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Applied Thermal Engineering 62 (2014) 398e406

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Numerical and experimental analysis of floor heat storage and releaseduring an intermittent in-slab floor heating process

Dengjia Wang*, Yanfeng Liu, Yingying Wang, Jiaping LiuSchool of Environmental and Municipal Engineering, Xi’an University of Architecture and Technology, No. 13 Yanta Road, Xi’an 710055, China

h i g h l i g h t s

� The relationship between the intermittent time and the preheating time is obtained.� The heat storageerelease characteristics of intermittent heating floor are fully mastered.� The numerical simulation method is demonstrated to be at least accurate within 7%.

a r t i c l e i n f o

Article history:Received 20 May 2013Accepted 17 September 2013Available online 25 September 2013

Keywords:Intermittent heatingSurface temperatureFloor heat storage and releaseCOMSOL

* Corresponding author. Tel.: þ86 29 82202506, þ8E-mail address: wangdengjia1020@163.com (D. W

1359-4311/$ e see front matter � 2013 Elsevier Ltd.http://dx.doi.org/10.1016/j.applthermaleng.2013.09.02

a b s t r a c t

In this paper, the floor heat storage in the preheating period and the heat release in the intermittentperiod during an intermittent in-slab floor heating process are investigated. Numerical simulations areused to determine the effect of the design and operating parameters, i.e., the pipe spacing, the fillinglayer thickness and the pipe water temperature, on the floor heat storage and heat release. The rela-tionship between the intermittent time and the preheating time is also obtained. The results show thatpipe spacing has the dominant effect on the preheating time. In the intermittent period, 2 h later, thetwo-dimensional heat transfer process can be modeled as a one-dimensional vertical heat transferprocess, and the filling layer thickness has a relatively large effect on the heat release time. The nu-merical simulation method is shown to be accurate to at least within 7% of the experimentalmeasurements.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

An in-slab floor heating system offers many advantages, such asamenity, energy conservation, aesthetics, etc. [1,2]. However, peo-ple’s life patterns frequently result in the intermittent operation ofthe in-slab floor heating system, where the operation mode isdetermined by the heat gain from the floor and the floor heatstorage and release. Most importantly, the floor heat storage andrelease are affected by several factors, including the floor structure,the filling layer thickness, the material properties, the spacing be-tween the laid pipes, the pipe diameter and the water temperature,making it difficult to determine the operation mode of the inter-mittent heating.

Previous studies have mainly focused on modeling and simu-lating floor heating systems [3e6]. Computational steady state

6 13279455510 (mobile).ang).

All rights reserved.8

methods have been widely applied to the in-slab heating floortransfer process [7,8]. In 1992, Kilkis [9] introduced a steady heattransfer composite-fin model, in which the areas between thepipes were modeled as plate fins. A fin efficiency was used toaccount for the difference between the indoor air temperatureand the mean radiant temperature and to incorporate contribu-tions to the floor surface heat transfer from both the convectionheat between the upper floor surface and the indoor air and theradiant heat from other internal surfaces. In 1995, the afore-mentioned models were simplified and the modeling procedureswere programmed in FORTRAN. The calculated results weresummarized using a convenient series of charts [10,11]. S.T. Hu[12] developed a two-dimensional steady state mathematicalmodel for floor heat transfer: a dynamic simulation programbased on the finite element method was used to calculate theoperating parameters, such as the highest floor surface temper-ature, the indoor operating temperature, the heat-flow densityand the pre-heating time, for different pipe water supply tem-peratures and pipe spacings. X.M. Feng and Y.Q. Xiao [13]

-l/2 l/2

facing brick

x

y

0

S

pipes

filling layer

thermal insulation layer

1 m

Fig. 1. Schematic of an in-slab heating floor.

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406 399

developed a two-dimensional unsteady state floor heat transfermodel to determine the relationships among the floor surfacetemperature, the pipe spacing, the filling layer thickness and thepipe water temperature. I. Pyeongchan [14] developed a two-dimensional unsteady state floor heat transfer model, whichwas validated by comparing results from experiments with thosefrom numerical simulations of the model. Y.F. Liu [15] developed amathematical model to describe the thermal processes in a floorheating room. The solver of this model was programmed usingthe Duhamel theorem. Gilles Fraisse [16] analyzed the relation-ships among the required pre-heating time of the intermittentheating system, the pre-heating time, the thermal comfort leveland the energy consumption. Other researchers [5] have primarilystudied the heat exchange process and the system performance.The aforementioned studies have served as a foundation for thepresent study.

The aforementioned models are used in this study to investigatethe floor heat storage in the preheating period and the heat releasein the intermittent period for an intermittent in-slab floor heatingprocess. Numerical simulations are used to determine the effects ofthe design and operating parameters, i.e., the pipe spacing, thefilling layer thickness and the pipe water temperature, on the floorheat storage and heat release, and to obtain a relationship betweenthe intermittent time and the preheating time. In the followingsections, the numerical simulation results are verified by compar-ison with experimental measurements.

2. Theoretical analysis

2.1. Differential equation for heat conduction

The fundamental assumptions used in the model are givenbelow.

(i) The materials in each layer are homogeneous with constantproperty parameters.

(ii) The pipe surface is insulated during the heating system stops.(iii) The heat conduction along the pipe axis is neglected, and the

heat conduction inside the floor is modeled as a two-dimensional steady state process [17e19].

(iv) The pipelines are symmetrically distributed.(v) The bottom of the pipe is insulated.

A differential equation describing two-dimensional unsteadystate heat-conduction in an embedded-pipe heated floor has beenpreviously developed [20,21] and is given in Equation (1).

vtvs

¼ a

v2tvx2

þ v2tvy2

!(1)

The schematic of an in-slab heating floor is shown in Fig. 1. Theinitial and boundary conditions are prescribed during the pre-heating period and the intermittent period, respectively.

2.2. Definite conditions

2.2.1. Pre-heating periodWe first consider the case in which the intermittent time is

sufficiently long that the temperature of the in-slab heating floor isapproximately equal to that of the indoor air. We next consider thecase with a short intermittent time such that the initial tempera-ture of the in-slab heating floor is the same as the temperature atthe end of the intermittent period.

(1) Boundary conditions① The boundary surfaces along the x-axis are assumed to be

adiabatic and can be described by the Equation (2), and itrelates to the surfaces not contacting the pipes.

vtvx

����x¼� l

2

¼ vtvx

����x¼ l

2

¼ 0 (2)

② The boundary surfaces along the y-axis are modeled usingthe following equations:

vtvy

����y¼0

¼ 0 (3)

and

�lvtvy

����y¼h

¼ ðac þ arÞ � ðt � taÞ (4)

where ac and ar are the heat convection coefficient and the radiantheat transfer coefficient for the floor surface, respectively, in W/(m2 K), the values for which are taken from the literature [22].

③ The boundary of the pipe surface is described by

tjðxþ l2Þ2þðy�RÞ2¼R2 ¼ tjðx� l

2Þ2þðy�RÞ2¼R2 ¼ ts (5)

(2) Initial condition

The initial condition for the first case is given by

ts0 ¼ ta (6)

The initial condition for the second case is given by

ts0 ¼ g�xi; yj;n

�(7)

Where g(xi,yi,n) is the temperature field at the end of the inter-mittent period. MATLAB is used to construct the interpolatingfunction int (x,y,n).

2.2.2. Intermittent period

(1) Boundary condition

The pipe surface is assumed to be adiabatic. The boundarycondition on the pipe surface is given by Equation (8).

vtvR

����ðxþ l2Þ2þðy�RÞ2¼R2

¼ vtvR

����ðx� l2Þ2þðy�RÞ2¼R2

¼ 0 (8)

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406400

The other boundary conditions are the same as those specifiedfor the pre-heating period.

(2) Initial condition

The initial condition is given by

ts0 ¼ f�xi; yj

�(9)

where f(xi,yj) is the internal steady state temperature field of the in-slab continuous heating floor. Interpolation processing of thesimulated steady state simulation results is performed usingMATLAB. The resulting temperature distribution law correspondsto the interpolating function int (x,y), which is used as the initialcondition in the numerical simulation of the intermittent period.

2.3. Mathematical model of floor heat storageerelease

The unit length in-slab heating floor in the computations isdefined as follows: the width equals the pipe spacing l and thelength is 1 m. A schematic of the floor is shown in Fig. 1 also.

2.3.1. Pre-heating periodDuring the pre-heating period, the instantaneous heat release

capacity of the floor surface and the pipe surface per unit length ofthe in-slab heating floor can be expressed by Equations (10) and(11), respectively:

qf ¼ 2Zl=20

q1dx (10)

qp ¼ 2Zs

q2ds (11)

The internal instantaneous heat storage capacity per unit lengthof the in-slab heating floor is the difference between the heatrelease capacity of the pipe surface and that of the floor surface, asgiven in Equation (12):

qs ¼ qp � qf ¼ 2

0B@Z

l=2

0

q1dx�Zs

q2ds

1CA (12)

This theoretical analysis can be numerically simulated. Thus, thevalue of the instantaneous heat storage capacity during the pre-heating process qs(si) can be calculated. An analytical expressioncan be obtained by fitting the discrete solution results. Finally, thetotal heat storage capacity of the floor is obtained by integrating thefollowing expression:

qSðsÞ ¼ fit½qsðs1Þ; qsðs2Þ;.; qsðsnÞ� ¼ qS;fitðsÞ (13)

QS;t ¼Zt0

qs;fitðsÞds (14)

where qS(s) is the instantaneous heat storage capacity per unitlength of the in-slab heating floor, in W, during the preheatingperiod. The fitted expression for the instantaneous heat storage, inW, of the floor is denoted by qS,fit(s). The total heat storage capacityper unit length of the in-slab heating floor, in J, during the pre-heating period is denoted by QS,t.

2.3.2. Intermittent periodDuring the intermittent period, the instantaneous heat release

capacity of the floor surface and the pipe surface per unit length ofthe in-slab heating floor can be expressed by Equations (15) and(16), respectively:

qr ¼ 2Zl=20

q3dx (15)

qp ¼ 0 (16)

The pipe surface is assumed to be insulated during the inter-mittent period. Thus, the heat release capacity of the pipe surface qpequals zero.

The total heat release capacity during the intermittent period istreated similarly to the total heat storage capacity during the pre-heating period. The relationship between the total heat releasecapacity per unit floor during the intermittent period and the heatrelease time can be obtained using Equations (17) and (18):

qRðsÞ ¼ fitðqrðs1Þ; qrðs2Þ;.; qrðsnÞÞ ¼ qR;fitðsÞ (17)

QR;t ¼Zt0

qR;fitðsÞds (18)

where qR(s) is the instantaneous heat release capacity per unitlength of the in-slab heating floor, in W, during the intermittentperiod. The fitted expression for the instantaneous heat releasecapacity of the floor, in W, is denoted by qR,fit(s). The total heatrelease capacity per unit length of the in-slab heating floor, in J/m,during the intermittent period is denoted by QR,t.

3. Methodologies

3.1. Numerical simulation method

COMSOL Multiphysics 4.1 software is used to solve the afore-mentioned mathematical model. The initial condition of the tem-perature field is determined using interpolation processing withMATLAB, which produces the interpolating functions int (x,y) orint (x,y,n).

The geometrical configuration is shown in Fig. 1. The simulationmodel is a two-dimensional transient heat conduction model. Thetwo-dimensional unsteady state heat-conduction differentialequation consists of Equations (1)e(9) above. The geometry wasmeshed using the FREE mesh generator which is efficient to thesimpler models. In order to generate a finer mesh, triangular meshand quadrilateral mesh were used. And then, mesh-independencywere studied with mesh refinement level growing stepwise froma coarse mesh of roughly 0.5 thousand cells through a normal mesh1 thousand cells, a refined mesh 2 thousand, a very refined mesh 5thousand cells approximately to the extremely refined mesh 10thousand cells. By comparing the simulated result under thedifferent condition of mesh refinement level, and considering thestability of numerical calculation, the very refined mesh ofapproximately 5 thousand cells were selected to solve the heattransfer model [23].

3.2. Conditions used in numerical simulations

Table 1 provides values for the pipe water temperature, thefilling layer thickness and the pipe spacing for the different casesconsidered.

Table 1Values for pipe water temperature, filling layer thickness and pipe spacing fordifferent cases.

Pipe water temperature/�C 40 50 60Pipe spacing/mm 100 200 300Filling layer thickness/mm 50 60 70Pipe diameter/mm 16/20

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406 401

3.2.1. Main floor structureFacing brick layer e brick setting: thickness d1 ¼10 mm; density

r1 ¼ 1900 kg/m3; thermal conductivity l1 ¼ 1.1 W/(m K); specificheat c1 ¼ 1.05 kJ/(kg K); and heat storage coefficient (24 h)S1 ¼ 12.72 W/(m2 K).

Filling layers e crushed stone concrete: density r2 ¼ 2300 kg/m3; thermal conductivity l2 ¼ 1.51 W/(m K); specific heatc2 ¼ 0.92 kJ/(kg K); and heat storage coefficient (24 h) S2¼ 15.36W/(m2 K).

3.3. Experimental verification

3.3.1. Experimental site and instrumentThe experiments are taken as part of a solar heating demon-

stration project at a herdsman settlement in Gangcha County,Qinghai Province, China. The indoor air temperature is tested usinga TR-72U self-recording thermometer, which has a sensitivity of0.2�Cand takes recordings every 30 min. The floor surface tem-perature is measured using a R70B heat flux and temperaturemeterdeveloped by the Physics Department of the China Academy ofBuilding Research. Measurements were recorded every 10 min.Fig. 2 shows the test site, the controller, the water segregator andthe collector, the water circulating pump and the measurementinstruments.

3.3.2. Experimental objectiveThe pipe spacing is 300 mm.

3.3.2.1. Main floor structure. Face brick layer e ceramic tile: thick-ness d1 ¼ 5 mm, density r1 ¼ 1900 kg/m3, thermal conductivityl1 ¼ 1.1 W/(m K), specific heat c1 ¼ 1.05 kJ/(kg K), and heat storagecoefficient (24 h) S1 ¼ 12.72 W/(m2 K).

Filling layers e crushed stone and mortar: thicknessd2 ¼ 50 mm, density r2 ¼ 2300 kg/m3, thermal conductivityl2 ¼ 1.51 W/(m K), specific heat c2 ¼ 0.92 kJ/(kg K), heat storagecoefficient (24 h) S2 ¼ 15.36 W/(m2 K).

Thermal insulation layer e polystyrene cystosepiment: thick-ness d3 ¼ 50 mm, density r3 ¼ 30 kg/m3, thermal conductivityl3 ¼ 0.027 W/(m K), specific heat c3 ¼ 2.0 kJ/(kg K), heat storagecoefficient (24 h) S3 ¼ 0.34 W/(m2 K).

Pipe diameter: 16/20 mm.

3.3.3. Comparison between experimental and simulation resultsTable 2 compares the simulation and the experimental average

floor surface temperatures during the continuous heating period.Figs. 3 and 4 compare the simulation and the experimental values,respectively, for the average floor surface temperatures during thepre-heating and intermittent periods.

Table 2 shows that the error in the simulation results for themaximum, minimum and average values of the floor surface tem-perature during the continuous heating period are 5%, 6.9% and6.6%, respectively.

Figs. 3 and 4 show a maximum difference of 0.8 �C between thesimulation and the experimental values for the average floor sur-face temperature during the preheating period. The average dif-ference between the simulation and the experimental values is0.5 �C. There is a maximum difference of 0.9 �C between the

simulation and the experimental values for the average floor sur-face temperature during the intermittent period. The average dif-ference between the simulation and the experimental values is0.6 �C. However, from Figs. 3 and 4 we can also see that the dif-ference between the simulation results and experimental datatends to increase with time, and the simulation results are ingeneral higher than experimental data. It can be explained by thefollowing reasons. In response to the first problem, indoor airtemperature is considered to be constant during the pre-heatingand intermittent periods in the simulate process. In fact, it gradu-ally increases during the pre-heating and gradually decreasesduring intermittent period. For the second problem, this differencecan be attributed to the assumption, which is made to simplify thenumerical calculations, that the bottom of the pipe is insulated.Thus, the numerical simulation method is accurate to at leastwithin 7% of the experimental values.

All of the errors are within 7%, showing that the numericalsimulation method is relatively accurate.

4. Simulation results and analysis

4.1. Trends in the temperature and the heat flux

4.1.1. Intermittent periodFig. 5 shows the floor surface temperature and the heat flux

density for different pipe water temperatures during the inter-mittent period. Fig. 6 shows the average temperature of the floorsurface for different filling layer thicknesses. Fig. 7 shows theaverage temperature of the floor surface for different pipe spacings.

Fig. 5 shows that at the beginning of the intermittent period, thetemperature and heat flux density of the peak floor surface of thepipe is higher than that of the central floor surface of the pipe.However, these differences gradually disappear with time, i.e.,approximately 2 h later. The isotherm may be considered to behorizontal at this time. Thus, the average value of the floor surfacetemperature is used in the follow-up analysis. The floor surfacetemperature is also shown for pipe water temperatures of 50 �C,40�Cand 30 �C. The floor surface temperature tends to the roomtemperature of approximately 16 �C 20 h later. The floor surfaceheat-flow density tends to zero. The floor heat storage has thusbeen fully released. The temperature field is clearly similar to theheat-flow density field.

Fig. 6 shows that the filling layer thickness has less of an effecton the average floor surface temperature. Thus, at the beginning ofthe intermittent period, the average floor surface temperatures aresimilar for different filling layer thicknesses. However, the thinnerthe filling layer, the higher is the average floor surface temperature.The temperature decreases relatively rapidly during the intermit-tent period because the heat storage capacity decreases for thinnerfilling layers. After 1 h, the average floor surface temperature for athin filling layer decreases to less than that for a thick filling layer.Thus, the heat storage capacity increases with the thickness of thepacking layer. The process of heat release during the intermittentperiod is relatively slow.

Fig. 7 shows that the average floor surface temperature is higherfor smaller pipe spacings. A similar trend is observed for thedecrease in the temperature field at different pipe watertemperatures.

4.1.2. Pre-heating period

(1) Complete release of floor heat storage

Fig. 8 shows the average floor surface temperature and the heatflux density at different pipe water temperatures. Figs. 9 and 10

Fig. 2. Test site, system control devices and measurement instruments.

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406402

show the average floor surface temperature at different filling layerthicknesses and pipe spacings, respectively.

Fig. 8 shows that the average floor surface temperature and theheat flux density follow similar trends during the preheatingperiod. Higher pipe water temperatures cause more rapid increasesin the average floor surface temperature and the heat flux densityand vice versa. However, the preheating time for different pipewater temperatures is essentially the same at approximately 5 h.Thus, the pipe water temperature clearly has less of an effect on thepreheating time.

Fig. 9 shows that with thinner filling layers, the average floorsurface temperature is higher and the preheating time is shorterand vice versa. However, little difference is observed in the pre-heating times for different filling layer thicknesses. Thus, the fillinglayer thickness also does not significantly affect the preheatingtime.

Fig. 10 shows for smaller pipe spacings, the average floor surfacetemperature is higher and the preheating time is shorter. The pipespacings are 100 mm, 200 mm and 300 mm. The correspondingpreheating times are 2.5 h, 5 h and 7.5 h, respectively. Thus, the pipespacing clearly has a relatively large effect on the preheating time.

In conclusion, the pipe spacing has a relatively large effect on thepreheating time. Smaller pipe spacings correspond to shorter

Table 2Comparison between numerical and measured values of the floor surface temper-ature during the continuous heating period.

Maximum value Minimum value Mean value

Experimental 23.8 21.5 22.8Simulation 22.6 20.0 21.3Error 5% 6.9% 6.6%

preheating times. The pipe water temperature and the thickness offilling layers do not significantly affect the preheating time.

(2) Incomplete release of floor heat storage

Figs. 11 and 12 show the average floor surface temperatures fordifferent pipe water temperatures and pipe spacings.

Fig. 11 shows that for intermittent times of 2 h, 4 h and 10 h, thecorresponding preheating times are approximately 2 h, 3.5 h and

Fig. 3. Comparison between simulation and the experimental values of the averagefloor surface temperature during the preheating period.

Fig. 4. Comparison between simulation and the experimental values of the averagefloor surface temperature during the intermittent period.

Fig. 5. Floor surface temperature and heat flux density for different pipe water tem-peratures during the intermittent period (pipe spacing: 200mm; filling layer thickness).

Fig. 6. Average floor surface temperatures for different filling layer thicknesses duringthe intermittent period (pipe spacing: 200 mm; pipe water temperature: 40 �C).

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406 403

4.5 h, respectively. For short intermittent times, the preheatingtime corresponds to the intermittent time. For long intermittenttimes, the preheating time is shorter than the intermittent time.The heat storage capacity can be considered to be fully released forsufficiently long intermittent times. The preheating time for theseintermittent times is approximately 5 h. The pipe water tempera-ture only affects the average floor surface temperature and has lessof an effect on the preheating time.

Fig. 12 shows that for a pipe spacing of 100 mm, the averagefloor surface temperature increases relatively rapidly. The corre-sponding preheating time is relatively short. For the same inter-mittent time, a smaller pipe spacing corresponds to a shorterpreheating time. Table 3 shows the relationship between theintermittent time and the preheating time for different pipespacings.

Fig. 7. Average floor surface temperatures for different pipe spacings during theintermittent period (filling layer thickness: 60 mm; pipe water temperature: 40 �C).

Fig. 8. Average floor surface temperature and heat flux density for different pipe watertemperatures during the preheating period (pipe spacing: 200 mm; filling layerthickness: 60 mm).

Fig. 9. Average floor surface temperature for different filling layer thicknesses duringthe preheating period (pipe spacing: 200 mm; pipe water temperature: 40 �C).

Fig. 10. Average floor surface temperature for different pipe spacings during thepreheating period (filling layer thickness: 60 mm; pipe water temperature: 40 �C).

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406404

4.2. Floor heat storage and release

4.2.1. Intermittent periodFig. 10 shows the total heat release capacity per unit length of

the in-slab heating floor for different filling layer thicknesses dur-ing the intermittent period, which was obtained using the afore-mentioned theoretical analysis: the pipe spacing is 200 mm, thepipe water temperature is 40 �C and the filling layer thicknesses are50 mm, 60 mm and 70 mm.

Fig. 13 shows relatively large differences in the total heat releasecapacity per unit floor for filling layer thicknesses of 50mm, 60mmand 70mm. A thicker filling layer corresponds to a higher total heatrelease capacity and vice versa. After an intermittent period ofapproximately 20 h (72,000 s), the values of the total heat releasecapacity per unit length of the in-slab heating floor are 315 � 105 J/m, 4.62 � 105 J/m and 5.25 � 105 J/m for filling layer thicknesses of50 mm, 60 mm and 70 mm, respectively.

4.2.2. Pre-heating periodFig. 14 shows the behavior of the total heat storage capacity per

unit length of the in-slab heating floor for different filling layerthicknesses during the preheating period, which was obtainedusing the aforementioned theoretical analysis: the pipe spacing is200 mm, the pipe water temperature is 40 �C and the filling layerthicknesses are 50 mm, 60 mm and 70 mm, respectively.

Fig. 14 shows relatively large differences in the total heat storagecapacity per unit length of the in-slab heating floor for filling layerthicknesses of 50 mm, 60 mm and 70 mm. A thicker filling layercorresponds to a larger total heat storage capacity of the floor. Atthe same time, it takes relatively a long time for the total heatstorage capacity per unit floor to attain its maximum value: athinner filling layer corresponds to a smaller total heat storagecapacity. For filling layer thicknesses of 50 mm, 60 mm and 70 mm,

Fig. 11. Average floor surface average temperatures for different pipe water temper-atures and different intermittent times during the preheating period (pipe spacing:200 mm; filling layer thickness: 60 mm).

Table 3Relationship between the intermittent time and the preheating time for differentpipe spacings (filling layer thickness: 60 mm; pipe water temperature: 40 �C).

Intermittent time/h 0.5 1 2 4 6 10 Infinite

Preheating time/h Space between pipes100 mm

0.5 0.7 1 1.5 1.7 2 2.5

Space between pipes200 mm

0.5 1 2 3.5 4 4.5 5

Space between pipes300 mm

0.5 1 2 3.8 5.5 7 7.5

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406 405

the values of the total heat storage capacity per unit length of thein-slab heating floor are 3.2� 105 J/m, 4.7� 105 J/m and 5.3� 105 J/m, respectively. The corresponding times needed to attain themaximumvalue of the total heat storage capacity per unit length ofthe in-slab heating floor are approximately 7 h, 10 h and 12.5 h,respectively.

Fig. 13. Total heat release capacity per unit floor for different filling layer thicknesses

5. Conclusions

The floor heat storage during the preheating period and the heatrelease during the intermittent period are investigated for theheating of an intermittent in-slab floor. The following conclusionsare drawn from the results of the study.

Fig. 12. Average floor surface temperatures for different pipe spacings and differentintermittent times during the preheating period (filling layer thickness: 60 mm; pipewater temperature: 40 �C).

(1) During the preheating period, the pipe spacing has a largeeffect on the preheating time. The pipe water temperatureand the filling layer thickness have less of an effect on thepreheating time. The relationship between the intermittent

during the intermittent period (pipe spacing: 200 mm; pipe water temperature:40 �C).

0 2 4 6 8 10 12 140

100

200

300

400

500

600

Time/h

Totle

hea

t sto

rage

/kJ/

m

Filling layer thickness 50mmFilling layer thickness 60mmFilling layer thickness 70mm

Fig. 14. Total heat storage capacity per unit floor for different filling layer thicknessesduring the preheating period (pipe spacing: 200 mm; pipe water temperature: 40 �C).

D. Wang et al. / Applied Thermal Engineering 62 (2014) 398e406406

time and the preheating time were obtained. The heat stor-age characteristics of a floor with intermittent heating werewell understood.

(2) In the intermittent period, after 2 h of intermittent heating,the two-dimensional floor heat transfer process can beapproximated by a one-dimensional vertical heat transferprocess. After 20 h, the heat release process may be consid-ered to be complete. The pipe water temperature and thepipe spacing have a relatively smaller effect on the heatrelease time. The filling layer thickness has a significant effecton the heat release time. The heat release characteristics of afloor with intermittent heating floor were well understood.

(3) The values of the total heat storage and release capacity lie inthe same range between 3 � 105 J/m and 5 � 105 J/m. Thenumerical simulationmethod was shown to be accurate to atleast within 7% of the experimental results.

Acknowledgements

We wish to thank the National Natural Science Foundation ofChina (Project No. 51078302) for funding support. This work wasalso made possible by a grant from the Creative Research Groups ofChina (Project No. 50921005).

Nomenclature

a thermal diffusion coefficient, m2/sh vertical ordinate of upper surface of floor, ml pipe spacing, mmq1 heat-flow density distribution of floor surface during the

pre-heating period, W/m2

q2 heat-flow density distribution of pipe surface during thepre-heating period, W/m2

q3 heat-flow density distribution of floor surface during theintermittent period, W/m2

qf floor surface instantaneous heat release capacity per unitlength of the in-slab heating floor, W

qp pipe surface instantaneous heat release capacity per unitlength of the in-slab heating floor, W

qR(s) instantaneous heat release capacity per unit length of thein-slab heating floor during the intermittent period, W

qR,fit(s) fitted expression for floor instantaneous heat releasecapacity per unit length of the in-slab heating floor, W

QR,t total heat release capacity per unit length of the in-slabheating floor during the intermittent period, J

qS(s) instantaneous heat storage capacity per unit of the in-slabheating floor during the preheating period, W

qS,fit(s) fitted expression for instantaneous floor heat storagecapacity per unit length of the in-slab heating floor, W

QS,t total heat storage capacity per unit length of the in-slabheating floor during the preheating period, J

R pipe radius, mS half-circumference of the pipe, mt temperature, �Cta indoor air temperature, �Cts pipe water temperature, �Cts0 initial temperature, �C

Greek symbolsl thermal conductivity of the facing brick, W/(m K)ac heat convection coefficient of floor surface, W/(m2 K)ar radiant heat transfer coefficient of floor surface, W/(m2 K)

Subscriptsa indoor airc convectionf floorp piper radiationR releaseS storage

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