfaces temperature and internal surfaces heat flow, we calculated room cooling load, separating cooling load, radiation heat and convection heat.

Experimental test plan

The main survey parameters were temperature and heat flow, in addition to indirect parameters related to the cooling load. The input power of the heating film was also measured in this experiment. The temperature mainly included the surface temperature, the supply air temperature and return air temperature, while the heat flow included the heat flow of six surfaces, as shown in Figure 4.

Figure 4.

Testing points distribution sketch. (a) temperature points, (b) heat flow points.

A total of 19 temperature points and 7 heat flow points were arranged in the experiment. The south surface with heating film was arranged with 4 temperature points and 2 heat flow points; east surface, north surface, west surface, ceiling and floor were arranged with 2 temperature points and 1 heat flow point. And there were 3 temperature points to measure the indoor air temperature.

The test instruments and performance parameters involved in the experiment were presented in Table 1. The thermal resistance sensors were used to measure the indoor air temperature, the supply air temperature, return air temperature and internal surfaces temperature. Draft hood was used to measure the air volume, and heat flow density plates were used to measure the surface heat flow. The test instruments must be calibrated to ensure its accuracy before using.

Table 1.

Laboratory instruments.

Survey parameters	Test instruments	Test range	Resolution
Surfaces temperature	Temperature sensor	−20 to + 85°C	0.1°C
Surfaces heat flow	Heat flow meter	0 to + 300 W/m²	0.1 W/m²
Air volume	Draft hood	0 to + 1000 m³/h	1 m³/h
Supply air and return air temperature	Temperature sensor	−20 to + 85°C	0.1°C
Air temperature	Temperature sensor	−20 to + 85°C	0.1°C

Experimental conditions

In the experiment, the temperature data-collection interval of instrument was one minute, which value was the average of 60 data in one hour. The air volume was measured by the draft hood. The pre-experiment showed that the air volume was stable in the same condition and fluctuated within 2%. The heat flow data-collection interval of instrument was 20 s, which value was the average of 180 data in one hour. In order to simulate the dynamic experimental conditions under the cyclic disturbance, the surface heating films adopted the cyclic heating mode with its power set to the cyclic curve as the Eq.(13). The experimental conditions were described in Table 2. For the heat transfer condition of building surfaces under cyclic heat flow, the preliminary experiment showed that the experiment entered the periodic heat transfer state and the air temperature was stable after 3 h. After eliminating the influence of envelope structure, the experimental data collected within 24 h were analyzed in this study.

Table 2.

Experimental conditions.

Conditions	Disturbance form	Average of disturbance /W	Experimental period /h	Supply air volume /(m³/h)	Average of supply air /°C
Case 1	$P = 360 \cdot (\sin (2 π / 1440) t + 1.5)$	540	24	501	22.33
Case 2	$P = 300 \cdot (\sin (2 π / 1440) t + 1.5)$	450	24	501	22.89
Case 3	$P = 110 \cdot (\sin (2 π / 1440) t + 2.18)$	240	24	501	24.07
Case 4	$P = 300 \cdot (\sin (2 π / 1440) t + 1.5)$	450	24	335	21.64
Case 5	$P = 300 \cdot (\sin (2 π / 1440) t + 1.5)$	450	42	662	23.50

The input power of the heating film changed periodically, and the return air temperature was kept constant by controlling the supply air temperature. The surface temperature, heat flow, indoor air temperature, supply air and return air temperature were measured in the pre-experiment. The average indoor air temperature and return air temperature were 25.5 °C and 25.2 °C respectively, and they indicated that the system control was stable and accurate. The preliminary experiment showed that the relative error between the 24-h cooling load taken away by return air and room cooling load was 3.34% in the measured chamber, and it indicated that the heat balance of chamber was well and the experimental data was reliable.

P = a (\sin \frac{2 π}{1440} t + b)

(13)

Research results and analysis

Room cooling load and separating cooling load

The room cooling load is mainly carried about the supply air and return air, the separating cooling load is the sum of the convection heat of all surfaces. In the experiment, the room cooling load was calculated by the measured data of supply air temperature, return air temperature and supply air volume. The separating cooling load was obtained by the convection and radiation separating method. The accuracy of the convection and radiation separating method could be verified from the measured value. Figure 5 showed the validation of room cooling load and separating cooling load under 5 different conditions. It could be seen that the room cooling load and the separating cooling load changed periodically since the heat flow of the south heating surface changed periodically.

Figure 5.

Room cooling load and separating cooling load. (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5.

The room cooling load was fairly closed to the separating cooling load, and the error analysis was shown in Table 3. We could see from the Table 3, case 1, case 2, and case 3 indicated that supply air volume stayed constant and the surfaces heat flow was gradually reducing with both the peak value of the room cooling load and the separating cooling load declining. Cases 2, case 4, and case 5 suggested that the surfaces heat flow kept constant and the supply air volume was gradually increasing with both the peak value of room cooling load and the separating cooling load diminishing. Overall, the maximum of peak error under 5 conditions was 4.69%, the mean error was less than 6.07%, and the maximum of the average relative error was 8.22%, which illustrated that the separating cooling load was basically consistent to the room cooling load. Thus it is reliable to use the convection and radiation separating method in this paper. For the thermal environment analysis of air conditioned room, it is very important to compare and verify the inner surface heat transfer with the room cooling load. In this paper, the analysis indexes of peak error, mean error and average relative error were proposed, which had guiding significance and reference value for the study of heat transfer process under periodic perturbation.

Table 3.

Error analysis of separating cooling load.

Conditions	Peak value of room cooling load/W	Peak value of separating cooling load/W	Peak error/%	Mean error/%	Average relative error/%
Case 1	811	803	−0.96	2.55	5.24
Case 2	679	665	−2.14	0.88	4.65
Case 3	307	321	4.69	6.07	6.85
Case 4	707	684	−3.24	0.48	4.09
Case 5	660	673	2.02	5.39	8.22

Dynamic temperature analysis of building surfaces

Figure 6 showed the temperatures of east surface, south surface, ceiling, supply air, return air and indoor air of the environmental chamber. There were lots of measured data in the experiment, and the hourly average value was selected for analysis. It could be seen from Figure 6 that the heating film on the south surface began to be heated periodically during the experiment, and the south surface temperature was the highest and changed periodically. The east surface and the ceiling were at low temperature, their temperature originally increased and then decreased, and the differences of them from the indoor air temperature did not exceed 4.5°C.

Figure 6.

Temperature variation trend of building surfaces. (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5.

In the experiment, the return air temperature was controlled and it was constant. For the indoor environment, the return air temperature was stable and the temperature difference between the return air and the indoor air was within 0.5°C as shown in Figure 6. The supply air temperature changed periodically due to the heat flow changing periodically. In order to eliminate indoor residual heat, the supply air temperature was low when the heat flow surged, and the supply air temperature was high when the heat flow dropped. The low temperature surfaces and the south heating surface exited radiation heat transfer, then released the heat into the indoor air by convection, and finally took away by the return air. Building surfaces temperatures are the basis of thermal environment analysis of traditional convection air conditioning room, and also an important basis of thermal environment analysis of radiation air conditioning.

Dynamic convection heat and radiation heat analysis of building surfaces

According to the convection and radiation separating method, we calculated the convection heat and radiation heat of the building surfaces, and chose the hourly average value for analysis as shown in Figure 7. In the experiment, south surface was heated and transferred heat into the room, and there was radiation heat transfer between high temperature south surface and other low temperature surfaces. The south surface convection heat and radiation heat were both positive. The other surfaces were low temperature surfaces, which absorbed the radiation heat from high temperature south surface and then gradually released it into the room air as convection heat. Therefore, the radiation heat was negative and the convection heat was positive. We could see from Figure 7, since the south surface was heating surface, the radiation heat and convection heat were most, while the other surfaces were low temperature with less convection heat and radiation heat.

Figure 7.

Convection heat and radiation heat of building surfaces. (a) case 1, (b) case 2, (c) case 3, (d) case 4, (e) case 5.

Similarly, as shown in Figure 7, the radiation heat of the south surface increased firstly and then decreased. The radiation heat of the east surface and the ceiling decreased firstly and then increased. That was because south surface temperature and other surfaces temperature all increased firstly and then decreased under the simulated periodic disturbance, and the south surface temperature ascended significantly. The convection heat of the east surface and the ceiling firstly rose and then reduced, and the peak value of convection heat basically corresponded to the foot value of the radiation heat. The reason was the low temperature surface absorbed the radiation heat and stored it, then released it as convection heat. The direction of the peak value of convection heat and the foot value of the radiation heat was opposite. And the quantitative values of them were approximately, the relative error was 1.9%-2.2%. For common convection air conditioning and radiation air conditioning, the calculation and analysis of surface convection heat transfer and radiation heat transfer are the basis of system design and performance analysis.^29,30 At present, the radiation heat transfer and convection heat transfer of radiant surface and other surfaces in radiant air conditioning are calculated. However, the comparison and verification of surface radiation heat transfer and convection heat transfer were not carried out from the surface heat balance. This is the embodiment of the new research work in this paper.

Analysis on dynamic heat transfer characteristics of building surfaces

Based on the above temperature dynamic distribution, convection heat and radiation heat, the dynamic heat transfer process of the building surfaces was analyzed.

For usual air conditioning room, the indoor air temperature was uniform, and the heat entering the room included radiation heat and convection heat. The convection heat directly became the air conditioning cooling load, while the radiation heat was first absorbed by the low temperature surfaces and then gradually released into the room air and became air conditioning cooling load finally. As shown in Table 4, for 5 experimental conditions, the average temperature of the heating south surface was the highest and the temperature mean value was 30.7°C-35.9°C. The temperatures of east surface and ceiling were at low temperature, and the temperature mean value was 26.3°C-27.7°C. The indoor air temperature and the return air temperature were basically stabilized, the temperature mean value was 25.2°C-25.6°C. The supply air temperature mean value was 21.6°C-24.1°C. The convection heat and radiation heat of the heating south surface were also the most, the east surface and the ceiling absorbed the radiation heat from the south surface, which were negative, and then released into the room as convection heat, and the convection heat were positive.

Table 4.

Analysis on dynamic heat transfer characteristics.

Conditions	Mean temperatures / °C
Conditions	East surface	South surface	Ceiling	Indoor air	Supply air	Return air
Case 1	26.6	35.9	27.7	25.5	22.3	25.2
Case 2	26.7	34.8	27.5	25.6	22.9	25.3
Case 3	26.3	30.7	26.5	25.6	24.1	25.3
Case 4	26.8	34.9	27.7	25.6	21.6	25.3
Case 5	26.4	34.3	26.9	25.5	23.5	25.3
Conditions	Mean values of convection heat and radiation heat/W
	East surface		South surface		Ceiling
	Convection	Radiation	Convection	Radiation	Convection	Radiation
Case 1	63.8	−67.2	221.1	289.5	17.4	−15.9
Case 2	48.5	−51.3	168.9	252.4	16.8	−15.3
Case 3	22.6	−24.3	92.5	139.1	12.0	−12.9
Case 4	48.0	−50.4	172.4	254.2	12.4	−10.8
Case 5	48.2	−49.8	176.8	247.8	27.5	−26.5

In Table 4, the supply air temperature varied according to the south surface temperature and the supply air volume. The larger the average temperature of the south surface was, the smaller the mean temperature of the supply air was; the smaller the air flow was, the larger the mean temperature of the supply air was. The results further illustrated that the building surface released heat into the room air as convection heat after absorbing radiation heat. For evolutionary mechanisms of absorption, storage and release of surface radiation heat, Evola³¹ proposed a dynamic parameter to describe the thermal reaction process of radiant heat, and Yan³² proposed a simple model to analyze and evaluate the role of radiant heat and air conditioning load. In this paper, based on the measured data, the dynamic heat transfer process of surface was analyzed on the basis of convection heat transfer and radiation heat transfer. It has guiding and reference significance for the analysis of the evolution process (absorption, storage and heat release) of radiation heat transfer in the surfaces space area.

Conclusions

This paper calculated the surface radiation heat, constructed the convection and radiation separating method to study the dynamic heat transfer process of the building surfaces, and obtained the dynamic temperature distribution and dynamic heat transfer results of the building surfaces.

The room cooling load was fairly closed to the separating cooling load. The results of 5 conditions showed that the maximum peak error was 4.69%, the mean error was less than 6.07% and the average relative error was less than 8.22%. It showed that the separating cooling load was basically consistent with the room cooling load, the convection and radiation separating method was reliable in this paper. The proposed indexes, such as peak error, mean error and average relative error, have guiding and reference significance to the analysis of heat transfer process under periodic disturbance.

There was a periodic heat flow on the south surface and the surface temperature increased firstly and then decreased under the simulated cyclic disturbance. The east surface and the ceiling were at low temperature, their temperature originally increased firstly and then decreased, and the differences of them from the indoor air temperature did not exceed 4.5°C. In order to keep the indoor air temperature steady, the supply air temperature was decreased firstly and then increased. The temperature difference between the return air and the indoor air was within 0.5°C

There was a periodic dynamic radiation heat between the south surface and the low temperature surfaces. When the heat flow became larger, the supply air temperature was lower; when the heat flow became smaller, the supply air temperature was higher. Due to the significant increasing of the south surface temperature, the radiation heat absorbed by the low temperature surfaces increased firstly and then decreased, and the convection heat released into the room air. The direction of the foot value of convection heat and the peak value of the radiation heat was opposite. And the quantitative values of them were approximately, the relative error was 1.9%-2.2%. The convection and radiation separation method is used to obtain the convection heat transfer and radiation heat transfer of the surfaces, and the comparison and analysis of the errors can enrich and supplement the heat transfer analysis of air conditioning room and the calculation of air conditioning load.

The indoor air temperature was well distributed for the usual air conditioning room, and radiation heat and convection heat entering indoor air directly acted on the air conditioning zone. During an experimental cycle, the mean value analysis of surface temperature, air temperature, convection heat and radiation heat showed that the low temperature surfaces was higher than return air temperature and indoor air temperature, and the low temperature surfaces absorbed the radiation heat from the high temperature surfaces and then released into the indoor air as convection heat. The hourly average values of radiation heat and convection heat of the building surfaces also confirmed the heat transfer characteristics of the building surfaces. Based on the dynamic analysis of convection heat transfer and radiation heat transfer, the dynamic heat transfer process of the surface is studied, which provides a lead and reference for the analysis of the evolution of heat absorption, storage and heat release in the surfaces space area.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

This research was supported by Scientific Research Fund of Zhejiang Provincial Education Department No.Y202147475.

Authors’ contributions

Liugen Lv, Yi Xiang and Chen Huang conceived and designed the research plan;

Liugen Lv, Yi Xiang, Zhipan Gu and Chen Huang performed the implement of theory research;

Liugen Lv, Yi Xiang, Zhipan Gu and Chen Huang analyzed the data, drafted and prepared the paper;

Liugen Lv, Yi Xiang, Zhipan Gu and Xiangjiang Zhou contributed materials/analysis tools.

ORCID iD

Liugen Lv

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