Influences of corner surface temperatures

Transcription

1 Influences of corner surface temperatures 1 Research goal Risk of condensation and mould growth at interior construction surfaces are largely influenced by the relative humidity at the surfaces. Often the temperature of indoor corner surfaces against the façade is a bit lower than the mean wall surface temperature during heating season. Because lower temperatures result in higher relative humidity s, these corner surfaces could be risk areas for mould growth, as can be seen in Fig. 1. The goal of this study is to receive more insight in the temperature distribution by corner surfaces and the factors that influence this.

2 2 Theoretical background Beside visual and mechanical damage, condensation and mould growth can also lead to respiratory problems. Fungal spores contaminate the air and can cause health complaints when they are inhaled. Fig. 1 Corner surfaces with mould grow A rough criterion to prevent mould growth is that the monthly mean relative humidity at the surfaces must be lower than 80%. When this condition is met, the risk of mould growth is acceptable, but still not excluded. Because it is difficult or impossible in many cases to determine whether these conditions are met, a simplified standard to determine the risk of mould growth has been developed. The most obvious choice for a standard to prevent moisture problems would have been to make a standard for the lowest admissible surface temperature calculated with the standard climate. The Temperature Ratio is a dimensionless quantity, which is used in the Dutch building code. The calculated temperature ratio is a value between 0 and 1, this represents a scale between respectively high to low risk of moisture problems. The temperature ratio is defined as: With: f n = T si T e T a T e T si = T e = T a = lowest interior surface temperature [K or ⁰C]; effective outdoor temperature [K or ⁰C]; indoor air temperature [K or ⁰C]; The standard climate in the Netherlands is given as an effective outdoor temperature of 0⁰C and a reference indoor air temperature of 18⁰C (at 1,7m. above the floor in middle of the room). When the ratio f n >= 0.65, the risk of moisture problems is called acceptable. So the lowest surface temperature T si should be higher than 11,7⁰C. At the reference temperatures and an indoor relative humidity of 53%, this means that the R.H. at the surface is 80%. When the heat flow through the construction is one-dimensional, and the temperature ratio is known, the surface temperature can be easily determined for all different outdoor and indoor air 2

3 temperatures. Also when the thermal conductivity of the structure is known, the interior surface temperature can be calculated for all values of outdoor and indoor air temperatures, when indoor and outdoor surface heat coefficients are well estimated: With: R i R m R m T s = T R i + R e + T m R i + R i = T e + (T m R i + R i T e ) m T s = interior surface temperature [K or ⁰C]; T e = exterior air temperature [K or ⁰C]; T a = indoor air temperature [K or ⁰C]; R m = Total thermal resistance between the surface and exterior air [m 2.k /W]; R i = Surface heat transfer resistance at the inside [m 2.k /W]; Note that the surface temperature is strongly dependent on the indoor surface coefficient of heat transfer. Even though this coefficient is mostly considered as a constant value by heat loss calculations, it should not been done by evaluating risk of moisture problems. Especially in corners this coefficient differs from open surfaces due to a difference in radiation exchange, caused by an aberrant view factor with another (mostly lower) average ambient temperature. Also the airflow velocities near the corners differ from the mean intern airflow. These influences will be examined during this study. Besides the problem of uncertain surface coefficients of heat transfer at indoor corners, the heat flow through the construction is not one-dimensional and often adjacent to several external temperatures like: outside air, ground or adjacent room temperature. In this case we can use superposition to determine a general solution for the corner surface temperature at a certain position, for all different bordering temperatures. When there are n different bordering temperatures, we need n-1 different temperature-independent functions. Let a structure be bounded by n different bordering temperatures T e1, T e2,..,t en. Then: 1 k n λ k ( T ) n k = h ek (T ek T sk ) Suppose a k (x,y,z) T ek is the solution of the differential equations where, except for the surface, all bordering temperatures equal zero. From linearity of the equations with boundary conditions then follows that a k (x,y,z) is a solution of the equations with: T ek =1 and other boundary temperatures are 0. If we do this for all surfaces in a 3-dimensial case, the general solution is: n T(x, y, z) = a k (x, y, z) T ek k=1 The functions a i (x,y,z) are independent of the bordering temperatures. If T ek = T e for 1 i n then also: T(x,y,z)=T e, so: n a k (x, y, z) = 1 k=1 3

4 We have applied the superposition method on a practical example. We assumed an indoor corner whose construction is bordered to the outdoor temperature and an unheated room. The wall is only insulated on the outside. We use COMSOL Multiphysics to simulate this corner construction with exposition to four different ambient temperatures as can be seen in Fig. 2. We use the simulated corner surface temperatures of the first two simulation variants to calculate the a k (x,y,z) with superposition. After that, we use these constant values to calculate the corner surface temperature, which should apply for the ambient air temperatures as were simulated in variant 4. This calculated value which is obtained by superposition, will be compared with the simulation result of variant 4. Fig. 2 Simulation variants with used ambient air temperatures The construction properties we have applied to the simulations are: Concrete walls: Thickness= 20 cm Lambda λ= 2 W/m.K h e = 25 W/m 2.k Insulation material: (against outside wall) Thickness= 10 cm Lambda λ= 0,04 W/m.K h i = 7,7 W/m 2.k 4

5 In Fig. 3 the simulated construction temperatures were visualized, the concerning corner surface temperatures are also given. Fig. 4 shows also the corresponding heat flux streamlines. Fig. 3 Simulation results: construction and indoor corner surface temperature Fig. 4 Simulation results: construction temperature and heat flux streamlines For the superposition method we use only the first two simulated corner temperatures to determine the other concerning temperatures: Ts = a1 T e 1 + a2 T e 2 + a3 T e 3 Ts variant 1 = 1,62⁰C = a1 0 + a2 5 + a3 0 So: a2= 0,324 Ts variant 2 = 12,77⁰C = a a2 0 + a3 0 So: a1= 0,639 5

6 n a k (x, y, z) = 1 Thus: a3 = 1 a1 a2 = 1 0, ,324 = 0,038 k=1 Variant 3: Ts = a1 0 + a ,038 ( 10) = 0,38⁰C (Simulated temperature is 0,38⁰C) Variant 4: Ts = 0, , ,038 ( 10) = 14,02⁰C (Simulated temperature is 14,00⁰C) So the calculated values are in good agreement with the simulation results. As we mentioned before, the surface temperature is strongly dependent on the indoor surface coefficient of heat transfer. This coefficient is mostly considered as a constant value. In Fig. 5 the indoor and outdoor surface coefficients of heat transfer were shown, which were usually used for heat loss calculations in the Netherlands: Fig. 5 Surface heat transfer coefficients, used for heat loss calculations Fig. 6 also shows a table with surface coefficients of heat transfer. These were used for power calculations of thermal activated elements such as concrete core activation. The temperature difference between surface and air in all these cases is 5 ⁰C. Distinction is made in heating or cooling function and between ceiling, floor and wall elements. 6

7 Fig. 6 Surface heat transfer coefficients, used for thermal power supply calculations of thermal activated slabs [2] When we need more accurate values, the separate heat transfer coefficients for radiation and convection can be approached by the following formulas (isso-pub.48): Heat transfer coefficient by free convection Depend on the situation and direction of energy flow, Floor heating/ceiling cooling: h c = 2 T 0,31 Floor cooling /ceiling heating: h c = 0,54 T 0,31 Vertical slab, wall cooling/heating: With: h c = 1,6 T 0,31 T= [W/(m 2.K)] [W/(m 2.K)] [W/(m 2.K)] the temperature difference between surface in indoor air temperature. Where: With: Heat transfer coefficient by radiation h r = 4 C T 3 [W/(m 2.K)] C = the resulting radiation constant = ε 1 ε 2 σ [W/(m 2.K 4 )] ε 1 and ε 2 = the emission coefficients of respectively the considered slab and the other interior surfaces. σ = the Stefan-Boltzmann constant= 5,67*10-8 [W/(m 2.K 4 )] T= the mean temperature of the considered slab and other interior surfaces [k]. 7

8 This method is used for good approximations. When an even more accurate value is necessary, the radiation exchange between the considered slab and other interior surfaces should be calculated, taking into account the surface temperatures, view factors and emission factors. The simulations out of this study should give insight in the factors that influence temperature differences along internal construction surfaces. 3 Method We use the software program COMSOL Multiphysics 4.1 to make computer simulations of the heat flow problems. Herewith we try to find out which influence several factors have on the interior temperature difference between mean slab surface temperature and corner surface temperatures. The influence factors that were considered in this study are: Surface area ratio between inside and outside the corner. Because the one-room model is a cubic, the external surface areas are greater than the interior surfaces, because the construction elements have a certain thickness. We also simulate variants with the same effective intern and extern surface area. Simulations with constant surface transfer coefficients for convection and radiation. These constant coefficients were combined with a constant interior air temperature. Free convection caused by temperature differences. The air density depends on the air temperature and is entered by the ideal gas law. In case of free convection, a heating volume inside the room provides the energy to the air. Surface tot surface radiation between the construction elements (empty room). Surface to surface radiation between construction elements themselves and a warm internal surface. We use a sphere in the middle of the room, which propose the internal warm objects like furnishing. By introducing or leaving out these factors into the simulations, we should be able to derive the separate influences from the results. The simulations were done on a simple one-room building with dimensions (H,W,D) 3,4 x 4 x 4m. The construction elements are 20 cm thick and have a thermal resistance (Rc) of 2,5 m 2.K/W. Unfortunately, the simulations with CFD failed in this three-dimensional model. So we used a twodimensional model of this construction, to investigate the influence of free convection with the CFD module. 8

9 We assume that the outside room-model boundaries are everywhere adjacent to an outside air temperature of -10⁰C. So this factor should not result in surface temperature differences at the inside. More information about the models is given in the Model section. The different simulation variants in this study are visualized in Table 1: Table 1 Simulation variants in this study (total 19) Nr 2D or 3D Constant heat transfer coefficient hc (convection) hr (radiation) Free convection Radiation between: Construction And warm elements indoor surface Equal indoor/ outdoor surface area 1 2D X X X 2 2D X X 3 2D X 4 2D X X X X 5 2D X X X 6 2D X X 7 2D X X 8 2D X(different) X 9 2D X 10 2D X X X 11 2D X X 12 2D X X X X 13 2D X X X 14 3D X X X 15 3D X X 16 3D X 17 3D X X X X 18 3D X X X 19 3D X X 9

10 4 The model The physical modules in Comsol that are applied in this study to solve this heat problem are: Surface to surface radiation Heat Transfer in fluids and solids Non-Isothermal (laminar) Flow Geometry and mesh properties The symbol (*) means that the indicated property mentioned below is not applied in all the simulation variants. 2-D Model Dimensions [m]: Indoor air square (WxH) = 3,6x3,0 Thickness floor, ceiling and wall elements = 0,2 * Circle in middle of the of room (diameter) = 1 *Heat source Ellipses (semiaxis a x b ) = 0.1 x 0,3183 Fig. 7 visualizes the two-dimensional model of the one-room building. The colours in this picture indicate the different thermal conductivities of the materials. The red circle in the middle represents the warm interior surface, which exchanges radiated energy with the construction surfaces. The two white ellipses represent convective heat sources that supply warmth to the air. The air is indicated as the large blue area. The light blue rectangles on sides are the construction elements: walls, ceiling and floor. In some simulation variants, the edges of these elements are modified to high insulated material, to get the same effective outside surface area as on the inside for heat conduction. Fig. 7 Visualization of the 2D model 10

11 3-D Model Dimensions [m]: Indoor air block (WxDxH) = 3,6x3,6x3,0 Thickness floor, ceiling and wall elements = 0,2 *Sphere in middle the of room (diameter) = 1 Fig. 8 shows the three-dimensional model of the one-room building. The colours in the slice frames indicate the different thermal conductivities of the materials. The air is excluded because this model containts no CFD study. This is replaced by imitated boundary conditions. Fig. 8 Visualization of the 3D model Note that some properties, which are present in the pictures above, are not applicable for all the simulation variants. 11

12 Mesh settings: The mesh of the complete 2D construction consists of elements, and the 3D construction of elements. Fig. 9 shows the mesh statistics of the 2D model and the mesh geometry is visualized in Fig. 10. The statistics of the 3D model were present in Fig. 11: Fig. 9 Mesh statistics of the 2D model Fig. 10 Mesh geometry of the 2D simulation model Fig. 11 Mesh statistics of the 3D model Fig. 12 Mesh geometry of the 3D simulation model 12

13 Boundary Conditions Convective Cooling: Air temperature outdoor (outside boundaries) = K (outside boundaries) Surface heat transfer coefficient outside = 25 W/m 2.K (outside boundaries) *Constant Air temperature inside = 3D-Models: K; 2D-Models: K (Only in combination with constant surface heat transfer coefficients) *Constant surface heat transfer coefficients (inside wall and ceiling surfaces): h c +h r = 7,7 W/m 2.K (convection + radiation), h c = 3,0 W/m 2.K (only convection) *Constant surface heat transfer coefficients (inside floor surface): h c +h r = 6,0 W/m 2.K (convection + radiation), h c = 1,3 W/m 2.K (only convection) *Constant temperature (exclusive CFD variants) = K (surface circle/sphere) *Surface tot surface radiation (method: Hemicube): Between construction element surfaces and circle/sphere surface. Emissivity surfaces ε : = 0,9 Ambient temperature: = T *Non-isothermal Flow Laminar airflow Air volume boundary conditions = No slip Air Volume Force (density differences) = Total Volume heat sources = 190W per meter depth (2D model) (spread over one or more ellipses) Material Properties and Initial Condition Thermal conductivity k: Construction elements = 0,08 [W/m.K] *Indoor circle/sphere = 0,5 [W/m.K] *High insulation corner elements = [W/m.K] 13

14 *Air = E-4*(T)^ E-8*(T)^ E- 11*(T)^ E-15*(T)^4 [W/m.K] Density ρ: Construction elements = 2300 [kg/m 3 ] *Indoor circle/sphere = 1500 [kg/m 3 ] *High insulation corner elements = 500 [kg/m 3 ] *Air = nitf.pa*mw_a/(r_const*(t)) [kg/m 3 ] (nitf.pa = absolute pressure, Mw_a= molar mass=28.97[g/mol], R_const=general gas constant) Heat capacity at constant pressure C p : Construction elements = 840 [J/(kg*K)] *Indoor circle/sphere = 700 [J/(kg*K)] *High insulation corner elements = 300 [J/(kg*K)] Air = *(T)^ E - 4*(T)^ E-7 * (T)^ E-10 * (T)^4 [J/(kg*K)] P ref = 1 [atm.] Solver Settings Except the simulations that include CFD, all simulations were done with a stationary solver. 2-Dimensional Models, Time Dependent solver: Type of analysis: Non-isothermal flow (nitf) Relative tolerance: 0,01 Simulation time range: range(0,0.1,5) range(5,0,2,15) range(15,0,5,60) range(60,1,1000) range(1000,3,1800) range(1800,5,3600) range(3600,10,4*3600). 3-Dimensional Models, Stationairy solver: Type of analysis: Conjugate heat transfer (nitf) Relative tolerance: 0,001 14

15 5 Results In this result section a part of the total simulation results are presented. These results give a good representation of the influences caused by the separate factors to the surface temperature distribution. All the other results are presented in the appendix and some movies from the CFDsimulations are attached as digital appendix. Variant 16. This 3D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation and CFD is not included. Graphs 1 Surface temperatures variant 16; Ceiling (left) and Floor (right) 15

16 Variant 3. This 2D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation and CFD is not included. Graphs 2 Surface temperatures variant 3; Ceiling (left) and Floor (right) Variant 19. This 3D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation exchange between the construction elements is analyzed. CFD is not included. Graphs 3 Surface temperatures variant 19; Ceiling (left) and Floor (right) 16

17 Variant 11. This 2D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation exchange between the construction elements is analyzed. CFD is not included. Graphs 4 Surface temperatures variant 11; Ceiling (left) and Floor (right) Variant 18. This 3D variant is simulated with only a constant surface coefficient of heat transfer for convection(hc). The model has different inside and outside surface areas. Radiation exchange between construction surfaces themselves and the warm indoor surface is analyzed. CFD is not included. Graphs 5 Surface temperatures variant 18; Ceiling (left) and Floor (right) 17

18 Variant 13. This 2D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation exchange between construction surfaces themselves and the warm indoor surface is analyzed. CFD is not included. Graphs 6 Surface temperatures variant 13; Ceiling (left) and Floor (right) Variant 7. This 2D variant is simulated without radiation or constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Free convection is included. Graphs 7 Surface temperatures variant 7; Ceiling (left) and Floor (right) 18

19 Variant 8. This 2D variant is simulated without radiation or constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Free convection is included, but the air is heated in a different way than in the other simulation variants with CFD. Graphs 8 Surface temperatures variant 8; Ceiling (left) and Floor (right) 19

20 6 Conclusion & Discussion Conclusion Based on the simulation results we can conclude that all simulated influencing factors are visible on the inside surface temperatures. They also provide good information about the separate influences of the different factors in our 2D and 3D model. So the main cause of surface temperature difference is the surface area ratio between inside and outside. The larger outside surface area in the corners causes a larger heat flux in the construction near the inside corner surface, so the temperature drops until it is ca. 6⁰C beneath the surface temperature in the middle. When we look at the influence of radiation in an empty room, the simulations show that the temperature differences will be flattened. Due to the exchange of radiated energy between hot and cold surfaces the temperatures approach each other a bit. The cold corners and floor surfaces has a negative radiative heat flux, which implies that they absorb more radiated energy than they emit. So the surface temperatures in the corners and middle of the floor could rise up to ca. 2⁰C. The surface temperature in the middle of the ceiling decreases more than the surface temperature towards the borders of the ceiling, because the view factor to the cold floor is larger in the middle of the ceiling. The floor surface is colder, because the constant surface coefficient of heat transport by convection, that we have entered, is 2.7 W/m 2.K lower than for the ceiling and the walls. In the simulations that include CFD, the surfaces do not have such a constant coefficient, but the floor surface temperatures are also lower than the others because of the air temperature gradient and the cold construction element surfaces. Simulations with a warm surface (circle/sphere) in the middle of the room, with a temperature almost equal to the air temperature, are done to imitate the influence of warm indoor surfaces from e.g. furniture on construction surface temperatures. Because the view factor of this warm surface is larger to the middle of the construction elements than towards the corners, the radiation exchange is greater towards the middle. As result the temperature in the middle of the surface will increase up to ca. 0,5⁰C more than towards the corners of the surface. The influence of free convection on the surface temperatures is quite large. It causes peaks of temperature differences up to ca. 6⁰C. The temperature pattern is strongly dependent on the way the air is heated. In the discussion section the realization of those temperature profiles due to free convection will be further discussed. 20

21 Discussion Even though the simulation results give us good insight in the influence of the different factors, the effects in practice are still strongly dependent on building geometry, building physics properties and the way of air treatment. Also the interior of a room could have great influences on radiation exchange and the convective air streams. Unfortunately it was not possible to simulate the effect of free convection in the threedimensional model. This means that the results out the 2D-model only give information about the surface temperature difference near the corners of two perpendicular construction elements. It is likely that the differences are greater in corners of three perpendicular elements. Most likely the airflow will be lower in these 3D corners. Because the simulations with free convection (CFD) were not stationary and include heat sources in the room instead of a constant indoor air temperature, there is fairly large difference between the final air temperatures. This also influenced the construction surface temperature, so keep this in mind during comparing the simulation variants. Because we are mainly interested in the temperature differences along the surfaces, this is not a big problem. Comparing the surface temperatures out of simulation variants with constant surface coefficients of heat transfer (hc &hr) and surface temperatures out of the variants that include simulated radiation and free convection, we can conclude that the constant coefficients which we implemented are too high for our models. The constant coefficients that we have used are: - Ceiling and walls: h radiation = 4,7 W/m 2.K; h convection = 3,0 W/m 2.K - Floor: h radiation = 4,7 W/m 2.K; h convection = 1,3 W/m 2.K These constants were coupled with the constant air temperature. The radiation coefficient is possibly too high, because all surfaces have nearly the same temperature. In our models all construction elements border the cold outdoor air. In practice most rooms also contain warm indoor construction elements and more other warm surfaces when it is furnished etc. The total main surface temperature is than closer to the air temperature. Also the convective heat transfer is probably greater in practice, because the effect of natural and/or mechanical ventilation on the air velocity. The results show a recurring surface temperature pattern in the simulation variants with free convection. Temperature peaks arise toward the ceiling corners, which also collapse just before the corner, as we can see for example in Graphs 7. In the middle of the ceiling surface, there will also be a rise in temperature. This pattern probably arises because of the following phenomenon: The heat source in the air and the cold surfaces cause an ongoing circulation of the indoor air. The heated air rises up and displaces the local air downwards. The two main flow patterns how this is happen are shown in Fig. 14, Fig. 13 and Fig. 15. The warm airflow rises up from the middle or from the sides of the room and deflects near the ceiling. Note that the deflection point on the sides is a bit from the corner and that the airflow in the corner itself is lower. That would explain the decrease of temperature near the corner. 21

22 Fig. 14 Flow pattern from outside to inside Fig. 13 Flow pattern from inside to outside The temperature peaks near the sides of the floor surfaces can be explained by the displaced warm air from above, that drops down along the walls and deflects on the floor toward the heat source, as can be seen in the figures. The temperature peak on the floor surface does not drop down near the corner, because the wall temperature is higher than the floor temperature and the velocity in the lower corners is relative high compared the velocity elsewhere just above the floor. Fig. 15 Flow pattern from outside to inside with circle in the middle and two heat sources 22

23 Bibliography 1 M.h. de Wit, [2009]: Heat, air and moisture in building envelopes. Course book Eindhoven University of Technology: blz H.M. Bruggema, 2007; Vergelijking van systemen Betonkernactivering,klimaatplafonds, wand- en vloerverwarming. TVVL Magazine 3/

24 Annex 1: Simulation results with 2D-model 24

25 Variant 1. This 2D variant is simulated with constant surface coefficients of heat transfer (hc+hr) and with the same outside surface area as on the inside. Radiation and CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 16 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 9 Ceiling surface temperature distribution (left); 25

26 Floor Surface: Graphs 10 Floor surface temperature distribution (left); Left Wall Surface: Graphs 11 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 12 Right wall surface temperature distribution (left); 26

27 Variant 2. This 2D variant is simulated with constant surface coefficients of heat transfer (hc+hr). The model has different inside and outside surface areas. Radiation and CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 17 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 13 Ceiling surface temperature distribution (left); 27

28 Floor Surface: Graphs 14 Floor surface temperature distribution (left); Left Wall Surface: Graphs 15 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 16 Right wall surface temperature distribution (left); 28

29 Variant 3. This 2D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only. The model has different inside and outside surface areas. Radiation and CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 18 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 17 Ceiling surface temperature distribution (left); 29

30 Floor Surface: Graphs 18 Floor surface temperature distribution (left); Left Wall Surface: Graphs 19 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 20 Right wall surface temperature distribution (left); 30

31 Variant 4. This 2D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only and with the same outside surface area as the inside. Also radiation exchange between construction themselves and warm indoor surface. CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 19 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 21 Ceiling surface temperature distribution (left); 31

32 Floor Surface: Graphs 22 Floor surface temperature distribution (left); Left Wall Surface: Graphs 23 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 24 Right wall surface temperature distribution (left); 32

33 Variant 5. This 2D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only. The model has different inside and outside surface areas. Radiation exchange between construction themselves and warm indoor surface is analyzed. CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 20 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 25 Ceiling surface temperature distribution (left); 33

34 Floor Surface: Graphs 26 Floor surface temperature distribution (left); Left Wall Surface: Graphs 27 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 28 Right wall surface temperature distribution (left); 34

35 Variant 6. This 2D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only. The model has different inside and outside surface areas. Radiation exchange between the construction elements is analyzed. CFD is not included. The colors in the figure below indicate the temperature of the construction elements: Fig. 21 Temperature of construction elements The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 29 Ceiling surface temperature distribution (left); 35

36 Floor Surface: Graphs 30 Floor surface temperature distribution (left); Left Wall Surface: Graphs 31 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 32 Right wall surface temperature distribution (left); 36

37 Variant 7. This 2D variant is simulated without radiation or constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Free convection is included. The colors in the figure below indicate the air temperature in the room: Fig. 22 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 33 Ceiling surface temperature distribution (left); 37

38 Floor Surface: Graphs 34 Floor surface temperature distribution (left); Left Wall Surface: Graphs 35 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 36 Right wall surface temperature distribution (left); 38

39 Variant 8. This 2D variant is simulated without radiation or constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Free convection is included, but the air is heated in a different way than in the other simulation variants with CFD. The colors in the figure below indicate the air temperature in the room: Fig. 23 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 37 Ceiling surface temperature distribution (left); 39

40 Floor Surface: Graphs 38 Floor surface temperature distribution (left); Left Wall Surface: Graphs 39 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 40 Right wall surface temperature distribution (left); 40

41 Variant 9. This 2D variant is simulated without radiation or constant surface coefficients of heat transfer. The model has different inside and outside surface areas. Free convection is included. The colors in the figure below indicate the air temperature in the room: Fig. 24 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 41 Ceiling surface temperature distribution (left); 41

42 Floor Surface: Graphs 42 Floor surface temperature distribution (left); Left Wall Surface: Graphs 43 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 44 Right wall surface temperature distribution (left); 42

43 Variant 10. This 2D variant is simulated without constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Radiation exchange between the construction elements is analyzed. Free convection is also included. The colors in the figure below indicate the air temperature in the room: Fig. 25 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 45 Ceiling surface temperature distribution (left); 43

44 Floor Surface: Graphs 46 Floor surface temperature distribution (left); Left Wall Surface: Graphs 47 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 48 Right wall surface temperature distribution (left); 44

45 Variant 11. This 2D variant is simulated without constant surface coefficients of heat transfer. The model has different inside and outside surface areas. Radiation exchange between the construction elements is analyzed. Also free convection is included. The colors in the figure below indicate the air temperature in the room: Fig. 26 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 49 Ceiling surface temperature distribution (left); 45

46 Floor Surface: Graphs 50 Floor surface temperature distribution (left); Left Wall Surface: Graphs 51 Left Wall surface temperature distribution (left); Right Wall Surface: Graphs 52 Right wall surface temperature distribution (left); 46

47 Variant 12. This 2D variant is simulated without constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Radiation exchange between construction themselves and warm indoor surface is analyzed. Free convection is also included. The colors in the figure below indicate the air temperature in the room: Fig. 27 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 53 Ceiling surface temperature distribution (left); 47

48 Floor Surface: Graphs 54 Floor surface temperature distribution (left); Left Wall Surface: Graphs 55 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 56 Right wall surface temperature distribution (left); 48

49 Variant 13. This 2D variant is simulated without constant surface coefficients of heat transfer. The model has different inside and outside surface areas. Radiation exchange between construction themselves and warm indoor surface is analyzed. Free convection is also included. The colors in the figure below indicate the air temperature in the room: Fig. 28 Indoor air Temperature The indoor surface heat fluxes and temperatures are shown in the following graphs: Ceiling Surface: Graphs 57 Ceiling surface temperature distribution (left); 49

50 Floor Surface: Graphs 58 Floor surface temperature distribution (left); Left Wall Surface: Graphs 59 Left wall surface temperature distribution (left); Right Wall Surface: Graphs 60 Right wall surface temperature distribution (left); 50

51 Annex 2: Simulation results with 3D-model 51

52 Variant 14. This 3D variant is simulated with constant surface coefficients of heat transfer (hc+hr) and with the same outside surface area as the inside. Radiation and CFD is not included. The colors in the figure below indicate the temperature of the indoor surfaces: Fig. 29 Temperatures of the indoor surfaces The temperatures of surface diagonals from ceiling and floor are shown in the graphs below: Graphs 61 Temperature of ceiling surface diagonals (left); Floor surface diagonals (right); 52

53 Variant 15. This 3D variant is simulated with constant surface coefficients of heat transfer (hc+hr). The model has different inside and outside surface areas. Radiation and CFD is not included. The colors in the two figures below indicate the temperature of the indoor surfaces: Fig. 30 Temperatures of the indoor surfaces 53

54 Fig. 31 Temperatures of the indoor surfaces The indoor temperatures of surface diagonals and borders from ceiling and floor are shown in the graphs below: Graphs 62 Temperature of ceiling surface diagonals and borders (left); Floor surface diagonals and borders (right); 54

55 Variant 16. This 3D variant is simulated with only a constant surface coefficient of heat transfer for convection (hc). The model has different inside and outside surface areas. Radiation and CFD is not included. The colors in the figure below indicate the temperature of the indoor surfaces: Fig. 32 Temperatures of the indoor surfaces The indoor temperatures of surface diagonals and borders from ceiling and floor are shown in the graphs below: Graphs 63 Temperature of ceiling surface diagonals and borders(left); Floor surface diagonals and borders (right); 55

56 Variant 17. This 3D variant is simulated without constant surface coefficients of heat transfer. The model has the same outside surface area as the inside. Radiation exchange between construction themselves and warm indoor surface is analyzed. CFD is not included. The colors in the two figures below indicate the temperature of the indoor surfaces: Fig. 33 Temperatures of the indoor surfaces 56

57 Fig. 34 Temperatures of the indoor surfaces The indoor temperatures of surface diagonals and borders from ceiling, floor and wall are shown in the graphs below: Graphs 64 Temperature of ceiling surface diagonals and borders (left), floor surface (middle) and wall surface diagonals (right); 57

58 The figures below visualize the net radiative heat flux and incoming irradiation of the inner surfaces: Ceiling Surface: Fig. 35 Radiative heat flux of the ceiling surface Fig. 36 Irradiation on the ceiling surface 58

59 Floor Surface: Fig. 37 Radiative heat flux of the floor surface Fig. 38 Irradiation on the floor surface 59

60 Wall Surface: Fig. 39 Radiative heat flux of the wall surface Fig. 40 Irradiation on the wall surface 60

61 Variant 18. This 3D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only. The model has different inside and outside surface areas. Radiation exchange between construction themselves and warm indoor surface is analyzed. CFD is not included. The colors in the two figures below indicate the temperature of the indoor surfaces: Fig. 41 Temperatures of the indoor surfaces 61

62 Fig. 42 Temperatures of the indoor surfaces The indoor temperatures of surface diagonals and borders from ceiling and floor are shown in the graphs below: Graphs 65 Temperature of ceiling surface diagonals and borders (left); Floor surface diagonals and borders (right); 62

63 The figures below visualizes the net radiative heat flux and incoming irradiation of the inner surfaces: Ceiling Surface: Fig. 43 Radiative heat flux of the ceiling surface Fig. 44 Irradiation on the ceiling surface 63

64 Floor Surface: Fig. 45 Radiative heat flux of the floor surface Fig. 46 Irradiation on the ceiling surface 64

65 Wall Surface: Fig. 47 Radiative heat flux of the floor surface Fig. 48 Irradiation on the wall surface 65

66 Variant 19. This 3D variant is simulated with a constant surface coefficient of heat transfer for convection (hc) only. The model has different inside and outside surface areas. Radiation exchange between the construction elements is analyzed. CFD is not included. The colors in the two figures below indicate the temperature of the indoor surfaces: Fig. 49 Temperatures of the indoor surfaces 66

67 Fig. 50 Temperatures of the indoor surfaces The indoor temperatures of surface diagonals and borders from ceiling and floor are shown in the graphs below: Graphs 66 Temperature of ceiling surface diagonals and borders (left); Floor surface diagonals and borders (right); 67

68 The figures below visualizes the net radiative heat flux and incoming irradiation of the inner surfaces: Ceiling Surface: Fig. 51 Radiative heat flux of the ceiling surface Fig. 52 Irradiation on the ceiling surface 68

69 Floor Surface: Fig. 53 Radiative heat flux of the floor surface Fig. 54 Irradiation on the floor surface 69

70 Wall Surface: Fig. 55 Radiative heat flux of the wall surface Fig. 56 Irradiation on the wall surface 70