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Thermal response of wall implanted with heat pipes: Experimental analysis
Renewable Energy 143 (2019) 1687e1697
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Thermal response of wall implanted with heat pipes: Experimental analysis Chang Liu*, Zhigang Zhang School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 November 2018 Received in revised form 2 May 2019 Accepted 28 May 2019 Available online 31 May 2019
A wall implanted with heat pipes (WIHP) features effective heat transfer between indoor and outdoor environments due to the pipe’s unidirectional thermal conductivity; the implant also resolves the contradiction between the wall’s insulation and solar energy utilization. The thermal performance of walls is crucial in terms of reducing a building’s energy consumption and improving its indoor thermal environment. The heat transfer process of the condensing section is the focus of the present study. We establish a dynamic heat transfer model of the condensing section based on the Z-transfer function, and introduces the temperature rise coefficient (TRC) concept. The thermal response characteristics of an ordinary wall and WIHP are determined via theoretical analysis and experimentation. The WIHP shows a faster thermal response to weather variations than the ordinary wall. In a typical day, the efficient heat transfer and long running time (7 h 30 min) of the heat pipe improve the average inside-surface temperature of the WIHP by 0.5 C and the average TRC by 0.16. A portion of the heat released from the pipe is also stored by the wall, which staves off temperature attenuation and minimizes temperature fluctuations in the inside surface, thereby creating a more comfortable indoor thermal environment. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Wall implanted with heat pipes Thermal response Time lag Decrement factor Temperature rise coefficient
1. Introduction The building sector accounts for about 30e40% of the world’s total energy consumption. China’s buildings sector currently accounts for 27.6% of the country’s total energy use and is projected to increase to 35% by 2020 [1,2]. Laying an insulation layer on the outside surface of the wall structure is a common approach to energy savings, as it reduces indoor heat loss in winter and heat gain in summer months [3]. The insulation performance of wall directly affects the level of the building’s energy consumption [4,5]. However, the solar radiation absorbed on the outside surface of south-facing walls does not effectively transfer into the room in winter, due to the thick insulation layer. If this solar energy could be utilized effectively, the heating load would be reduced and the indoor thermal comfort markedly further improved [6e8]. “Passive walls” such as PCM walls [9,10] or heating-based types of Trombe wall including the classic Trombe wall (CTW), Trombe-Michel wall (TMW), water Trombe wall (WTW), and solar trans-wall (STW) have emerged as researchers attempt to better utilize solar
* Corresponding author. E-mail address: [email protected] (C. Liu). https://doi.org/10.1016/j.renene.2019.05.123 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
radiation for efficient heating [11e13]. Zhang et al. [14] combined a gravity heat pipe with a wall to construct a novel passive solar energy utilization technology, the wall implanted with heat pipes (WIHP). As a result of efficient heat transfer, one-way thermal conductivity, and thermal switch of the heat pipe, heat can be transferred into the room in winter and out of the room in summer through a phase change in the pipe medium (Fig. 1). Intelligent control valves are installed on the adiabatic section in the south wall and north wall, respectively. In winter, when the indoor temperature is lower than the set temperature of the valve on the south wall, the valve there will open while the valve on the north wall is closed; in summer months, the opposite occurs. This facilitates beneficial heat transfer between indoor and outdoor environments while resolving the contradiction between the wall insulation and solar energy utilization. They established a steady-state heat transfer model of the WIHP and analyzed its thermal performance and applicability accordingly. However, the heat transfer of the building envelope is a complex process. It includes three basic processes: heat absorption, heat release, and heat conduction of the envelope. These processes involve three basic heat transfer modes: conduction, convection, and radiation. Meteorological parameters such as air temperature and solar radiation intensity constantly change along seasonal and diurnal
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tc tm
Nomenclature
ar aa [Gi] A(s) Rr,Ra
li ai ci
ri
li S
jyn nyn un Aan 4n tz tr
Convective heat transfer coefficient of the inside wall surface (W$m2$K1) Convective heat transfer coefficient of the outside wall surface (W$m2$K1) submatrix matrix elements thermal resistance of convective heat transfer (m2$K$W1) Thermal conductivity (W$m1$K1) Thermal diffusivity (m2$h1) Specific heat capacity (kJ$ kg1$K1) Density (kg$m3) Thickness (m) Fundamental temperature frequency Time lag Decrement factor Frequency of the thermal wave Amplitude Initial phase Solar air temperature ( C) Indoor temperature ( C)
tair
t
E R
a I ho bi, ci, di q z Q n
Dqm a Dqm i
Condensing section temperature ( C) Temperature of the ordinary wall at the same location ( C) Outdoor temperature ( C) Time Exponential function Thermal resistance of the inner plaster layer (m2$K$W1) Surface absorptivity Solar radiation intensity (W$m2) Convective heat transfer coefficient (W$m2$K1) Transfer coefficient Heat flux (W$m2) Z-transform heat transfer capacity (W) time Solar air temperature amplitude at time m ( C) Inside surface temperature amplitude at time m ( C)
Abbreviation WIHP Wall implanted with heat pipes TRC Temperature rise coefficient THTC Total heat transfer capacity
Fig. 1. WIHP structure and principle.
variations, thus the indoor air temperature and envelope surface temperature also change constantly. The heat flux through the envelope also changes with time in an unsteady heat transfer process. The decrement factor and time lag are two important parameters in unsteady heat transfer, which represent the resistance of the wall and the response time to thermal waves, respectively; they are often used to evaluate the thermal performance of a wall. Many previous scholars have studied thermal response in walls. Ciril et al. [15], for example, designed a thin (68 mm) composite timber facade wall with improved thermal response where heat wave propagation time lag falls between 9 h and 12 h at the optimal wall composition. Reza et al. [16] investigated the effects of various parameters such as wall thickness, inner and outer heat transfer
coefficients, and thermal insulation layers in sandwich walls on the time lag and decrement factor. The decrement factor of the wall is in inverse relation to the thickness of the insulation layer and changes with the combined convection and radiation heat transfer coefficients of the wall’s inside and outside. Asan et al. [17] researched the effects of thermal properties and wall thickness on time lag and decrement factor based on one-dimensional numerical models. They found that time lag has a positive correlation with the thermal capacity and the thickness of the wall, but a negative correlation with the wall’s thermal conductivity. The decrement factor has a negative correlation with the thermal capacity and thickness, but a positive correlation with thermal conductivity. Available methods for analyzing unsteady heat transfer can be
C. Liu, Z. Zhang / Renewable Energy 143 (2019) 1687e1697
divided into four categories: numerical analysis, harmonic analysis, reaction coefficient method, and Z-transfer function method. Koray et al. [18] analyzed the effects of solar energy falling onto the outside surface of a wall on the inside environment based on a onedimensional transient heat conduction model. Oliveti et al. [19] proposed a non-dimensional periodic global transmittance model where in the ratio of heat flux which is transferred to the indoor environment and the external heat flux describes the wall’s harmonic thermal behavior. Tian et al. [20] built three heat transfer models by reaction coefficient method to study the dynamic thermal response performance of concrete radiant cooling slab; they also introduced the “core temperature layer” concept. Francesco et al. [21] used the heat transfer matrix method to analyze the dynamic thermal performance of different multi-layered walls. Zorana et al. [22] established a novel approach for estimating thermal impulse response (TIR) functions and determining the dynamic thermal characteristics of a multilayer facade wall with unknown thermal properties, structure, and dimensions. Ruivo et al. [23] developed a transient heat transfer model based on the finite difference method to predict the thermal behavior of external walls under realistic outdoor conditions. In a numerical analysis model, all parameters must be recalculated when the boundary conditions change. This makes the calculation process highly complex. The harmonic analysis method is only suitable for solving the periodical heat conduction differential equation. The reaction coefficient method is slow in calculating the unsteady heat transfer of the wall, especially for heavy walls. The Z-transfer function can be used to solve the equation more quickly and accurately. As early as 1971, Stephenson [24] used the Z-transfer function method to calculate the transient heat flux through a wall. Mitalas [25] and Peavy [26] later analyzed Ztransfer function properties and the relationship between transfer and reaction coefficients. Similar to the reaction coefficient, the transfer coefficient reflects the dynamic thermal characteristics of a wall but can be calculated more easily. Therefore, the Z-transfer function method was chosen to analyze the unsteady heat transfer of the wall in this study. The unsteady heat transfer process of a WIHP consists of heat transfer in the heat pipe and the ordinary wall. Further research on dynamic heat transfer characteristics and energy-saving potential of this structure has important practical significance. The present study was conducted to investigate the thermal response characteristics of WIHPs such as the actual response time, temperature
3 1 " 1 An ðsÞ AðsÞ BðsÞ 6 ar 7 7 ½G ¼ ¼6 5 4 Cn ðsÞ CðsÞ DðsÞ 0 1 3 2 1 # " A1 ðsÞ B1 ðsÞ 6 1 a 7 a7 6 5 4 C1 ðsÞ D1 ðsÞ 0 1 1 1 Rr ¼ ; Ra ¼ "
ar
#
2
Bn ðsÞ Dn ðsÞ
#
Fig. 2. Schematic diagram of multi-layered wall.
2. Methodology 2.1. Ordinary wall heat transfer matrix The heat transfer matrix method, also referenced as the “thermal quadrupole method”, is an important part of the Z-transfer function process and often used to describe heat conduction in onedimensional structures [21]. The transfer matrix represents the thermal performance of the wall, which is related to the thermal parameters of the wall materials and is irrelevant to the input or output parameters, as shown in Fig. 2. It is a bridge connecting the temperature and flux of the inside and outside wall surfaces. In the case of a multi-layered wall consisting of a sequence of n homogeneous layers, each submatrix should be multiplied sequentially from the output side to the input side, i.e., from indoor to outdoor. The transfer matrix ½G can thus be evaluated as follows:
½G ¼ ½Gr ½Gn / ½Gi / ½G1 ½Ga
(1)
i.e.
" /
1689
Ai ðsÞ
Bi ðsÞ
Ci ðsÞ
Di ðsÞ
# /
(2)
aa
increase, and temperature distribution under real-world conditions. The results of this study may provide workable guidelines for subsequent optimization.
where [Gi] is a submatrix; A(s), B(s), C(s) and D(s) are matrix elements; ar and aa are convective heat transfer coefficient of the inside and outside wall surfaces, W/(m2$K); Rr and Ra are the thermal resistance of convective heat transfer, (m2$K)/W.
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Each element in the matrix can be calculated according to the thermophysical properties of each layer of the wall.
rffiffiffiffi s Ai ðsÞ ¼ Di ðsÞ ¼ cosh li ai rffiffiffiffi 1 rffiffiffiffi s s li sinh li ai ai
(4)
Ci ðsÞ ¼
rffiffiffiffi rffiffiffiffi s s sinh li li ai ai
(5)
li
where ai is thermal diffusivity, m2/h; li is the thermal conductivity, W/(m$K); ci is the specific heat capacity, kJ/(kg$K); ri is the density, kg/m3; li is the thickness, m; and S is the fundamental temperature frequency.
#
"
Bi Z
∞ X
# Bi eai Dt
(11)
i¼1
where z is Z-transform. The Z-transfer function is usually expressed in the form of the ratio of two Z-polynomials to reduce the quantity of Z-polynomials and the calculation time. Thus, the Z-transfer function of the wall GY (z) is: BðzÞ
GY ðzÞ ¼ (6)
ci ,ri
∞ X i¼1
(3)
Bi ðsÞ ¼
ai ¼
" z½qY ðtÞ ¼ Z½K t þ Z
P∞ i¼1 1
Dt
eaiDt Z 1
¼
b0 þ b1 Z 1 þ b2 Z 2 þ / 1 þ d1 Z 1 þ d2 Z 2 þ /
(12)
The coefficient of the denominator is equal on both sides of the equation. The transfer coefficients di and bi can be obtained by solving the roots -ai of B(s) in the transfer matrix. When the indoor temperature is constant, the heat transfer capacity of the wall at time n is:
QY ðnÞ ¼
m X i¼0
bi tz ðn iÞ
m X
di Q ðn iÞ tr
i¼1
m X
ci
(13)
i¼0
2.2. Ordinary wall frequency response The frequency response is the time lag jyn and decrement factor nyn of the wall to the sine wave as outdoor frequency varies while the indoor air temperature is maintained at 0 C. The imaginary part of the exponential function E(t) is the thermal wave to be input:
EðtÞ ¼ Aan ½cosðun t þ 4n Þ þ i sinðut þ 4n Þ ¼ Aan eiðun tþ4n Þ
(7)
where E is the exponential function; t is time; Aan is amplitude; un is the frequency of the thermal wave; 4n is the initial phase; i is an imaginary unit. The time lag jyn is equal to the argument of element B (iun) in the transfer matrix. The time lag jyn and decrement factor nyn are expressed as follows:
jyn ¼ arctan nyn ¼ ar
Bðiun ÞIm Bðiun ÞRes
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Bðiun ÞRes þ BðiuÞIm
(8)
(9)
where jyn is time lag; nyn is decrement factor.
2.3. Ordinary wall unsteady heat transfer capacity The transient heat flux through the wall can be calculated via Ztransfer function method. The Z-transfer function of the wall system is the Z-transform of the response to the unit isosceles triangular-shaped pulses, i.e., the Z-transform of the reaction coefficient sequence of the wall. The thermal response of the wall to the unit oblique wave, i.e., the heat flux influenced by the unit oblique wave, is as follows:
qY ðtÞ ¼ K t þ
∞ X
Bi 1 eai t
Where Q is heat transfer capacity, W; n is time; tz is solar air temP Pm perature, C; tr is indoor temperature, C; m i¼0 ci ¼ i¼0 bi .
2.4. WIHP dynamic heat transfer model The solar radiation absorbed by the outside surface of the southfacing wall is transferred into the room through the wall and heat pipe, respectively. The dynamic heat transfer model of the WIHP can be regarded as a superposition of the ordinary wall and the condensing section of the heat pipe, as shown in Fig. 3. The condensing section, as a heating surface, is key in improving the inner-surface temperature of the wall and the indoor thermal environment. The heat transfer process of the condensing section is the focus of this study. In winter, the outside surface temperature increases as the building absorbs solar energy. When the outside surface temperature reaches evaporation temperature of the working medium, the medium begins to vaporize, i.e., the heat pipe starts to work. Heat is absorbed by the working medium in the evaporating section and rejected in the condensing section. During this time, a portion of the heat is transferred into the inside surface (q2 transient heat transfer) while the remainder is absorbed by the wall (q3 thermal storage). When the outside surface temperature drops below the evaporation temperature, the heat pipe stops working. The transient heat transfer then ceases and the stored heat is released constantly to the inside surface. Here, we apply some assumptions to simplify the model.
(10)
i¼1
where q is heat flux, W/m; K is the heat transfer coefficient, W/ (m2$K); Y is the transfer process of the wall. The Z-transform of Eq. (10) is discretized at an equal time interval Dt.
Fig. 3. WIHP dynamic heat transfer model.
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(1) The heat exchange between the evaporating section and inside surface is neglected. The insulation layer prevents the inside surface and indoor thermal environment from being influenced by the evaporating section. (2) The heat exchange between the wall and the adiabatic section covered by the insulation layer is neglected. (3) The thermal storage of the inner plaster layer (20 mm) is neglected due to its small thickness. Hence, the heat exchange between the condensing section and inside wall surface can be regarded as steady. The temperature wave is typically used as an input to solve unsteady heat transfer problems. In this paper, the heating surface temperature tc0 , an internal disturbance, serves as the input transient heat transfer and thermal storage:
t 0c ¼ tc tm
(14)
where tc is the condensing section temperature, C; tm is the temperature of the ordinary wall at the same location, C. The value of tc is always greater than or equal to that of tm, so the internal disturbance temperature tc0 is an hourly temperature variation higher than or equal to 0 C. At this time, the temperatures of the two wall sides are set to 0 C so that the heat transfer of the condensing section can be solved. Due to the high thermal resistance and thermal inertia of the wall, the heat transfer process from the condensing section to the outdoor region can be analyzed via Z transfer function theory (similar to the ordinary wall). The thermal storage q3 can be calculated by Eq. (13). As per the simplification (3) mentioned above, the transient heat transfer q2 can be calculated as follows:
q2 ¼
t ’c R
(15)
where R is the thermal resistance of the inner plaster layer, (m2$K)/ W.
3. Experimental procedures The dimensions of the test wall are 1720 1720 mm and its thermal properties are as listed in Table 1. Separate heat pipes are embedded in the inside and outside plastering layer respectively, as shown in Fig. 4. The size of the capillary net is 1000 600 mm and it consists of 24 capillary tubes with 2.7 mm inner and 4.2 mm outer diameters. The size of the adiabatic pipe, riser, and downcomer are F20 2.0 mm. All of the pipes are cylindrical and made of polypropylene random (PPR). We tested the thermal response of a WIHP using the building wall thermal insulation performance testing equipment shown in Fig. 5. There is a heater and an evaporator in the hot box and cold box, respectively. The temperature of the hot box and cold box can be controlled automatically or manually by the controller. We established four test cases listed in Table 2 to investigate the
Table 1 Wall thermal properties. Material
l/mm
l/[W/(m$K)]
r/[kg/m3]
cp/[kJ/(kg$K)]
Cement mortar Autoclaved aerated concrete blocks Molded polystyrene board Cement mortar
20 250
0.930 0.200
1800 500
1.050 1.461
50 20
0.041 0.930
22 1800
2.414 1.050
Fig. 4. Separate heat pipe.
thermal response of the WIHP under various outdoor temperatures. The experimental platform was in a basement laboratory rather than outdoors, so the outdoor temperature was simulated by manually controlling the hot box temperature. There were two main outdoor temperature settings used in the test. One was a constant 40 C; the other temperature setting enabled the outside surface temperature to reach the solar air temperature of a typical day. The hot box temperature was set every hour according to said typical solar air temperature. In addition, the inside surface was controlled as a stable indoor environment by opening the cold box, so the basement laboratory could provide stable temperature and humidity. Eighteen Pt1000 sensors were arranged on the inside and outside surfaces to record temperatures in different zones, as shown in Fig. 6. All of the sensors were calibrated to accuracy of 0.1 C. The temperature signals are collected with a GP10 data acquisition device that has accuracy of ±(temperature reading 0.05% þ 0.3 C). 4. Results and discussion The results of the four test cases are discussed in this section. Cases A and C mainly center on the time lag/decrement factor of the ordinary wall and the thermal wave attenuation law, respectively. The calculation method was validated through these experiments in regards to the accuracy of the unsteady heat transfer of WIHP. Cases B and D mainly center on the response time and temperature rise coefficient (TRC) of the WIHP. The heat transfer capacity was calculated by using the Z-transfer function method. 4.1. WIHP response time and TRC Decrement factor and time lag, as discussed above, are two important parameters for studying the heat transfer characteristics of a wall in a periodic thermal environment. The decrement factor is the ratio of solar air temperature amplitude to the inside surface temperature amplitude when the indoor temperature is constant, which can be defined as follows:
nyn ¼
Dqm a Dqm i
(16)
where Dqm a is the outdoor disturbance (solar air temperature)
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(a)
(b) Fig. 5. Building wall thermal insulation performance testing equipment.
Table 2 Experimental setup parameters. Case A B C D
Hot box temperature
40 C 40 C e e
Outside surface temperature
Wall
e e Solar air temperature Solar air temperature
Ordinary wall WIHP Ordinary wall WIHP
amplitude at time m, C; Dqm i is the inside surface temperature amplitude at time m, C. We calculated the decrement factor by plugging our experimental data into Eq. (16). The time lag is the temporal difference between the peak
Fig. 6. Measuring points arrangement.
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Fig. 7. Ordinary wall surface temperature (Case A).
temperature of the solar air temperature and that of the inside surface when the indoor temperature is constant. Case A. The WIHP is composed of an ordinary wall and heat pipes. It is necessary to investigate the thermal behavior of the ordinary wall before studying the WIHP. We measured the average temperature of the inside and outside surfaces of the ordinary wall as shown in Fig. 7. We considered the heat transfer to be steady once the rate of temperature variation of the inside and outside surfaces were within 0.1 C/h and 0.5 C/h, respectively. The average temperature during the steady period can be regarded as a peak value. The amplitude is defined here as the difference between the peak value and initial value. As shown in Fig. 7, the outside surface temperature tends to be
steady from 11:00 to 16:00 (Point A) while the inside surface temperature is from 14:00 to 16:00 (Point B); the time lag is about 3 h. The amplitude of the outside and inside surface temperatures are 11.9 C and 1.5 C, respectively, with a decrement factor of about 7.9. The time lag and decrement factor we calculated according to Eqs. (8) and (9) are 3.5 h and 7. When calculating the response of the wall theoretically, the default indoor air temperature is 0 C. However, the indoor air temperature is not 0 C in any experiment due to natural, slight fluctuations, thereby causing some errors. Our calculated values do agree well with the experimental values, so the established mathematical model is appropriate to further analyze the WIHP. Case B. Nine temperature sensors on the inside surface were divided into three rows, and the average values of each row were
Fig. 8. WIHP surface temperature (Case B).
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(Point B), the temperature increase in the first row gradually slowed down. The temperature of the third row is slightly higher than that of the ordinary wall during heat pipe operation. This indicates that the direction of heat transfer is not only transverse but also longitudinal. As time progresses, the temperatures among rows tend toward stability. In this study, we utilized the TRC to evaluate the improvement remitted by heat pipes in regards to the inside wall surface under indoor and outdoor temperature variations. TRC is expressed as follows:
b¼
Fig. 9. Meteorological parameters of a typical day.
compared with the inside surface temperature of the ordinary wall as shown in Fig. 8. About 40 min after the beginning of the experiment, the medium in the evaporating section begin to evaporate and the resulting steam condensed in the condensing section to drive up the temperature of the first row. The start-up time of the heat pipes is the response time of the WIHP. The temperature rose quickest from 8:40 to 9:00 in the first row (Point C), which was 0.3 C higher than that of the zone without heat pipes (third row Point D) and 0.5 C higher than that of the ordinary wall at the same location (Point E). This indicates that the medium circulates well with complete heat exchange in the condensing section and rapidly improves the inside surface temperature. The outside surface temperature increased from 9:00 to 11:00 as the evaporation intensity gradually increased (Point A). However, the steam could not be condensed back to the evaporating section immediately due to the small temperature difference between the condensing section and the indoor air, so the system reached the condensation limit. The heat transfer capacity of the heat pipes is weak when the heat dissipation capacity of the condensing section does not match the heat absorption capacity of the evaporating section. At this point
tc tm tz tr
(17)
where tc is the condensing section temperature, C; tm is the temperature of the ordinary wall at the same location, C; tz is the solar air temperature, C; tr is the indoor air temperature, C. The maximum TRC was 0.11 during the operating time of our experiment. The solar air temperature tz and inside surface temperature tm are lower in winter, so the TRC will be relatively higher. 4.2. WIHP thermal response: a typical day Periodic heat transfer, an unsteady heat transfer process, has a significant impact on any given building. The rising and setting of the sun creates a 24-h period variation in outdoor temperature which affects the heat transfer through buildings. In the northern hemisphere, the south-facing wall surface is influenced by outdoor air temperature, solar radiation, the ground and atmospheric long wave radiation. We propose solar air temperature as a simple express ion of this synthetic impact; the outdoor air temperature increases the equivalent temperature of a solar radiation. The original equation is as follows:
tz ¼ tair þ
aI Qlw ho
(18)
where tair is outdoor temperature, C; a is surface absorptivity; I is solar radiation intensity, W/m2; Qlw is long wave radiation, W/m2; ho is the convective and radiative heat transfer coefficient, W/
Fig. 10. Ordinary wall surface temperature on a typical day (Case C).
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Fig. 11. WIHP surface temperature on a typical day (Case D).
(m2$K). The intensity of solar radiation is much greater than that of long wave radiation, the long wave radiation during daytime hours, so the long wave radiation can be neglected. The original equation can thus be simplified as follows:
Table 3 Summary of Case results. Time lag Case A Case B
tz ¼ tair þ
aI ho
(19)
Case C
WIHP performance is markedly influenced by weather. In northern China, the period between the heating season and cooling season, i.e., the “transition season”, extends from about mid-March to mid-May. During this period, the outdoor temperature and solar radiation increase while the indoor temperature may easily fall too low for comfort. WIHPs have better operating conditions in the transition season than other times during the year and indeed can improve the indoor thermal environment compared to ordinary walls. We selected a typical day (April 1) during which the outdoor temperature and radiation intensity are close to the average outdoor temperature and average radiation intensity of the transitional season. The solar air temperature on April 1 was calculated as
Case D
Decrement factor
Theoretical Experimental Theoretical Experimental 3.5 h 3h 7 7.9 Response time TRC (max) 40min 0.11 The high-frequency component of the outdoor disturbance curve can be mostly eliminated through the wall, which makes the decrement factor at each time a distinct variable. Response time TRC (max) 20min 0.39
shown in Fig. 9. We simulated this solar air temperature as the hourly outside surface temperature by adjusting the heating power of the hot box to reflect the periodic heat transfer process in the wall. Case C. As shown in Fig. 10, the curve of the inside surface temperature is smoother rather than mimicking the ladder-like curve of the outside surface temperature. This is because the irregular periodic wave is composed of N simple harmonic waves. The inside surface temperature at any given time is affected by the simple harmonic wave of the previous few hours. The wall also has varying decrement factors for simple harmonic waves of varying frequency e the decrement is more drastic when the frequency is high. Therefore, the high-frequency component of the outdoor disturbance curve (the steep part shown in Fig. 10) can be mostly eliminated through the wall, which makes the decrement factor at each time a distinct variable. Case D. The heat pipe begins working once the evaporating section temperature exceeds that of the condensing section, that is, when the outside surface temperature is higher than inside surface temperature. According to the solar air temperature curve of the typical day we assessed, Case D extends from 9:00 to 17:00 when the meteorological parameters are favorable for heat pipe operation. This period includes start-up (9:00e9:20) and running (9:20e17:00) of the heat pipe. As shown in Fig. 11, the heat pipe starts to work when the outside surface temperature reaches
Fig. 12. The TRC of WIHP.
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middle period, the heat pipe is operating under the condensation limit and the temperature difference between indoor and outdoor environments is largest, so the improvement is less remarkable. During the operating period, the maximum and average TRC are 0.39 and 0.16 and the average temperature of the inside surface is increased by 0.5 C. The result of each case is summarized in Table 3. 4.3. Heat transfer capacity
Fig. 13. Heat transfer capacity of ordinary wall on a typical day.
27.5 C; this is similar to the start-up temperature shown in Fig. 8. At 9:20e11:40, the maximum temperature rise of the first row is 0.7 C greater than the ordinary wall. The heat pipe reaches the condensation limit upon reaching a certain outside surface temperature, but continues to operate under the condensation limit. At 13:00, the heat transfer capacity of the pipe begins to weaken gradually as the outside surface temperature decreases. The heat pipe stops once the outside surface temperature falls below the evaporating (or condensing) temperature. The temperature drop of the third row is very close to that of the ordinary wall. The temperature drop in the first and second row, conversely, are relatively slow and the temperatures are significantly higher than the third row. This is because a portion of the heat is transferred into the room while the remainder is absorbed by the wall and then released constantly to heat the inside surface, thereby postponing the temperature attenuation. The TRC of the WIHP is shown in Fig. 12, where as indoor and outdoor temperatures fluctuate, TRC first decreases and then increases. The inside surface temperature is improved considerably in the initial and later periods compared to other time points. In the
The building envelope is constantly subjected to a periodic thermal wave which causes changes in the heat flux over time. The temperature fluctuation of the inside wall surface is a direct reflection of transient heat flux variations. We calculated the heat transfer capacity of the ordinary wall and WIHP in a typical day based on steady-state heat transfer and unsteady heat transfer theories, respectively, as shown in Figs. 12 and 13. Under steadystate heat transfer, the heat transfer process in the past N hours has no influence; heat transfer capacity is calculated by using the heat transfer coefficient, temperature difference, and area (Q ¼ KFDt). In actuality, however, the heat transfer process is unsteady. The effects of the previous N hours and the thermal storage of the wall must be taken into account. As shown in Fig. 13, the unsteady curve is delayed by 50 min compared to the steady curve. During the experimental period, the cumulative steady heat transfer capacity through the wall was about 811 J/m2 and the unsteady heat transfer capacity was about 1040 J/m2, which is 229 J/m2 higher due to the heat stored in the wall. As shown in Fig. 14, the heat transfer capacity of the heat pipe increased rapidly at 9:20e11:40 as the solar air temperature increased; the maximum value is about 6.76 W/m2. After reaching the condensation limit, the heat transfer capacity of the heat pipe decreased while the heat flux through the ordinary wall continued to rise. The total heat transfer capacity (THTC) of the WIHP continually increased until reaching a maximum of about 9.93 W/ m2 at 12:15. We found that the heat transfer capacity of the heat pipe and ordinary wall decreased significantly as solar air temperature decreased. The THTC of the WIHP was consistently higher than that
Fig. 14. WIHP heat transfer capacity on a typical day.
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References
Table 4 WIHP heat transfer capacity composition. Transient heat transfer (J/m2)
Thermal storage (J/m2)
Heat pipe THTC (J/m2)
Ordinary wall THTC (J/m2)
WIHP THTC (J/m2)
1733
425
2158
902
3060
of the ordinary wall due to the heat transfer of the pipe and thermal storage released in the previous few hours. Table 4 shows the composition of the WIHP THTC and proportion comprised by each part. The heat transferred into the room (transient heat transfer) accounts for about 80% of the heat pipe’s THTC and that to the outdoors (thermal storage) accounts for about 20%. In the THTC of the WIHP, the heat transferred by heat pipe accounts for about 70% and through the ordinary wall accounts for about 30%. In effect, the heat pipe transfers a large amount of solar energy to the room thereby reducing the heating load and resolving the contradiction between the wall’s insulation and solar energy utilization.
5. Conclusion The thermal response of the ordinary wall and WIHP, including time lag, decrement factor, response time, and operating time were investigated in this study via experiment. The TRC variable was used to evaluate the extent to which heat pipes improve inside wall surface temperature. The Z-transfer function method was also used to calculate the heat transfer capacity of a WIHP on a typical day, and to assess the proportion of each part of the capacity. Our conclusions can be summarized as follows. (1) The time lag and decrement factor of the ordinary wall are about 3h-3.5 h and 7e7.9 times. The mathematical model asestablished can be used to accurately analyze the WIHP. (2) The WIHP has a faster response to weather variations than the ordinary wall. On a typical day, the highly efficient heat transfer and long running time of the heat pipe (7 h 30 min) improves the average inside surface temperature by 0.5 C. The average TRC is 0.16. (3) In the THTC of the WIHP, the heat transferred by the heat pipe accounts for about 70% and through the ordinary wall for about 30%. The heat released from the heat pipe is stored by the wall, which staves off temperature attenuation and reduces temperature fluctuations in the inside wall surface, thereby creating a more comfortable indoor thermal environment.
Acknowledgments This research has been supported by Natural Science Foundation of Tianjin (Grant No.17JCYBJC21400).
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Thermal response of wall implanted with heat pipes: Experimental analysis Chang Liu*, Zhigang Zhang School of Energy and Safety Engineering, Tianjin Chengjian University, Tianjin 300384, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 20 November 2018 Received in revised form 2 May 2019 Accepted 28 May 2019 Available online 31 May 2019
A wall implanted with heat pipes (WIHP) features effective heat transfer between indoor and outdoor environments due to the pipe’s unidirectional thermal conductivity; the implant also resolves the contradiction between the wall’s insulation and solar energy utilization. The thermal performance of walls is crucial in terms of reducing a building’s energy consumption and improving its indoor thermal environment. The heat transfer process of the condensing section is the focus of the present study. We establish a dynamic heat transfer model of the condensing section based on the Z-transfer function, and introduces the temperature rise coefficient (TRC) concept. The thermal response characteristics of an ordinary wall and WIHP are determined via theoretical analysis and experimentation. The WIHP shows a faster thermal response to weather variations than the ordinary wall. In a typical day, the efficient heat transfer and long running time (7 h 30 min) of the heat pipe improve the average inside-surface temperature of the WIHP by 0.5 C and the average TRC by 0.16. A portion of the heat released from the pipe is also stored by the wall, which staves off temperature attenuation and minimizes temperature fluctuations in the inside surface, thereby creating a more comfortable indoor thermal environment. © 2019 Elsevier Ltd. All rights reserved.
Keywords: Wall implanted with heat pipes Thermal response Time lag Decrement factor Temperature rise coefficient
1. Introduction The building sector accounts for about 30e40% of the world’s total energy consumption. China’s buildings sector currently accounts for 27.6% of the country’s total energy use and is projected to increase to 35% by 2020 [1,2]. Laying an insulation layer on the outside surface of the wall structure is a common approach to energy savings, as it reduces indoor heat loss in winter and heat gain in summer months [3]. The insulation performance of wall directly affects the level of the building’s energy consumption [4,5]. However, the solar radiation absorbed on the outside surface of south-facing walls does not effectively transfer into the room in winter, due to the thick insulation layer. If this solar energy could be utilized effectively, the heating load would be reduced and the indoor thermal comfort markedly further improved [6e8]. “Passive walls” such as PCM walls [9,10] or heating-based types of Trombe wall including the classic Trombe wall (CTW), Trombe-Michel wall (TMW), water Trombe wall (WTW), and solar trans-wall (STW) have emerged as researchers attempt to better utilize solar
* Corresponding author. E-mail address: [email protected] (C. Liu). https://doi.org/10.1016/j.renene.2019.05.123 0960-1481/© 2019 Elsevier Ltd. All rights reserved.
radiation for efficient heating [11e13]. Zhang et al. [14] combined a gravity heat pipe with a wall to construct a novel passive solar energy utilization technology, the wall implanted with heat pipes (WIHP). As a result of efficient heat transfer, one-way thermal conductivity, and thermal switch of the heat pipe, heat can be transferred into the room in winter and out of the room in summer through a phase change in the pipe medium (Fig. 1). Intelligent control valves are installed on the adiabatic section in the south wall and north wall, respectively. In winter, when the indoor temperature is lower than the set temperature of the valve on the south wall, the valve there will open while the valve on the north wall is closed; in summer months, the opposite occurs. This facilitates beneficial heat transfer between indoor and outdoor environments while resolving the contradiction between the wall insulation and solar energy utilization. They established a steady-state heat transfer model of the WIHP and analyzed its thermal performance and applicability accordingly. However, the heat transfer of the building envelope is a complex process. It includes three basic processes: heat absorption, heat release, and heat conduction of the envelope. These processes involve three basic heat transfer modes: conduction, convection, and radiation. Meteorological parameters such as air temperature and solar radiation intensity constantly change along seasonal and diurnal
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tc tm
Nomenclature
ar aa [Gi] A(s) Rr,Ra
li ai ci
ri
li S
jyn nyn un Aan 4n tz tr
Convective heat transfer coefficient of the inside wall surface (W$m2$K1) Convective heat transfer coefficient of the outside wall surface (W$m2$K1) submatrix matrix elements thermal resistance of convective heat transfer (m2$K$W1) Thermal conductivity (W$m1$K1) Thermal diffusivity (m2$h1) Specific heat capacity (kJ$ kg1$K1) Density (kg$m3) Thickness (m) Fundamental temperature frequency Time lag Decrement factor Frequency of the thermal wave Amplitude Initial phase Solar air temperature ( C) Indoor temperature ( C)
tair
t
E R
a I ho bi, ci, di q z Q n
Dqm a Dqm i
Condensing section temperature ( C) Temperature of the ordinary wall at the same location ( C) Outdoor temperature ( C) Time Exponential function Thermal resistance of the inner plaster layer (m2$K$W1) Surface absorptivity Solar radiation intensity (W$m2) Convective heat transfer coefficient (W$m2$K1) Transfer coefficient Heat flux (W$m2) Z-transform heat transfer capacity (W) time Solar air temperature amplitude at time m ( C) Inside surface temperature amplitude at time m ( C)
Abbreviation WIHP Wall implanted with heat pipes TRC Temperature rise coefficient THTC Total heat transfer capacity
Fig. 1. WIHP structure and principle.
variations, thus the indoor air temperature and envelope surface temperature also change constantly. The heat flux through the envelope also changes with time in an unsteady heat transfer process. The decrement factor and time lag are two important parameters in unsteady heat transfer, which represent the resistance of the wall and the response time to thermal waves, respectively; they are often used to evaluate the thermal performance of a wall. Many previous scholars have studied thermal response in walls. Ciril et al. [15], for example, designed a thin (68 mm) composite timber facade wall with improved thermal response where heat wave propagation time lag falls between 9 h and 12 h at the optimal wall composition. Reza et al. [16] investigated the effects of various parameters such as wall thickness, inner and outer heat transfer
coefficients, and thermal insulation layers in sandwich walls on the time lag and decrement factor. The decrement factor of the wall is in inverse relation to the thickness of the insulation layer and changes with the combined convection and radiation heat transfer coefficients of the wall’s inside and outside. Asan et al. [17] researched the effects of thermal properties and wall thickness on time lag and decrement factor based on one-dimensional numerical models. They found that time lag has a positive correlation with the thermal capacity and the thickness of the wall, but a negative correlation with the wall’s thermal conductivity. The decrement factor has a negative correlation with the thermal capacity and thickness, but a positive correlation with thermal conductivity. Available methods for analyzing unsteady heat transfer can be
C. Liu, Z. Zhang / Renewable Energy 143 (2019) 1687e1697
divided into four categories: numerical analysis, harmonic analysis, reaction coefficient method, and Z-transfer function method. Koray et al. [18] analyzed the effects of solar energy falling onto the outside surface of a wall on the inside environment based on a onedimensional transient heat conduction model. Oliveti et al. [19] proposed a non-dimensional periodic global transmittance model where in the ratio of heat flux which is transferred to the indoor environment and the external heat flux describes the wall’s harmonic thermal behavior. Tian et al. [20] built three heat transfer models by reaction coefficient method to study the dynamic thermal response performance of concrete radiant cooling slab; they also introduced the “core temperature layer” concept. Francesco et al. [21] used the heat transfer matrix method to analyze the dynamic thermal performance of different multi-layered walls. Zorana et al. [22] established a novel approach for estimating thermal impulse response (TIR) functions and determining the dynamic thermal characteristics of a multilayer facade wall with unknown thermal properties, structure, and dimensions. Ruivo et al. [23] developed a transient heat transfer model based on the finite difference method to predict the thermal behavior of external walls under realistic outdoor conditions. In a numerical analysis model, all parameters must be recalculated when the boundary conditions change. This makes the calculation process highly complex. The harmonic analysis method is only suitable for solving the periodical heat conduction differential equation. The reaction coefficient method is slow in calculating the unsteady heat transfer of the wall, especially for heavy walls. The Z-transfer function can be used to solve the equation more quickly and accurately. As early as 1971, Stephenson [24] used the Z-transfer function method to calculate the transient heat flux through a wall. Mitalas [25] and Peavy [26] later analyzed Ztransfer function properties and the relationship between transfer and reaction coefficients. Similar to the reaction coefficient, the transfer coefficient reflects the dynamic thermal characteristics of a wall but can be calculated more easily. Therefore, the Z-transfer function method was chosen to analyze the unsteady heat transfer of the wall in this study. The unsteady heat transfer process of a WIHP consists of heat transfer in the heat pipe and the ordinary wall. Further research on dynamic heat transfer characteristics and energy-saving potential of this structure has important practical significance. The present study was conducted to investigate the thermal response characteristics of WIHPs such as the actual response time, temperature
3 1 " 1 An ðsÞ AðsÞ BðsÞ 6 ar 7 7 ½G ¼ ¼6 5 4 Cn ðsÞ CðsÞ DðsÞ 0 1 3 2 1 # " A1 ðsÞ B1 ðsÞ 6 1 a 7 a7 6 5 4 C1 ðsÞ D1 ðsÞ 0 1 1 1 Rr ¼ ; Ra ¼ "
ar
#
2
Bn ðsÞ Dn ðsÞ
#
Fig. 2. Schematic diagram of multi-layered wall.
2. Methodology 2.1. Ordinary wall heat transfer matrix The heat transfer matrix method, also referenced as the “thermal quadrupole method”, is an important part of the Z-transfer function process and often used to describe heat conduction in onedimensional structures [21]. The transfer matrix represents the thermal performance of the wall, which is related to the thermal parameters of the wall materials and is irrelevant to the input or output parameters, as shown in Fig. 2. It is a bridge connecting the temperature and flux of the inside and outside wall surfaces. In the case of a multi-layered wall consisting of a sequence of n homogeneous layers, each submatrix should be multiplied sequentially from the output side to the input side, i.e., from indoor to outdoor. The transfer matrix ½G can thus be evaluated as follows:
½G ¼ ½Gr ½Gn / ½Gi / ½G1 ½Ga
(1)
i.e.
" /
1689
Ai ðsÞ
Bi ðsÞ
Ci ðsÞ
Di ðsÞ
# /
(2)
aa
increase, and temperature distribution under real-world conditions. The results of this study may provide workable guidelines for subsequent optimization.
where [Gi] is a submatrix; A(s), B(s), C(s) and D(s) are matrix elements; ar and aa are convective heat transfer coefficient of the inside and outside wall surfaces, W/(m2$K); Rr and Ra are the thermal resistance of convective heat transfer, (m2$K)/W.
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Each element in the matrix can be calculated according to the thermophysical properties of each layer of the wall.
rffiffiffiffi s Ai ðsÞ ¼ Di ðsÞ ¼ cosh li ai rffiffiffiffi 1 rffiffiffiffi s s li sinh li ai ai
(4)
Ci ðsÞ ¼
rffiffiffiffi rffiffiffiffi s s sinh li li ai ai
(5)
li
where ai is thermal diffusivity, m2/h; li is the thermal conductivity, W/(m$K); ci is the specific heat capacity, kJ/(kg$K); ri is the density, kg/m3; li is the thickness, m; and S is the fundamental temperature frequency.
#
"
Bi Z
∞ X
# Bi eai Dt
(11)
i¼1
where z is Z-transform. The Z-transfer function is usually expressed in the form of the ratio of two Z-polynomials to reduce the quantity of Z-polynomials and the calculation time. Thus, the Z-transfer function of the wall GY (z) is: BðzÞ
GY ðzÞ ¼ (6)
ci ,ri
∞ X i¼1
(3)
Bi ðsÞ ¼
ai ¼
" z½qY ðtÞ ¼ Z½K t þ Z
P∞ i¼1 1
Dt
eaiDt Z 1
¼
b0 þ b1 Z 1 þ b2 Z 2 þ / 1 þ d1 Z 1 þ d2 Z 2 þ /
(12)
The coefficient of the denominator is equal on both sides of the equation. The transfer coefficients di and bi can be obtained by solving the roots -ai of B(s) in the transfer matrix. When the indoor temperature is constant, the heat transfer capacity of the wall at time n is:
QY ðnÞ ¼
m X i¼0
bi tz ðn iÞ
m X
di Q ðn iÞ tr
i¼1
m X
ci
(13)
i¼0
2.2. Ordinary wall frequency response The frequency response is the time lag jyn and decrement factor nyn of the wall to the sine wave as outdoor frequency varies while the indoor air temperature is maintained at 0 C. The imaginary part of the exponential function E(t) is the thermal wave to be input:
EðtÞ ¼ Aan ½cosðun t þ 4n Þ þ i sinðut þ 4n Þ ¼ Aan eiðun tþ4n Þ
(7)
where E is the exponential function; t is time; Aan is amplitude; un is the frequency of the thermal wave; 4n is the initial phase; i is an imaginary unit. The time lag jyn is equal to the argument of element B (iun) in the transfer matrix. The time lag jyn and decrement factor nyn are expressed as follows:
jyn ¼ arctan nyn ¼ ar
Bðiun ÞIm Bðiun ÞRes
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 Bðiun ÞRes þ BðiuÞIm
(8)
(9)
where jyn is time lag; nyn is decrement factor.
2.3. Ordinary wall unsteady heat transfer capacity The transient heat flux through the wall can be calculated via Ztransfer function method. The Z-transfer function of the wall system is the Z-transform of the response to the unit isosceles triangular-shaped pulses, i.e., the Z-transform of the reaction coefficient sequence of the wall. The thermal response of the wall to the unit oblique wave, i.e., the heat flux influenced by the unit oblique wave, is as follows:
qY ðtÞ ¼ K t þ
∞ X
Bi 1 eai t
Where Q is heat transfer capacity, W; n is time; tz is solar air temP Pm perature, C; tr is indoor temperature, C; m i¼0 ci ¼ i¼0 bi .
2.4. WIHP dynamic heat transfer model The solar radiation absorbed by the outside surface of the southfacing wall is transferred into the room through the wall and heat pipe, respectively. The dynamic heat transfer model of the WIHP can be regarded as a superposition of the ordinary wall and the condensing section of the heat pipe, as shown in Fig. 3. The condensing section, as a heating surface, is key in improving the inner-surface temperature of the wall and the indoor thermal environment. The heat transfer process of the condensing section is the focus of this study. In winter, the outside surface temperature increases as the building absorbs solar energy. When the outside surface temperature reaches evaporation temperature of the working medium, the medium begins to vaporize, i.e., the heat pipe starts to work. Heat is absorbed by the working medium in the evaporating section and rejected in the condensing section. During this time, a portion of the heat is transferred into the inside surface (q2 transient heat transfer) while the remainder is absorbed by the wall (q3 thermal storage). When the outside surface temperature drops below the evaporation temperature, the heat pipe stops working. The transient heat transfer then ceases and the stored heat is released constantly to the inside surface. Here, we apply some assumptions to simplify the model.
(10)
i¼1
where q is heat flux, W/m; K is the heat transfer coefficient, W/ (m2$K); Y is the transfer process of the wall. The Z-transform of Eq. (10) is discretized at an equal time interval Dt.
Fig. 3. WIHP dynamic heat transfer model.
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(1) The heat exchange between the evaporating section and inside surface is neglected. The insulation layer prevents the inside surface and indoor thermal environment from being influenced by the evaporating section. (2) The heat exchange between the wall and the adiabatic section covered by the insulation layer is neglected. (3) The thermal storage of the inner plaster layer (20 mm) is neglected due to its small thickness. Hence, the heat exchange between the condensing section and inside wall surface can be regarded as steady. The temperature wave is typically used as an input to solve unsteady heat transfer problems. In this paper, the heating surface temperature tc0 , an internal disturbance, serves as the input transient heat transfer and thermal storage:
t 0c ¼ tc tm
(14)
where tc is the condensing section temperature, C; tm is the temperature of the ordinary wall at the same location, C. The value of tc is always greater than or equal to that of tm, so the internal disturbance temperature tc0 is an hourly temperature variation higher than or equal to 0 C. At this time, the temperatures of the two wall sides are set to 0 C so that the heat transfer of the condensing section can be solved. Due to the high thermal resistance and thermal inertia of the wall, the heat transfer process from the condensing section to the outdoor region can be analyzed via Z transfer function theory (similar to the ordinary wall). The thermal storage q3 can be calculated by Eq. (13). As per the simplification (3) mentioned above, the transient heat transfer q2 can be calculated as follows:
q2 ¼
t ’c R
(15)
where R is the thermal resistance of the inner plaster layer, (m2$K)/ W.
3. Experimental procedures The dimensions of the test wall are 1720 1720 mm and its thermal properties are as listed in Table 1. Separate heat pipes are embedded in the inside and outside plastering layer respectively, as shown in Fig. 4. The size of the capillary net is 1000 600 mm and it consists of 24 capillary tubes with 2.7 mm inner and 4.2 mm outer diameters. The size of the adiabatic pipe, riser, and downcomer are F20 2.0 mm. All of the pipes are cylindrical and made of polypropylene random (PPR). We tested the thermal response of a WIHP using the building wall thermal insulation performance testing equipment shown in Fig. 5. There is a heater and an evaporator in the hot box and cold box, respectively. The temperature of the hot box and cold box can be controlled automatically or manually by the controller. We established four test cases listed in Table 2 to investigate the
Table 1 Wall thermal properties. Material
l/mm
l/[W/(m$K)]
r/[kg/m3]
cp/[kJ/(kg$K)]
Cement mortar Autoclaved aerated concrete blocks Molded polystyrene board Cement mortar
20 250
0.930 0.200
1800 500
1.050 1.461
50 20
0.041 0.930
22 1800
2.414 1.050
Fig. 4. Separate heat pipe.
thermal response of the WIHP under various outdoor temperatures. The experimental platform was in a basement laboratory rather than outdoors, so the outdoor temperature was simulated by manually controlling the hot box temperature. There were two main outdoor temperature settings used in the test. One was a constant 40 C; the other temperature setting enabled the outside surface temperature to reach the solar air temperature of a typical day. The hot box temperature was set every hour according to said typical solar air temperature. In addition, the inside surface was controlled as a stable indoor environment by opening the cold box, so the basement laboratory could provide stable temperature and humidity. Eighteen Pt1000 sensors were arranged on the inside and outside surfaces to record temperatures in different zones, as shown in Fig. 6. All of the sensors were calibrated to accuracy of 0.1 C. The temperature signals are collected with a GP10 data acquisition device that has accuracy of ±(temperature reading 0.05% þ 0.3 C). 4. Results and discussion The results of the four test cases are discussed in this section. Cases A and C mainly center on the time lag/decrement factor of the ordinary wall and the thermal wave attenuation law, respectively. The calculation method was validated through these experiments in regards to the accuracy of the unsteady heat transfer of WIHP. Cases B and D mainly center on the response time and temperature rise coefficient (TRC) of the WIHP. The heat transfer capacity was calculated by using the Z-transfer function method. 4.1. WIHP response time and TRC Decrement factor and time lag, as discussed above, are two important parameters for studying the heat transfer characteristics of a wall in a periodic thermal environment. The decrement factor is the ratio of solar air temperature amplitude to the inside surface temperature amplitude when the indoor temperature is constant, which can be defined as follows:
nyn ¼
Dqm a Dqm i
(16)
where Dqm a is the outdoor disturbance (solar air temperature)
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(a)
(b) Fig. 5. Building wall thermal insulation performance testing equipment.
Table 2 Experimental setup parameters. Case A B C D
Hot box temperature
40 C 40 C e e
Outside surface temperature
Wall
e e Solar air temperature Solar air temperature
Ordinary wall WIHP Ordinary wall WIHP
amplitude at time m, C; Dqm i is the inside surface temperature amplitude at time m, C. We calculated the decrement factor by plugging our experimental data into Eq. (16). The time lag is the temporal difference between the peak
Fig. 6. Measuring points arrangement.
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Fig. 7. Ordinary wall surface temperature (Case A).
temperature of the solar air temperature and that of the inside surface when the indoor temperature is constant. Case A. The WIHP is composed of an ordinary wall and heat pipes. It is necessary to investigate the thermal behavior of the ordinary wall before studying the WIHP. We measured the average temperature of the inside and outside surfaces of the ordinary wall as shown in Fig. 7. We considered the heat transfer to be steady once the rate of temperature variation of the inside and outside surfaces were within 0.1 C/h and 0.5 C/h, respectively. The average temperature during the steady period can be regarded as a peak value. The amplitude is defined here as the difference between the peak value and initial value. As shown in Fig. 7, the outside surface temperature tends to be
steady from 11:00 to 16:00 (Point A) while the inside surface temperature is from 14:00 to 16:00 (Point B); the time lag is about 3 h. The amplitude of the outside and inside surface temperatures are 11.9 C and 1.5 C, respectively, with a decrement factor of about 7.9. The time lag and decrement factor we calculated according to Eqs. (8) and (9) are 3.5 h and 7. When calculating the response of the wall theoretically, the default indoor air temperature is 0 C. However, the indoor air temperature is not 0 C in any experiment due to natural, slight fluctuations, thereby causing some errors. Our calculated values do agree well with the experimental values, so the established mathematical model is appropriate to further analyze the WIHP. Case B. Nine temperature sensors on the inside surface were divided into three rows, and the average values of each row were
Fig. 8. WIHP surface temperature (Case B).
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(Point B), the temperature increase in the first row gradually slowed down. The temperature of the third row is slightly higher than that of the ordinary wall during heat pipe operation. This indicates that the direction of heat transfer is not only transverse but also longitudinal. As time progresses, the temperatures among rows tend toward stability. In this study, we utilized the TRC to evaluate the improvement remitted by heat pipes in regards to the inside wall surface under indoor and outdoor temperature variations. TRC is expressed as follows:
b¼
Fig. 9. Meteorological parameters of a typical day.
compared with the inside surface temperature of the ordinary wall as shown in Fig. 8. About 40 min after the beginning of the experiment, the medium in the evaporating section begin to evaporate and the resulting steam condensed in the condensing section to drive up the temperature of the first row. The start-up time of the heat pipes is the response time of the WIHP. The temperature rose quickest from 8:40 to 9:00 in the first row (Point C), which was 0.3 C higher than that of the zone without heat pipes (third row Point D) and 0.5 C higher than that of the ordinary wall at the same location (Point E). This indicates that the medium circulates well with complete heat exchange in the condensing section and rapidly improves the inside surface temperature. The outside surface temperature increased from 9:00 to 11:00 as the evaporation intensity gradually increased (Point A). However, the steam could not be condensed back to the evaporating section immediately due to the small temperature difference between the condensing section and the indoor air, so the system reached the condensation limit. The heat transfer capacity of the heat pipes is weak when the heat dissipation capacity of the condensing section does not match the heat absorption capacity of the evaporating section. At this point
tc tm tz tr
(17)
where tc is the condensing section temperature, C; tm is the temperature of the ordinary wall at the same location, C; tz is the solar air temperature, C; tr is the indoor air temperature, C. The maximum TRC was 0.11 during the operating time of our experiment. The solar air temperature tz and inside surface temperature tm are lower in winter, so the TRC will be relatively higher. 4.2. WIHP thermal response: a typical day Periodic heat transfer, an unsteady heat transfer process, has a significant impact on any given building. The rising and setting of the sun creates a 24-h period variation in outdoor temperature which affects the heat transfer through buildings. In the northern hemisphere, the south-facing wall surface is influenced by outdoor air temperature, solar radiation, the ground and atmospheric long wave radiation. We propose solar air temperature as a simple express ion of this synthetic impact; the outdoor air temperature increases the equivalent temperature of a solar radiation. The original equation is as follows:
tz ¼ tair þ
aI Qlw ho
(18)
where tair is outdoor temperature, C; a is surface absorptivity; I is solar radiation intensity, W/m2; Qlw is long wave radiation, W/m2; ho is the convective and radiative heat transfer coefficient, W/
Fig. 10. Ordinary wall surface temperature on a typical day (Case C).
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Fig. 11. WIHP surface temperature on a typical day (Case D).
(m2$K). The intensity of solar radiation is much greater than that of long wave radiation, the long wave radiation during daytime hours, so the long wave radiation can be neglected. The original equation can thus be simplified as follows:
Table 3 Summary of Case results. Time lag Case A Case B
tz ¼ tair þ
aI ho
(19)
Case C
WIHP performance is markedly influenced by weather. In northern China, the period between the heating season and cooling season, i.e., the “transition season”, extends from about mid-March to mid-May. During this period, the outdoor temperature and solar radiation increase while the indoor temperature may easily fall too low for comfort. WIHPs have better operating conditions in the transition season than other times during the year and indeed can improve the indoor thermal environment compared to ordinary walls. We selected a typical day (April 1) during which the outdoor temperature and radiation intensity are close to the average outdoor temperature and average radiation intensity of the transitional season. The solar air temperature on April 1 was calculated as
Case D
Decrement factor
Theoretical Experimental Theoretical Experimental 3.5 h 3h 7 7.9 Response time TRC (max) 40min 0.11 The high-frequency component of the outdoor disturbance curve can be mostly eliminated through the wall, which makes the decrement factor at each time a distinct variable. Response time TRC (max) 20min 0.39
shown in Fig. 9. We simulated this solar air temperature as the hourly outside surface temperature by adjusting the heating power of the hot box to reflect the periodic heat transfer process in the wall. Case C. As shown in Fig. 10, the curve of the inside surface temperature is smoother rather than mimicking the ladder-like curve of the outside surface temperature. This is because the irregular periodic wave is composed of N simple harmonic waves. The inside surface temperature at any given time is affected by the simple harmonic wave of the previous few hours. The wall also has varying decrement factors for simple harmonic waves of varying frequency e the decrement is more drastic when the frequency is high. Therefore, the high-frequency component of the outdoor disturbance curve (the steep part shown in Fig. 10) can be mostly eliminated through the wall, which makes the decrement factor at each time a distinct variable. Case D. The heat pipe begins working once the evaporating section temperature exceeds that of the condensing section, that is, when the outside surface temperature is higher than inside surface temperature. According to the solar air temperature curve of the typical day we assessed, Case D extends from 9:00 to 17:00 when the meteorological parameters are favorable for heat pipe operation. This period includes start-up (9:00e9:20) and running (9:20e17:00) of the heat pipe. As shown in Fig. 11, the heat pipe starts to work when the outside surface temperature reaches
Fig. 12. The TRC of WIHP.
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middle period, the heat pipe is operating under the condensation limit and the temperature difference between indoor and outdoor environments is largest, so the improvement is less remarkable. During the operating period, the maximum and average TRC are 0.39 and 0.16 and the average temperature of the inside surface is increased by 0.5 C. The result of each case is summarized in Table 3. 4.3. Heat transfer capacity
Fig. 13. Heat transfer capacity of ordinary wall on a typical day.
27.5 C; this is similar to the start-up temperature shown in Fig. 8. At 9:20e11:40, the maximum temperature rise of the first row is 0.7 C greater than the ordinary wall. The heat pipe reaches the condensation limit upon reaching a certain outside surface temperature, but continues to operate under the condensation limit. At 13:00, the heat transfer capacity of the pipe begins to weaken gradually as the outside surface temperature decreases. The heat pipe stops once the outside surface temperature falls below the evaporating (or condensing) temperature. The temperature drop of the third row is very close to that of the ordinary wall. The temperature drop in the first and second row, conversely, are relatively slow and the temperatures are significantly higher than the third row. This is because a portion of the heat is transferred into the room while the remainder is absorbed by the wall and then released constantly to heat the inside surface, thereby postponing the temperature attenuation. The TRC of the WIHP is shown in Fig. 12, where as indoor and outdoor temperatures fluctuate, TRC first decreases and then increases. The inside surface temperature is improved considerably in the initial and later periods compared to other time points. In the
The building envelope is constantly subjected to a periodic thermal wave which causes changes in the heat flux over time. The temperature fluctuation of the inside wall surface is a direct reflection of transient heat flux variations. We calculated the heat transfer capacity of the ordinary wall and WIHP in a typical day based on steady-state heat transfer and unsteady heat transfer theories, respectively, as shown in Figs. 12 and 13. Under steadystate heat transfer, the heat transfer process in the past N hours has no influence; heat transfer capacity is calculated by using the heat transfer coefficient, temperature difference, and area (Q ¼ KFDt). In actuality, however, the heat transfer process is unsteady. The effects of the previous N hours and the thermal storage of the wall must be taken into account. As shown in Fig. 13, the unsteady curve is delayed by 50 min compared to the steady curve. During the experimental period, the cumulative steady heat transfer capacity through the wall was about 811 J/m2 and the unsteady heat transfer capacity was about 1040 J/m2, which is 229 J/m2 higher due to the heat stored in the wall. As shown in Fig. 14, the heat transfer capacity of the heat pipe increased rapidly at 9:20e11:40 as the solar air temperature increased; the maximum value is about 6.76 W/m2. After reaching the condensation limit, the heat transfer capacity of the heat pipe decreased while the heat flux through the ordinary wall continued to rise. The total heat transfer capacity (THTC) of the WIHP continually increased until reaching a maximum of about 9.93 W/ m2 at 12:15. We found that the heat transfer capacity of the heat pipe and ordinary wall decreased significantly as solar air temperature decreased. The THTC of the WIHP was consistently higher than that
Fig. 14. WIHP heat transfer capacity on a typical day.
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References
Table 4 WIHP heat transfer capacity composition. Transient heat transfer (J/m2)
Thermal storage (J/m2)
Heat pipe THTC (J/m2)
Ordinary wall THTC (J/m2)
WIHP THTC (J/m2)
1733
425
2158
902
3060
of the ordinary wall due to the heat transfer of the pipe and thermal storage released in the previous few hours. Table 4 shows the composition of the WIHP THTC and proportion comprised by each part. The heat transferred into the room (transient heat transfer) accounts for about 80% of the heat pipe’s THTC and that to the outdoors (thermal storage) accounts for about 20%. In the THTC of the WIHP, the heat transferred by heat pipe accounts for about 70% and through the ordinary wall accounts for about 30%. In effect, the heat pipe transfers a large amount of solar energy to the room thereby reducing the heating load and resolving the contradiction between the wall’s insulation and solar energy utilization.
5. Conclusion The thermal response of the ordinary wall and WIHP, including time lag, decrement factor, response time, and operating time were investigated in this study via experiment. The TRC variable was used to evaluate the extent to which heat pipes improve inside wall surface temperature. The Z-transfer function method was also used to calculate the heat transfer capacity of a WIHP on a typical day, and to assess the proportion of each part of the capacity. Our conclusions can be summarized as follows. (1) The time lag and decrement factor of the ordinary wall are about 3h-3.5 h and 7e7.9 times. The mathematical model asestablished can be used to accurately analyze the WIHP. (2) The WIHP has a faster response to weather variations than the ordinary wall. On a typical day, the highly efficient heat transfer and long running time of the heat pipe (7 h 30 min) improves the average inside surface temperature by 0.5 C. The average TRC is 0.16. (3) In the THTC of the WIHP, the heat transferred by the heat pipe accounts for about 70% and through the ordinary wall for about 30%. The heat released from the heat pipe is stored by the wall, which staves off temperature attenuation and reduces temperature fluctuations in the inside wall surface, thereby creating a more comfortable indoor thermal environment.
Acknowledgments This research has been supported by Natural Science Foundation of Tianjin (Grant No.17JCYBJC21400).
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