Heat Transfer of Radiant Cooling Panels

Heat Transfer to Radiant Cooling Panels JEAN-PIERRE EGGIMANN, Research Assistant, Solar Energy and Building Physics Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. JOHN R. THOME, Professor, Laboratory of Heat and Mass Transfer, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. CLAUDE-ALAIN ROULET, Senior Researcher, Solar Energy and Building Physics Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland.

ABSTRACT Radiant cooling ceiling panels are an alternative to air conditioning in some climates. However their heat transfer properties are not well-known and in consequence they are often poorly dimensioned. In the present study, we first made a physical model of heat transfer from a radiating panel to its environment and then programmed the equations representing the multiple heat exchanges in a computer program. Then, we made laboratory measurements in order to determine the amount of heat absorbed by the upper and lower faces of the panel respectively, and also to separate these heat flows into radiation, convection and conduction. Two causes explain the main differences between measurements and calculations. The space above these panels is usually colder than the space beneath them and thus the heat exchange to the upper face is smaller than calculated with a uniform temperature. The mean radiative temperature calculated only from the temperatures of the walls, ceiling and floor do not give a correct value. Heat sources in the room, although very small in size, have a high temperature and raise the mean radiative temperature seen by the panel from 0,4 to 3,5°C. A correct calculation of the heat transfer to radiant cooling panels should take into account the temperature asymmetry of its environment. Elements like windows, desk lamps, computer screens and other electrical devices have a higher temperature and increase the radiative heat transfer to cooling panels.

1. INTRODUCTION In order to provide a comfortable thermal working environment, it is often necessary to cool offices. For this, radiant cooling ceiling panels (Figure 1) are becoming more widely used in Europe in place of air conditioning (Roulet et al, 1999). These water climatic systems have many advantages over classical air conditioning: no noise, no draught, no risk of contaminant dissemination, less power for energy transport and use of "warmer" chilled water. In well-insulated buildings, they can also be used as radiant heaters and thus completely substitute the heating system. However the heat transfer properties of these systems are not well known and in consequence they are often poorly sized for the application.

Clima 2000/Napoli 2001 World Congress – Napoli (I), 15-18 September 2001

Heat Transfer to Radiant Cooling Panels

In temperate climates (central Europe for example) these systems can be used without any air conditioning. The air change, only to remove "pollutants" (odour, smoke, …) is done by natural ventilation or by a small mechanical ventilation. In more humid climates, it is necessary to have a small air conditioning to maintain the indoor dew point temperature below the surface temperature of the ceiling. The objective of a radiant cooling ceiling is not only to remove the heat from a room, but also for the same air temperature to provide a better thermal comfort sensation. According to the theory of thermal comfort, (Fanger 1982, ISO 1984), a temperature of 25°C (air and mean radiant temperatures) is the maximum limit for comfortable conditions (predicted mean vote PMV = 0.5) in an office (with an activity of 1.2 met and a clothing of 0.75 clo). With a constant surface temperature at 25°C, an air temperature of 21.5°C gives the ideal situation (PMV = 0) and 28.5°C leads to a real discomfort (PMV = 1). At the same conditions, a ceiling covered (75% of the surface) with radiant cooling panels at 18°C allows a temperature rise of 1°C for the same level of comfort. These gaps, 26°C or 25°C for PMV = 0.5, 29.5°C or 28.5°C for PMV = 1, are what really make a difference in office comfort.

Figure 1: Left: Radiant cooling panels in a large office. The panels are suspended at the ceiling, the air can freely move around the panels. Right: The panels can also be integrated in a suspended ceiling, creating two separated air spaces: above and under the panels.

To be able to correctly dimension these systems, the following heat flows should be known: • heat exchange to the upper / lower face of the panel; • heat exchange by radiation / convection / conduction to the panel. In this study, we first made a theoretical analysis of the physical phenomena, created a physical model of a radiating panel and than finally programmed the model and the equations representing the heat exchange in a software. We added to this theoretical part an experimental part. In a climatic chamber we made measurements on a radiant cooling panel in many configurations and compared measured and calculated values. In order to increase heat transfer, some manufacturers construct ceiling panels with fins. We will not consider these types of panels here. We also suppose that the panels are suspended at the ceiling without closing the space above them.



2. PHYSICAL PHENOMENA The function of a radiant cooling panel is to remove heat from a room. The word "radiant" presumes that the heat transfer is done by radiation. But a detailed study of the interactions of such a panel with its environment (Figure 2) shows that there exists: • forced convection between the water flow and the panel; • conduction in the metal (or other material) of the panel; • conduction in the possible insulation of the back side (top side) of the panel; • conduction in the fasteners used to fix the panel to the building structure (ceiling, wall); • free convection between the panel and the air; • radiation between the panel and the surrounding surfaces; • possible radiation between the panel and the air. These interactions give the energy fluxes shown in the Sankey diagram of Figure 3.

Figure 2: Interactions of a horizontal panel with its environment.



convection air radiation conduction Water radiation

surface

back environment

fasteners

surface front environment

convection

air

Figure 3: Sankey diagram (energy fluxes) of a radiating panel. The radiating heat transfer fluxes are larger than the corresponding convective ones. Heat transfer on the back is usually smaller than that on the front side as the back of the panel is often covered with insulation.

The theoretical equations to obtain the heat transfer by radiation are well established but the calculation can be very tedious (form factors, many surfaces with different temperatures and/or emissivity). A surface at a different temperature from that of the air gives rise to air currents, which can be turbulent (high temperature difference) or laminar (low temperature difference). When the temperature difference is very low, there is no air movement and we abusively speak of convection instead of conduction. Many authors (McAdams 1964, Glück 1982, VDI 1984, Incropera 1996, ASHRAE 1997) have studied convection from a horizontal surface (ascending or descending heat flux). Their results are sometimes quite different (Figure 4). The methods of ASHRAE (lowest values) and Glück (highest values) are the less reliable as their formulas do not take into account an important fact: the transition between laminar and turbulent flow occurs at different conditions according to the sense of the heat flux. The methods of Incropera, McAdams and VDI are very close. The Incropera formulas seem to be the best. He refers to (Goldstein 1973, Lloyd 1974) and slightly modifies the McAdams formulas to improve the accuracy. We will used them in the next calculations. Combining the formulas for ascending heat flux (lower face of the panel) and descending heat flux (upper face), we obtain the heat flux absorbed per square meter of panel as a function of the temperature difference generating the heat exchange (Figure 5). For a 10 K temperature difference, we obtain 156 W/m² with the following division: 33 % radiation total upper face 43 % 10 % convection 33 % radiation total lower face 57 % 24 % convection



Heat transfer coefficient by convection between air and a cold ceiling

Heat transfer coefficient [W/(m²·K)]

6 5 4 3 2

Glück VDI Incropera McAdams ASHRAE Radiation (for comparison)

1 0 0

10 5 Temperature difference Air - Radiating surface [K]

15

Figure 4: Heat transfer coefficient by convection between air ( at 24°C) and a cold ceiling (2.36 m long and 0.86 m wide) according to various authors. The heat transfer coefficient by radiation is shown for comparison.

Figure 5: Heat flux to a flat ceiling panel (without any insulation) absorbed per square meter versus the difference between the environment temperature (uniform at 24°C) and the water temperature.



3. MODEL In order to predict the heat that could be eliminated by a panel, a physical model of the panel was developed and programmed into a computer program. The physical model can be represented as an electrical circuit (Figure 6). The arithmetic mean of the inlet and outlet water temperatures was taken as "the" uniform water temperature of the panel. This assumption does not lead to a significant error if the water temperature rise in the panel element is small or if the temperature difference between the panel and its environment is large. Tsurf ins Tsurf water Rwater

Tsurf met

Rconv

Tair

Rrad

Tmr

Rcond

Rmet Rstruct

Tstruct

Rstruct

Tstruct

Back environ ment

Twater Tsurf water Rwater

Tsurf met Rmet

Tsurf ins

Rrad

Tmr

Rconv

Tair

Rcond

Front environ ment

Figure 6: Physical model of a panel. R = thermal resistance [m²·K/W] = inverse of heat transfer coefficient [W/(m²·K)] : cond, conv, rad = by convection, conduction, radiation; struct, met = conduction in the fasteners, in the material of the panel (usually metal); water = internal convection. T = temperature: water = fluid flowing in the panel, surf water = interface water–panel, surf met = interface metal–insulation, surf ins = interface insulation–air, air = air away from the panel, mr = mean radiant (temperature) of the surface.

Not only were convection and radiation at the surface of the panel accounted for but also all the other possible heat resistances. The heat transfer coefficient between the water and the internal surface of the panel (or of the pipe welded or crimped to the flat plate of the panel) is always very high (or the resistance very small) in comparison with the other coefficients. Thus, it does not need to be calculated precisely. The internal resistance due to the metal (or other materials) separating the water and the air is also very small. For the best panels, it is completely negligible. Fasteners are used to suspend the panels to the slab or eventually to fixed them to the wall. In a good construction, the heat transfer in the fasteners is very small (or the resistance very high) and this flux may sometimes be neglected. When a panel is integrated in a closed suspended ceiling, the upper face is often covered with insulation. This adds a very high thermal resistance. The model allows one to also put insulation on the lower face, but only to compare with our measurements. The thermal resistances for radiation and convection are not constant but depend on the temperatures. The other resistances are constant.



4. SOFTWARE A computer program was created to simulate the performances of ceiling panels. An input window allows one to easily input the necessary information, and the output is the Sankey diagram shown in Figure 7.

Figure 7 Output screen of the software (only in French). This example shows a 2.03 m² ceiling panel absorbing 200 W heat. Upper face 73 W (convection 21 and radiation 52), lower face 127 W (convection 65 and radiation 62).

The model described in Figure 6 has an explicit solution only if all resistances are constant. As the convection and radiation resistances are temperature dependant, the software makes iterations until convergence is reached. The program allows the user to define six different temperatures to describe the environment: the air temperatures above and under the panel, the mean radiative temperatures seen by the upper and lower faces of the panel and two temperatures for the possible thermal bridges due to the fasteners. For each face of the panel, the program calculates the radiation exchange with a simplified method which is correct for a uniform environment. If the room has many faces at different temperatures and different emissivities, this method gives only an approximation. For such cases we should calculate form factors for each couple of faces and then performing a matrix calculation. In a typical room, the emissivity of building material is always around 90% and the simplification we made in the software has no influence.



5. MEASUREMENTS A radiant cooling panel was installed in a climatic chamber (Figure 8). Different configurations (Table 1) were tested (experimental conditions are listed in Table 2) in order to identify the different heat fluxes of a ceiling panel. The results are shown in Figure 9. The ambient conditions are represented by four parameters: air temperatures under and above the panel, and mean radiant temperatures seen by the upper and the lower face. It is not possible to express the results as a function of these four parameters. We made a weighted average of these four values. The weights are given by the relative parts of respectively the heat transfer by convection under and above and by radiation under and above the panel. The mean radiative temperature under the panel was first calculated with the measured surface temperature of the walls and the floor. Then, we corrected this value to take into account the influence of the small heat sources (desk lamps and electric heater). This correction appears to be quite important (from 0.4 to 3.5°C).

Figure 8: Left: General view of the climatic chamber and a radiant cooling panel. In the foreground, the heat sources (electric heater and desk lamps) and some measurement devices (black ball for comfort temperature and ventilated Pt100 for air temperature). In the background, a suspended ceiling can be seen. This ceiling can easily be mounted at the panel level to separate the volume in two closed spaces above and under the panel. Right: detail of the panel tested.



Table 1: Configurations tested in the climatic chamber

Configuration standard lower face of the panel covered with a low emissivity foil upper face of the panel insulated and covered with a low emissivity foil upper face insulated and covered with a low emissivity foil lower face covered with a low emissivity foil lower face insulated and covered with a low emissivity foil upper and lower faces insulated and covered with a low emissivity foil

Expected effect suppression of radiation under the panel suppression of heat fluxes above the panel suppression of heat fluxes above the panel and suppression of radiation under the panel suppression of heat fluxes under the panel suppression of heat fluxes above and under the panel

abbrev. –/– –/e i/– i/e

–/i i/i

Measured performances of a radiant cooling panel in different configurations 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0

–/– –/e i/ – i/ e

Heat flux [W/m²]

–/i i/ i

0

1

2

3 4 5 6 7 8 9 10 11 12 Temperature difference Environment – Water [K]

13

14

15

16

Figure 9: Comparison of the performances of a ceiling panel in different configurations. – = the surface of the panel is naked, e = the (lower) face is covered with a 2% emissivity foil, i = the face (upper, lower or both) is covered with 10 cm insulation and a low emissivity foil. The bars for the "Temperature difference Environment – Water" do not show an error. There is not only one environment temperature but four: air temperature under and above the panel, mean surface temperature seen by the lower and upper faces of the panel. These bars show the minimum and maximum value of these differences. A weighted average (and corrected) is used to determine the points.



Table 2: Experimental conditions for the measurements

Climatic chamber

length: 4,80 m; width: 2,40 m; height: 2,43 m wall: average heat transfer coefficient: U = 0,40 W/(m²·K) Panel length: 2,365 m; width: 0,865 m; manufacturer: Energie Solaire SA Heat sources electrical heater (without fan), desk lamps insulation expanded polystyrene 20 kg/m³, thickness: 10 cm except around the water connections, 89% covered with a low emissivity foil Low emissivity foil emissivity: 2% Measurement devices temperatures (air, surfaces, water) taken by calibrated (± 0.1°C) Pt100 sensors (ventilated for the air) water temperature difference outlet – inlet directly measured by a sensitive and precise (± 0.025°C) multiple thermocouple water flow rate measured by a Coriolis flow-meter (± 0.2%) At a given temperature difference, for example 10 K, the values are shown in Table 3 for the various conditions. Table 3: Extrapolated performances at 10 K temperature difference for various configurations.

Configuration –/– –/e i/– i/e –/i i/i

heat flux [W/m²] 140 ± 5 83 ± 4 98 ± 4 49 ± 3 54 ± 3 13 ± 5

The last value, which is the one with the largest uncertainty, should be zero in an ideal situation with the panel absolutely insulated from the environment. Complementary analysis and calculations show that the measured value results from three causes: • The outlet – inlet temperature measurement is not directly on the tested panel but in the pipes a few meters away. The insulated pipes thus absorb a small quantity of heat. • The panel is fixed with metallic fasteners which create small thermal bridges. • The insulation of the panel is not perfect. Around the pipes and around the metallic fasteners, the insulation is not tight. Thus, of the 13 W/m², the heat transfer due to the insulated panel is estimated to be 6 W/m². Analysing these different configurations leads to the subdivision shown in Table 4. Table 4: Repartition of heat transfer according to the measurements

Upper face Lower face Total panel

Convection Radiation

Heat flux [W/m²] 39 ± 3

[%] 30 ± 3

40 ± 3 53 ± 4 132 ± 5

30 ± 3 40 ± 4 100

Division into convective and radiative parts is not possible from these measurements

This result is quite different from the theoretical calculation (Figure 5).



These differences have many origins: • Although the air could freely move around the panel, we observed an asymmetry: the air above the panel was colder than the air under the panel. • The mean radiative temperature presents the same asymmetry. • Another essential asymmetry is the one already mentioned: the influence of small heat sources with a high temperature. Measured and calculated performances of a radiant cooling panel (diff. config.) –/– –/–

–/e –/e

i/ – i/ –

i/ e i/ e

–/i –/i

i/ i i/ i

Heat flux [W/m²]

160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Temperature difference Environment – Water [K] Figure 10: Calculated performance (lines) of the panel for the measured configurations, but with uniform ambient conditions. For comparison, the measured performances (symbols) are also reported.

For the same measured configurations, we calculated the performances with our software (Figure 10). For the standard situation, the differences are small but in other cases they can be important. They are due to the following effects: • The calculation is made for a uniform environment. • The software does not take into account the pipes before and after the panel. • The quality of the thermal insulation during the measurement may not be as good as expected (air infiltration). • The effect of the low emissivity foil is not correctly calculated in the software (simplified calculation for multiple reflections). The difficulty of knowing exactly the ambient conditions, especially the presence of low emissivity material or of small objects at high temperatures, can lead to misinterpretation of measurements or to erroneous predictions with software.



6. CONCLUSIONS A precise calculation of the heat transfer paths involved with a radiant cooling panel requires not only the knowledge of the equations representing the different heat transfer modes (radiation, convection, conduction), but also a correct description the ambient conditions. Saying, for example, that the ambient temperature is 25°C will give only a theoretical value. In reality the air above the panel has a different temperature from the air under the panel. The mean radiative temperature seen by the panel (for each face) is not necessary an average of the temperatures of the walls, ceiling and floor. Many objects in the room have a surface temperature much higher. Windows, lamps, computer screens, electric heaters (for our experiment) and others electrical devices significantly increase the ambient temperature "seen" by the panel.

AKNOLEDGEMENTS The Swiss Commission for Technology and Innovation (CTI) sponsors this research, within the frame of the project RadiaClim, a collaboration between the EPFL, the EIVD (Vaud state Engineers School) and several industrial partners. The authors also express their gratitude to Pierre Loesch, whose help in installing the experimental setup is greatly appreciated.

REFERENCES ASHRAE 1997. 1997 ASHRAE Handbook-fundamentals. American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Atlanta, USA. Fanger O. 1982. Thermal Comfort. Ed. Robert E. Krieger, Malabar, Florida, USA. Glück B. 1982. Strahlungsheizung – Theorie und Praxis. Verlag C. F. Müller, Karlsruhe, Germany. Goldstein R. J., Sparrow E. M., Jones D. C. 1973. Natural convection mass transfer adjacent to horizontal plates. Int. J. Heat Mass Transfer, 16, 1025. Incropera F. P., DeWitt D. F. 1996. Fundamentals of Heat and Mass Transfer. John Wiley and Sons, New York, USA. ISO 1984. ISO 7730: Moderate thermal environments – Determination of the PMV and PPD indices and specification of the conditions for thermal comfort. International Organization for Standardization, Genève, Switzerland. Lloyd J. R., Moran W. R. 1974. Natural convection adjacent to horizontal surfaces of various platforms. ASME Paper 74-WA/HT-66. McAdams W. 1964. Transmission de la chaleur et thermodynamique. Masson et Cie, Paris, France. Roulet C.-A., Rossy J.-P., Roulet Y. 1999: Using Large Radiant Panels for Indoor Climate Conditioning. Energy and Buildings 30, pp121-126 VDI 1984. VDI-Wärmeatlas – Berechnungsblätter für den Wärmeübergang. Verein Deutscher Ingenieure, Düsseldorf, Germany.
