Parametric Study of Heating and Cooling Capacity of Interior Thermally Active Panels

ITAP panels interior thermally active panels with an integrated active surface in an innovative way combine existing building and energy systems into one compact unit, and thus create combined building and energy systems. These are building structures with an internal energy source. Low heat losses, respectively, thermal gains predestine for energy-efficient buildings the application of lowtemperature heating/high-temperature cooling systems such as large-area floor, wall, and ceiling heating/cooling. The main benefit of ITAP panels is the possibility of unified and prefabricated production. At the same time, they represent a reduction of production costs due to their technological process of production, a reduction of assembly costs due to a reduction of steps during implementation on the construction site and a reduction of implementation time due to their method of application.


Introduction
ITAP panels -interior thermally active panels with an integrated active surface are formed by a tubular or capillary energy system integrated in the thermal insulation part of a panel and a thermally active surface formed by a thermally conductive material (e.g., thin layer plaster, plasterboard, or sheet metal). They are applied in the same way as previously known panels with integrated tubular or capillary systems (e.g., in SD boards). ITAP panels are protected by European patent EP 2 572 057 B1 [1] from 15.10.2014 [2]. We focused our research in this area on the possibilities of application of ITAP panels for large-area low-temperature heating and high-temperature cooling with heat/cold sources based on RES [1,2,[3][4][5][6]. The subject of the research described in this paper is a parametric study of the method of heat/cold dissipation in a perimeter wall and interior wall fragment with concealed tube energy system and ITAP panels, optimization of appropriate thermal insulation thickness, tube dimensions and spacing of interior thermally active panels with an integrated active surface [1,2,[3][4][5][6].

Research methodology and methods
To solve the given research questions we have chosen the method of a parametric study. A mathematical-physical model of the perimeter wall with an ITAP panel was created. Stationary (time-stabilized) parametric studies were performed, where the following parameters changed: thickness of the thermal insulation (ITAP panel), spacing and dimension of the tubes, temperature gradient of the heat transfer medium and temperature in the interior, exterior, and adjacent room, respectively. All these parametric studies were performed at boundary conditions representing both winter and summer, [2,3,7,8].

Theory of calculation of large-area radiant heating
Calculation of the radiant heating surface is based on the assumption that the average surface temperature of the radiant heating surface does not exceed hygienically permissible values, while the heat output of the radiant heating surface will cover the heat losses of the heated space. Modified calculation for radiant hot water heating, [7,9,10]. Thermal permeability of the layer above/in front of the tubes Λ a (W/(m 2 .K)) is calculated as in Eq. (1): where: a is thickness of the layer above/in front of the tubes (m), λ a is thermal conductivity coefficient of the material of the respective layer (W/(m 2 .K)), h p is heat transfer coefficient (W/(m 2 .K)). Thermal permeability of the layer under/behind the tubes Λ b (W/(m 2 .K)) is calculated as in Eq. (2): where: b is thickness of the layer under/behind the tubes (m), λ b is thermal conductivity coefficient of the material of the respective layer (W/(m 2 .K)), h p is heat transfer coefficient (W/(m 2 .K)). Coefficient characterizing the heating plate in terms of heat dissipation m (m -1 ) is calculated as in Eq. (3): where: Λ a is thermal permeability of the layer above/in front of the tubes (W/(m 2 .K)), Λ b is thermal permeability of the layer under/behind the tubes (W/(m 2 .K)), λ d is thermal conductivity of the material of the layer in which the tubes are embedded (W/(m 2 .K)), d is tube diameter (m). Surface temperature of the heating surface θ p (°C) is calculated as in Eq. (4): where: θ p is floor surface temperature (°C), θ i is calculated indoor room temperature (°C), Λ a is thermal permeability of the layer above/in front of the tubes (W/(m 2 .K)), h p is heat transfer coefficient (W/(m 2 .K)), θ m is average temperature of heating water (°C), m is factor characterizing the heating plate in terms of heat dissipation (m -1 ), L is axial distance of tubes (m).
Specific heat output of the heating surface upwards q (W/m 2 ) is calculated as in Eq. (5): where: h p is heat transfer coefficient from the floor upwards (W/(m 2 .K)), θ p is floor surface temperature (°C), θ i is calculated indoor room temperature (°C).
Specific heat output of the heating surface downwards q' (W/m 2 ) is calculated as in Eq. (6): where: Λ b is thermal permeability of the layer under the tubes (W/(m 2 .K)), Λ a is thermal permeability of the layer above the tubes (W/(m 2 .K)), q is specific heat output of the underfloor heating surface upwards (W/m2).
Heating area S (m 2 ) is calculated as in Eq. (7): where: Q c is total heat loss (W), h p is heat transfer coefficient from the floor upwards (W/(m 2 .K)), θ p is floor surface temperature (°C), θ i is calculated indoor room temperature (°C), q is heat output of the heating surface towards the interior (W/m 2 ), q' is heat output of the heating surface towards the exterior (W/m 2 ). Heat output of the heating surface Q s (W) is calculated as in Eq. (8): where: q is heat output of the heating surface towards the interior (W/m 2 ), q' is heat output of the heating surface towards the exterior (W/m 2 ), S p is heating surface (m 2 ).

Mathematical-physical model
As a basis for the parametric study, a mathematical-physical model for concealed large-area heating was made (Figs. 1 and 2) and a mathematical-physical model for ITAP panel (Figs. 3 and 4). Color-differentiated materials can be seen on mathematical-physical models, which consist of characteristic fragments of the perimeter wall and the inner wall with a concealed energy system and ITAP panels. Material characteristics were assigned to individual materials [2,[5][6][7][8][9][10][11][12][13][14].

Perimeter (external) wall
Legend for Fig. 1: L is tube spacing (m), DN is tube dimension (m), θ m is mean temperature of heating medium (°C), θ i is interior temperature (°C), θ e is exterior temperature (°C), θ p is surface temperature of heating/cooling surface (°C), q i is heat output of the heating surface towards the interior (W/m 2 ), q e is heat output of the heating surface towards the exterior (W/m 2 ).
In Table 1 the values of physical quantities in individual layers of the building structure are given.

Inner (internal) wall
Legend for Fig. 2: L is tube spacing (m), DN is tube dimension (m), θ m is mean temperature of heating medium (°C), θ i is interior temperature (°C), θ i2 is interior temperature in the adjacent room (°C), θ p is surface temperature of heating/cooling surface (°C), θ i is heat output of the heating surface towards the interior (W/m 2 ), θ i2 is heat output of the heating surface towards the adjacent room (W/m 2 ).
In Table 2 the values of physical quantities in individual layers of the building structure are given.

Perimeter (external) wall with ITAP panel
Legend for Fig. 3: L is tube spacing (m), DN is tube dimension (m), θ m is mean temperature of heating medium (°C), θ i is interior temperature (°C), θ e is exterior temperature (°C), θ p is surface temperature of heating/cooling surface (°C), q i is heat output of the heating surface towards the interior (W/m 2 ), q e is heat output of the heating surface towards the exterior (W/m 2 ).
In Table 3 the values of physical quantities in individual layers of the building structure are given.

Inner (internal) wall with ITAP panel
Legend for Fig. 4: L is tube spacing (m), DN is tube dimension (m), θ m is mean temperature of heating medium (°C), θ i is interior temperature (°C), θ i2 is interior temperature in the adjacent room (°C), θ p is surface temperature of heating/cooling surface (°C), q i is heat output of the heating surface towards the interior (W/m 2 ), q i2 is heat output of the heating surface towards the adjacent room (W/m 2 ).     [15] In Table 4 the values of physical quantities in individual layers of the building structure are given.

Parametric study
Parametric study for the described mathematical-physical model -fragment of an inner wall with ITAP panel (Fig.4) and a perimeter wall with ITAP panel (Fig. 3) was performed on a mathematical configurator -Calculation of large-area radiant heating (VVSV) in MS Excel [15]. Input data that can be changed: thickness of thermal insulation (ITAP panel), spacing and dimensions of tubes, temperature gradient of heat transfer medium and temperature in the interior, exterior, or adjacent room, compositions and thicknesses of building structures in front of/above and behind/under tubes, thermal-technical properties of building materials (thermal conductivity of materials, heat transfer coefficient). Parametric calculations were performed at boundary conditions representing winter θ e = -11 °C and summer θ e = +32 °C. Table 1 shows the input criteria for the parametric study of a perimeter wall with ITAP panels -heating period: thermal insulation thickness 50 mm, tube dimension 15 mm, interior temperature +20 °C, exterior temperature -11 °C, mean heat transfer medium temperature +35 °C and tube spacing 100 mm. Using the mathematical configurator, the following parameters of large-area wall heating with ITAP panels on the perimeter wall were calculated. Outputs from the mathematical configurator -parametric study of the ITAP panel -heating period are given in Tables 5 to 7.

Winter season (heating period)
These are important results excluded from Tables 5 to 7: •  Tables 8 to 10 shows the input criteria for the parametric study of a perimeter wall with ITAP panels -summer: thermal insulation thickness 50 mm, tube dimension 15 mm, interior temperature +26 °C, exterior temperature +32 °C, mean temperature of the heat transfer medium is +17 °C, tube spacing 100 mm. Using the mathematical configurator, the following parameters of large-area wall cooling with ITAP panels on the perimeter wall were calculated. Outputs from the mathematical configuratorparametric study of the ITAP panel -summer season are given in Table 8 to 10.

Summer season
These are important results excluded from Tables 8 to 10: • Interior Interior  Table 5 Calculation of thermal permeability of the layer above/in front of the tubes towards the interior [15] Name of the quantity Value Dimension of tubes d (m) 0.015 Thickness of the layer before/above tubes toward the interior No.1 a 1 (m) 0.018 Thermal conductivity of the material in front of/above the tubes of the respective layer toward the interior No.1 λ d1 (W/(m 2 .K)) 1.160 Thickness of the layer before/above tubes toward the interior No.2 a 2 (m) 0.000 Thermal conductivity of the material in front of/above the tubes of the respective layer toward the interior No.2 λ d2 (W/(m 2 .K)) 0.000 Heat transfer coefficient in front of/above the tubes toward the interior floor heating h pi (W/(m 2 .K)) 9.600 Heat transfer coefficient in front of/above the tubes toward the interior ceiling heating h pi (W/(m 2 .K)) 7.300

Name of the quantity Value
Heat transfer coefficient in front of/above the tubes toward the interior wall heating h pi (W/(m 2 .K)) 10.000 Thermal permeability in front of/above the tubes towards the interior floor heating Λ a (W/(m 2 .K)) 7.954 Thermal permeability in front of/above the tubes towards the interior ceiling heating Λ a (W/(m 2 .K)) 6.308 Thermal permeability in front of/above the tubes towards the interior wall heating Λ a (W/(m 2 .K)) 8.227 Heat transfer efficiency Ratio between the heat flow to the interior and the total heat flow, efficiency of transfer of the end radiant surfaces floor heating 95.73% ceiling heating 94.51% wall heating 95.88%

Heat loss
Ratio between heat flow to the exterior and total heat flow -loss floor heating 4.27% ceiling heating 5.49% wall heating 4.12% Table 6 Calculation of thermal permeability of the layer under/behind the tubes towards the exterior [15] Name of the quantity Value   Total specific heat flow toward the exterior -wall heating (W/m 2 ) 103.967 Table 8 Calculation of thermal permeability of the layer above/in front of the tubes towards the interior [15] Name of the quantity Value Thickness of the layer before/above tubes toward the interior No.2 a 2 (m) 0.000 Thermal conductivity of the material in front of/above the tubes of the respective layer toward the interior No.2 λ d2 (W/(m 2 .K)) 0.000 Heat transfer coefficient in front of/above the tubes toward the interior floor heating h pi (W/(m 2 .K)) 9.600 Heat transfer coefficient in front of/above the tubes toward the interior ceiling heating h pi (W/(m 2 .K)) 7.300 Heat transfer coefficient in front of/above the tubes toward the interior wall heating h pi (W/(m 2 .K)) 10.000 Thermal permeability in front of/above the tubes towards the interior floor heating Λ a (W/(m 2 .K)) 7.954 Thermal permeability in front of/above the tubes towards the interior ceiling heating Λ a (W/(m 2 .K)) 6.308 Thermal permeability in front of/above the tubes towards the interior wall heating Λ a (W/(m 2 .K)) 8.227 Heat transfer efficiency  Table 9 Calculation of thermal permeability of the layer under/behind the tubes towards the exterior [15] Name of the quantity Value

Heating and cooling capacities of ITAP panels
Using the mathematical configurator, the heating and cooling heat flows of ITAP panels made of thermal insulation expanded polystyrene EPS-F (λ = 0.04 W/(m 2 .K) with thickness 50 mm with tube spacing 100 mm were calculated (Tables 11 and 12).
When calculating the heating heat flows, we considered the mean temperature of the heating medium of 25 °C, 30 °C, 35 °C, 40 °C, indoor temperatures of 16 °C, 18 °C, 20 °C, 22 °C, 24 °C. When calculating the cooling heat flows, we considered the mean temperature of the heating medium of 15 °C, 16 °C, 17 °C, 18 °C, indoor temperatures of 20 °C, 22 °C, 24 °C, 25 °C, 26 °C. In addition to heat flows to the interior, exterior, and total heat flow, the surface temperature of ITAP panels was also determined.

Discussion
Based on mathematical-physical models for concealed large-area radiant heating/cooling and for ITAP panels, a comparison of these two energy systems on the perimeter wall and on the inner wall of a building was performed for the following boundary conditions: mean temperature of heat transfer medium for heating is +35 °C, for cooling medium it is +17 °C, indoor temperature in the heating season is +20 °C, in the summer it is +26 °C, outdoor temperature in the heating season is -11 °C, in the summer +32 °C, room temperature behind the inner wall is +18 °C (winter) and +26 °C (summer), tube spacing is L = 100 mm, thickness of thermal insulation part of ITAP panel is 50 mm (EPS-F). It can be stated (Tables 13 to 14), that the application of large-area radiant heating/cooling of under plaster and using ITAP panels on perimeter walls (the composition meets the requirements of STN EN 73 0540 [8], U = 0.22 W/(m 2 .K)) in terms of energy show almost the same heating and cooling heat fluxes.
When applying large-area concealed radiant heating/ cooling and ITAP panels on internal walls (thickness of ceramic bricks 240 mm, thermal conductivity of the material 0.510 W/(m 2 .K)), which have worse thermal resistance than perimeter walls, ITAP panels show heating saving of approximately 13 % and for cooling of approximately 11 % compared to a concealed tube energy system thanks to thermal insulation, which adjusts the thermal permeability of the wall layers behind the tubes towards the adjacent room Λ b (W/(m 2 .K)). In addition to these savings, it is clear from Tables 15 and 16 that the ratio of heat flow towards the heated/cooled space is 78:22 for concealed pipe system with heating and 81:19 for cooling. The heat flow ratio towards the heated/cooled space is 93:7 for ITAP panels for heating and 94:6 for cooling.
Legend for Tables 13 to 14: Λ a is thermal permeability in front of/above the tubes towards the interior (W/(m 2 .K)), Λ b is thermal permeability behind/under the tubes towards the exterior (W (m 2 .K)), θ p is surface temperature of heating/cooling surface (°C), θ i is specific heat flow to the interior (W/m 2 ), θ e is specific heat flow to the exterior (W/m 2 ), q total is total specific heat flow (W/m 2 ).
Legend for Tables 15 and 16: Λ a is thermal permeability in front of/above the tubes towards the interior (W/(m 2 .K)), Λ b is thermal permeability behind/under the tubes towards the exterior (W/ (m 2 .K)), θ p is surface temperature of heating/cooling surface (°C), θ i is specific heat flow to the interior (W/m 2 ), θ e is specific heat flow to the exterior (W/m 2 ), q total is total specific heat flow (W/m 2 ).

Conclusions
Based on the parametric study of ITAP panels and the concealed tubular energy system on the perimeter wall and the inner wall between two rooms, it was determined that: • The thickness of thermal insulation of ITAP panels when applied to perimeter walls (the composition meets the requirements of STN EN 73 0540 [8], max. U = 0.22 W/(m 2 .K) has almost no effect in terms of energy requirements. Thermal heating and cooling flows are approximately the same as with the concealed tube system.
• When applying large-area radiant heating/cooling with a concealed tubular energy system and ITAP panels on interior walls that have worse thermal resistance than perimeter walls, ITAP panels show savings in heating and cooling compared to a concealed tubular energy system due to thermal insulation that adjusts thermal permeability of layers of the wall behind the tubes towards the adjacent room Λ b (W/(m 2 .K)). In the case of the inner wall (thickness of ceramic bricks 240 mm, thermal conductivity of the material 0.510 W/(m 2 .K), ITAP panels show savings of approximately 13 % in heating and approximately 11 % in cooling.
• The mean temperature of the heat transfer medium and the interior temperature of the heated/cooled space, has a significant effect on the heating and cooling capacity of ITAP panels, as well as the concealed tubular energy system.
• Tube spacing has significant influence on the heating and cooling capacity of ITAP panels, as well as of concealed tube energy system, e.g. when spacing is changed from L = 100 to 150 mm, capacity is reduced by about 15 to 20 % and to L = 200 mm capacity reduction is about 30 to 35 %.
• The influence of exterior temperature, respectively, temperature in the adjacent space for heating and cooling capacity of ITAP panels, as well as concealed tubular energy system, represents a deviation of about 5 % depending on the thermal insulation properties of building structures on which large-area radiant energy systems are applied.
• The effect of changing the tube dimensions of ITAP panels, as well as of the concealed tube energy system, from a diameter of d = 15 to 20 mm on the heating and cooling capacity represents a deviation of approximately 2.5 %.
The research will continue with parametric studies under other boundary conditions and search for optimal criteria for design, calculation, and assessment of energy-efficient, economically efficient and environmentally friendly large-area radiant energy systems. Another research task will be to establish criteria for ITAP panels with air as the heat-carrying medium in applications for floor, ceiling, and wall heating. After a mathematical-physical model is developed, parametric studies and mathematical simulations will be performed.
The research will also continue under laboratory conditions, where measurements will be performed on a fragment of a perimeter, interior wall, ceiling, and floor with ITAP panels and built-in tubular energy systems, as well as air ducts.
The main benefit of ITAP panels -interior thermally active panels with an integrated active area -is the possibility of unified and prefabricated production. At the same time, they represent a reduction of production costs due to their technologically simpler production process (DN of tubes for thermal insulation part of ITAP panels is not limited as for panels with pipes in SD), reduction of assembly costs due to fewer construction steps and less time needed for implementation with regard to their method of application.