A STUDY ON THE THERMAL PERFORMANCE SIMULATION TO EVALUATETHE PREFABRICATED RADIANT FLOOR HEATING PANELS

Myoung Souk Yeo and Kwang Woo Kim

Department of Architecture, Seoul National University, San56-1,Shinlim-Dong, Kwanak-Gu, Seoul, 151-742, Korea

ABSTRACTComputer models used for analyzing heat transferhave been developed and computerized for theprecise thermal analysis of two typical prefabricatedradiant floor heating panels. The developed computerprogram was validated by comparing the computersimulation results against the scaled model testresults. Computer simulations, for the sensitivityanalyses of the various design parameters and controlwater temperature shows the thermal performancewith the variations of these parameters and therelationship among these parameters.

INTRODUCTIONRadiant floor heating(Ondol in Korean) is a domesticheating method which has been used in Korea formore than 1,500 years. In ancient years, thetraditional radiant floor heating system(Ondol) wasdeveloped to form a furnace, heated air passages, anda chimney(from A.D. 100 to 1950’s). Recently, thefuel was changed from fire wood to anthracite coal.Currently the traditional system has been modernizdto use hot water running embedded tubes to heatfloors.

With the recent changing trends in housingproduction methods, from wet construction toprefabricated or dry construction, various types ofprefabricated radiant floor heating panels have beendeveloped and used. In order to develop a thermallyeffective alternative, a thermal evaluation using anexpensive and time consuming test would be needed.

In this study, for the precise thermal analysis of thevarious prefabricated radiant floor heating panels, aheat transfer analysis program has been developedand computerized for two selected typicalprefabricated panel types.

In an effort to assist the designer in determining theoptimum values for certain design variables in theearly design stages, sensitivity analyses using thecomputer simulation are conducted to see how thepanel will perform in different ranges of design andcontrol parameters.

SELECTION OF THE TYPICALPREFABRICATED PANEL TYPESThe prefabricated radiant floor heating panels can beclassified as panels with thermal mass and withoutthermal mass. In this study, two typical models wereselected based on this classification criteria, andanalysis models were developed for each of them.The details of two typical models are as follows.

A-modelAs shown in Fig.1, its structure is similar to that ofthe traditional radiant floor heating panel. Thedifferences are a thin thermal mass and the use of amortar as a thermal mass instead of gravel.

B-modelAs shown in Fig.2, heat from the pipe is transferred tothe heat emitting board(Aluminum plate) through theheat conducting conduit. The lower part is filled withpoly-urethane foam insulation.

Fig.2 Section of B-model Fig.1 Section of A-model

ALGORITHM

The heat transfer analysis methods, which so far, havebeen effective for the analysis of the radiant floorheating panel are the steady-state one dimensionalanalysis by Adlam[10], Kolmar Liese's Methodexplanied by Kim[3] and the unsteady-state analysisby M. Udagawa[8] and by R.W. Shoemaker[9].Recently, Zhang et al.(1989)[11] use steady statesemi-analytical equations to relate the supply watertemperature, panel heat output, and physicalcharacteristics of the panel. But the design methodfocuses on the panel heat output as a function ofsupply water temperature rather than panel surfacetemperature and model may not be applicable to thosestructures that deviated from the assumptions madeduring the model development. Another study on thecomparison between the thermal performance of aradiant heating system and a warm air system waspresented by Zmeureanu et al.(1988)[12], usingdetailed computer program to simulate the transientheat transfer processes occurring in a room. Thesimulation mainly focuses on the room airtemperature and other thermal comfort index,assuming that the radiant panel surface temperature iskept at 31.5&.

The effect of floor temperature on comfort is verysignificant in domestic housing because the Koreansusually sit or sleep on the warm floor which suppliesheat to the feet as well as the body by conduction. Sothe contact thermal sensation is unique due to theincreased contact between body and floor surfacefrom this kind of life style. It was indicated thatcomfort can be achieved by maintaining the floortemperature 2538.8&, average 31& under theroom air temperature condition 17.524.5&.Furthermore the uniformity of surface temperature isalso major factor on contact thermal comfort. So inthis study, heat transfer analysis computer models,which can calculate the temperatures of all the nodesin a panel, have been developed with the unsteady-state two dimensional analysis method using the finitedifference method(FDM) for the accurate analysis ofthe time varying thermal characteristics of the panel.As the heat flow in the panel is a three dimensionalunsteady state heat transfer, convection heat transferof hot water in the pipe and conduction heat transferin the panel should be calculated simultaneously inthree dimensional coordinates. This will requiretremendous amounts of calculations. The section ofpanel has equally spaced pipe layout and the specificheat of the water(the heating medium in the pipe) ishigher than that of the thermal mass. So, it can beassumed that the temperature gradient in the directionof the hot water pipes is negligible compared to thatin the direction perpendicular to the pipes. Thus theheat transfer in the panel was simplified by analyzingin section which is perpendicular to the pipes. This

will make it possible to get very close results with theminimum amount of calculations. As the hot waterpipes are equally spaced in this section, it can beassumed that the same unit section is symmetricallyrepeating.

In this study, the heat transfer in the panel is analyzedas a two dimensional unsteady-state heat transfer inthe unit section perpendicular to the pipe.

Conduction in panelThe two dimensional unsteady-state conductionequation becomes,

k T

X+

T

Y = Cp

T

t

2

2

2

2

0

0

0

0ç

0

0

⋅ ⋅ . (1)

Convection and radiation on panelThe heat flow on the panel surface can be found bythe following equation according to Newton's coolinglaw.

q = E A (T - T )air surface⋅ (2)

Where, E = h + hc r

(A) Convective heat transfer coefficient

The convective heat transfer coefficient(hc) becomes,

h = 2.26 Tc4

� ∆ . (3)

(B) Radiative heat transfer coefficientThe radiative heat transfer coefficient(hr) between thepanel surface and the wall surface is calculated asfollows.

h = 4 Tr m3

�Û� �σ (4)

Convection in the pipe

(A) Convective heat transfer coefficient in water flowThe convective heat transfer coefficient(hw) betweenthe water and the smooth inside surface of the circularpipe is as follows.

h = Nu k

Dw D� (5)

For the fully developed turbulent flow(ReD>2,300) inthe circular pipe, values from Dittus-Boelter'sequation[2] is adapted.

Nu = 0.023 Re PrD D 0.8 0.3

� � (6)

(B) Heat transfer when the flow is stoppedAfter the flow is stopped, the lumped capacitancemethod[2] is applied assuming the stopped fluid as auniform solid body.

Boundary ConditionsThe following boundary conditions as in Fig.3 andFig.4, are established for the analysis models.

(A) Convection boundary (CB)During the hot water supply, the convective heattransfer occurs between the water and the insidesurface of the pipe.

(B) Isotropic boundary(IB-L, IB-R, IB-D )The vertical center line of the pipe and the verticalline at half of the pitch are the isotropic boundary,and an symmetrical temperature distribution isattained. Below the panel is perfectly insulated, and itis assumed that no heat loss occurs.

(C) Radiation and convection boundary(RCB)The surface of the panel is exposed to the radiativeand the convective heat transfer.

(D) conduit boundary(CDB)

For the analysis of the complex heat transfer alongthe heat conducting conduit of B-model, a simplifiedconduction model is developed.

DEVELOPMENT OF A COMPUTERMODELIn this study, the numerical solution of the finitedifference method is attained by the implicit methodwhich can get the stable result regardless of the timeincrement. For the solution of the implicit method, theGauss-Seidel iteration method is utilized. In thatiteration, the calculations, to get the temperatures ofnodes for the next iteration step, are repeated until the

Fig.6 Grid system of B-model

Fig.7 The flow chart of the program

(a) Section of A-model (b) Control volumeFig.3 Boundary conditions of A-model

Fig.5 Grid system of A-model

(a) Section of B-model (b) Control volumeFig.4 Boundary conditions of B-model

solution converges. The convergence criterionadapted for this study was,

Grid systemThe grid systems established in dividing the inside ofthe panel into finite nodes are illustrated in Fig. 5 andFig. 6.

The structure of the programThe flow of the developed computer program isshown in Fig. 7.

ValidationThe developed computer simulation program wasvalidated by comparing with the scaled model testresults, which were conducted in the previousstudy[7]. The comparisons of the panel surfacetemperatures above the pipe and at half of pitch, andpanel bottom temperatures below the pipe and at halfof pitch are shown for the validation from Fig.8 toFig.11. The temperature differences between thesimulated results and test results were generally less

than 0.5&. But some temperature deviation showedat the panel bottom nodes when hot water issupplying.

SIMULATIONFor the analysis of the thermal performance of thepanel, the maximum difference of surfacetemperatures and the average surface temperature ofthe panel were evaluated while the room temperatureis maintained at 21&.

EvaluationKIER(Korea Institute of Energy Research)[7]proposed the acceptable ranges of the temperature asfollows ; room temperature 21�2&, panel surfacetemperature 31�2&, and maximum surfacetemperature difference limit 4&. The ProclamationNo.396 (1987.8.19) [14], that restricts the floor panelstructure and sizing, by the Ministry of Constructionin Korea is as follows ; thermal mass layer4070mm, finishing layer 15mm25mm abovethe pipe, pipe diameter over 15mm, and pipe spacing150400mm.

Fig.8 Validation of A-model(surface temperature) Fig.9 Validation of A-model(bottom temperature)

Fig.10 Validation of B-model(surface temperature) Fig.11 Validation of B-model(bottom temperature)

T - T

T 1 1 0

i , jk - 1

i , jk

i , jk

- 3∑

∑≤ × . (7)

The apartment building in Korea is operated based ontwo kinds of heating modes (intermittent heating withtime schedule and continuous heating with indoortemperature feedback). The former is non-feedbackcontrol which just gives 3 or 4 times of hot watersupply from the central plant. Despite of a large roomtemperature fluctuations, this intermittent heating ismore dominant than the continuous heating becauseof the advantages in the initial cost, simpleinstallation, ease of maintenance and the lower stand-by loss of the system.

The survey of the intermittent heating schedule inexisting apartment building[13] shows that theheating cycle rate is 24 cycles per day, the periodof one cycle is 2 to 3 hours, and the supply watertemperature is 5070&. The simulation results wereevaluated on the basis of the comfort range, operatingcondition and structural regulation.

Simulation variablesThermal performance of floor heating panel isaffected by two main parameters. Those are thedesign parameter and the control parameter. So, thesimulation was done through the followingprocedures.

First, both models were simulated with the variationsof pipe spacing, pipe diameter and supply watertemperature to examine the interrelated effects ofthem. Second, the application of both models in twoheating modes were checked and the desirableimprovement was suggested. Both models weresimulated with the variations of pipe spacing andsupply water temperature, additionally B-model withthe variations of thickness and thermal conductivityof heat emitting board, for the continuous heatingmode. A-model was intensely simulated with thevariations of thermal mass and depth of pipe bury forthe intermittent heating mode.

Supply water temperature and pipe diameterFig.12, Fig.13, Fig.14 and Fig.15 show the averagesurface temperature and the temperature difference ofthe panel with the variations of the supply watertemperature and pipe diameter based on two differentpipe spacing (A-model : 200mm, 100mm, B-model :140mm, 70mm). As the pipe diameter increases, theaverage surface temperature becomes higher and thetemperature difference slightly increases. The pipediameter has more effect on the average surfacetemperature than the surface temperature difference.In the case of narrow pipe spacing, this effectbecomes trivial(Fig.13, Fig.15). And the surfacetemperature is more affected by the pipe spacing andsupply water temperature rather than the pipediameter.

Supply water temperature and pipe spacingThe simulation with the variations of supply watertemperature and pipe spacing was conducted. Fig.16and Fig.17 show that the average surface temperatureis inversely proportional to the pipe spacing. Thesurface temperature difference between maximumand minimum surface temperatures of the panel isproportional to the pipe spacing. The slope of thesetwo curves becomes smooth as the supply watertemperature decreases. The desirable supply watertemperature and pitch can be selected by the averagesurface temperature and the temperature differencelimit.

A-model : 35& of water temperature and 260mm ofpipe spacing are desirable due to the average surfacetemperature and difference within the comfort rangeproposed by KIER. With the existing panel design,A-model is not applicable to intermittent heatingmode because high water temperature causesdiscomfort surface temperature. But the increase ofmaterial thickness could make it possible to fit for theintermittent heating mode.

B-model : 35& of water temperature and 175mm ofpipe spacing are desirable due to the average surfacetemperature and difference within the comfort rangeproposed by KIER. B-model is not applicable tointermittent heating mode, either. It has no effectivealternatives for the application of the intermittentheating mode. So this model must be installed for thecontinuous heating mode if it were not for the greatmodification of panel design.

Depth of pipe bury in fixed thermal mass thickness(A-model)A-model was intensely simulated with the thicknessvariations of thermal mass and depth of pipe bury forthe intermittent heating mode (60& of supply watertemperature and 1 cycle heat supply for 2-hours). Forthe intermittent heating mode, the increase of materialthickness is needed. So within 95mm of the maximumallowable thickness of thermal mass and finishinglayer according to Proclamation No.396 (1987.8.19),the effect of depth of pipe bury on the panel surfacetemperature is examined. In Fig.18 and Fig.19, whenthe pipe is embedded in upper part of the panel, theaverage surface temperature becomes very high andthe panel has quick response to heating start and stop.When the pipe is embedded in lower part of panel,the surface temperature difference becomes less andeven temperature distribution can be obtained.

The material thickness above the pipe has more effecton the uniform surface temperature and the thermalstorage effect than the thickness below the pipe.Through the additional simulations, it can be noticedthat the increase of material thickness below the pipe

has no great effect on the thermal storage and surfacetemperature differences of the panel. So the increaseof the thickness below the pipe is not desirable for theintermittent heating application.

Material thickness above the pipe (A-model)The step increment of material thickness above thepipe from existing thickness was simulated. As shownin Fig.20, it fails to maintain the comfortable surfacetemperature ranges (31�2&) proposed by KIER(They didn’t specify the heating mode to maintainthat comfort range. It seems that ranges are notappropriate for the intermittent heating mode). Butthe thickness from 42.5 to 65mm keeps surfacetemperature within the comfortable ranges (2538.8&) for longer periods compared to otherthickness. And it shows a little slow response toheating start and stop. In Fig.21, 65mm of thicknessabove the pipe can satisfy the temperature differencelimit (4&). So it is desirable to have less than 65mmabove the pipe for the intermittent heating mode forA-model.

Thickness and thermal conductivity of heat emittingboard(B-model)With the increased thickness and thermal conductivityof the heat emitting board, the average surfacetemperature becomes higher and the temperaturedifference lessens. But the change was so small, andhas no great effect on panel surface temperature.

CONCLUSIONSFor the precise thermal analysis of the variousprefabricated radiant floor heating panels, a heattransfer analysis model was developed andcomputerized for the selected two typical panel types,and verified by comparing with the results of modeltests. The developed computer program simulationresults can be summarized as follows.

1. The average surface temperature is more affectedby the hot water pipe spacing and supply watertemperature rather than by the pipe diameter. Thesize of pipe diameter has more effect on theaverage surface temperature than on the surfacetemperature difference.

2. The pipe spacing and the water temperature are theimportant variables. The desirable supply watertemperature and pipe spacing for the continuousheating mode can be selected as follows.

a) A-model : 35& of water temperature and 260mmof pipe spacing are desirable. With the existingpanel design, A-model is not appropriate forintermittent heating mode.

b) B-model : 35& of water temperature and 175mmof pipe spacing are desirable. B-model is notappropriate for intermittent heating mode, either.

3. The increase of thickness above the pipe iseffective in A-model for the intermittent heatingmode. Less than 65mm above the pipe is desirablefor the comfortable panel surface temperature.

4. The variations of thickness and thermalconductivity of heat emitting board show no greateffect for B-model. So this model must be installedfor the continuous heating mode if it were not forthe great modification of panel design.

REFERENCES1. Adams, J. Alam, „Computer aided heat transfer

analysis“, McGraw-Hill, 1973.

2. Incropera, F.P., and D.P. Dewitt, „Introduction toheat transfer“, John Willey & Sons, 1981.

3. Hyo Kyung Kim, „Building mechanical systemengineering pocket book“, Kidary, 1983.

4. Kwang Woo Kim, „Thermal storage and heattransfer medium in Ondol“, Ondol Seminar; ASpecial Meeting by the Architectural Institute ofKorea, Sep., 1990.

5. Laszlo J. Banhidi, „Radiant heating systems designand applications“, Pergamon press, 1991.

6. Lilley, David G., and D.R.Croft, „Heat transfercalculations using finite difference equations“,Applied Science Publishers, 1977.

7. KIER(Korea Institute of Energy Research), „TheNew Housing Technology Development Program;The Development of the Low-Cost and HighEfficiency Heating System(§)“, Ministry ofScience & Technology, 1992.

8. M, Udagawa, „Simulation of panel coolingsystems with linear subsystem model“, ASHRAETransactions DE93-3-2, 1993.

9. Richard Woolsey Shoemaker, „Radiant heating“,McGRAW-Hill, 1954.

10. T.Napier Adlam, „Radiant heating“,The industrialPress, 1949.

11. Zhang, Z and M.B.Pate, „A new approach fordesigning heating panels with embedded tubes“,ASHRAE Transactions No.3227, 1989.

12. Zmeureanu, R., P.P. Fazio and F.Haghighat,„Thermal performance of radiant heating panels“,ASHRAE Transactions No.3148, 1988.

13. KICT (Korea Institute of ConstructionTechnology), „Improvement of environmentalperformance in multi-family housing“, KICT,Dec., 1991.

14. Ministry of Construction in Korea, „Thearchitectural code and regulations“, 1990.

NOMENCLATURE

T Temperature in node

k Thermal conductivity

ç Density

Cp Specific heat

hc Convective heat transfer coefficient

hr Radiative heat transfer coefficient

Û Effective emittance

è Stefan-Boltzmann constant

∆T The temperature difference between the roomair and the panel surface

Tm The average surface temperature of the walls andthe panel

hw Convective heat transfer coefficient in pipe

NuD Nusselt number

k Thermal Conductivity of water

D Diameter of the pipe

ReD Reynols number

Pr Prantle number

Fig.12 Variations of supply water temperature and pipediameter(A-model, pipe spacing 200mm)

Fig.13 Variations of supply water temperature and pipediameter(A-model, pipe spacing 100mm)

Fig.14 Variations of supply water temperature and pipediameter(B-model, pipe spacing 140mm)

Fig.15 Variations of supply water temperature andpipe diameter(B-model, pipe spacing 70mm)

Fig.16 Variations of supply water temperature and pipespacing (A-model)

Fig.17 Variations of supply water temperature and pipespacing (B-model)

Fig.18 Variations of depth of pipe bury in fixedthermal mass thickness (A-model, average surfacetemperature)

Fig.19 Variations of depth of pipe bury in fixedthermal mass thickness (A-model, surfacetemperature difference)

Fig.20 Variations of material thickness above thepipe(A-model, average surface temperature)

Fig.21 Variations of material thickness above thepipe(A-model, surface temperature difference)