EN ISO 11855-2:2015

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.Umweltgerechte Gebäudeplanung - Planung, Auslegung, Installation und Steuerung flächenintegrierter Strahlheizungs- und -kühlsysteme - Teil 2: Bestimmung der Auslegungs-Heiz- bzw. Kühlleistung (ISO 11855-2:2012)012)Conception de l'environnement des bâtiments - Conception, dimensionnement, installation et contrôle des systèmes intégrés de chauffage et de refroidissement par rayonnement - Partie 2 : Détermination de la puissance calorifique et frigorifique à la conception (ISO 11855-2:2012)Building environment design - Design, dimensioning, installation and control of embedded radiant heating and cooling systems - Part 2: Determination of the design heating and cooling capacity (ISO 11855-2:2012)91.140.30VLVWHPLVentilation and air-conditioning91.140.10Sistemi centralnega ogrevanjaCentral heating systemsICS:Ta slovenski standard je istoveten z:EN ISO 11855-2:2015SIST EN ISO 11855-2:2015en,fr,de01-oktober-2015SIST EN ISO 11855-2:2015SLOVENSKI
STANDARD
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
EN 11855-2
August 2015 ICS 91.140.10; 91.140.30 English Version
Building environment design - Design, dimensioning, installation and control of embedded radiant heating and cooling systems - Part 2: Determination of the design heating and cooling capacity (ISO 11855-2:2012)
Conception de l'environnement des bâtiments - Conception, dimensionnement, installation et contrôle des systèmes intégrés de chauffage et de refroidissement par rayonnement - Partie 2 : Détermination de la puissance calorifique et frigorifique à la conception (ISO 11855-2:2012)
Umweltgerechte Gebäudeplanung - Planung, Auslegung, Installation und Steuerung flächenintegrierter Strahlheizungs- und -kühlsysteme - Teil 2: Bestimmung der Auslegungs-Heiz- bzw. Kühlleistung (ISO 11855-2:2012)012) This European Standard was approved by CEN on 30 July 2015.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre:
Avenue Marnix 17,
B-1000 Brussels © 2015 CEN All rights of exploitation in any form and by any means reserved worldwide for CEN national Members. Ref. No. EN 11855-2:2015 ESIST EN ISO 11855-2:2015

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights. According to the CEN-CENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom. Endorsement notice The text of ISO 11855-2:2012 has been approved by CEN as EN ISO 11855-2:2015 without any modification. SIST EN ISO 11855-2:2015

Reference numberISO 11855-2:2012(E)© ISO 2012
INTERNATIONAL STANDARD ISO11855-2First edition2012-10-01Building environment design — Design, dimensioning, installation and control of embedded radiant heating and cooling systems — Part 2: Determination of the design heating and cooling capacity Conception de l'environnement des bâtiments — Conception, construction et fonctionnement des systèmes de chauffage et de refroidissement par rayonnement — Partie 2: Détermination de la puissance calorifique et frigorifique à la conception
ISO 11855-2:2012(E)
©
ISO 2012 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body in the country of the requester. ISO copyright office Case postale 56  CH-1211 Geneva 20 Tel.
+ 41 22 749 01 11 Fax
+ 41 22 749 09 47 E-mail
copyright@iso.org Web
www.iso.org Published in Switzerland
ii
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved
iii Contents Page Foreword . iv Introduction . v 1 Scope . 1 2 Normative references . 1 3 Terms and definitions . 2 4 Symbols and abbreviations . 2 5 Concept of the method to determine the heating and cooling capacity . 3 6 Heat exchange coefficient between surface and space . 4 7 Simplified calculation methods for determining heating and cooling capacity or surface temperature . 6 7.1 Universal single power function . 7 7.2 Thermal resistance methods . 9 8 Use of basic calculation programs . 11 8.1 Basic calculation programs . 11 8.2 Items to be included in a complete computation documentation . 11 9 Calculation of the heating and cooling capacity . 12 Annex A (normative)
Calculation of the heat flux . 13 Annex B (normative)
General resistance method . 36 Annex C (normative)
Pipes embedded in wooden construction . 42 Annex D (normative)
Method for verification of FEM and FDM calculation programs . 50 Annex E (normative)
Values for heat conductivity of materials and air layers . 54 Bibliography . 56
ISO 11855-2:2012(E) iv
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved
v Introduction The radiant heating and cooling system consists of heat emitting/absorbing, heat supply, distribution, and control systems. The ISO 11855 series deals with the embedded surface heating and cooling system that directly controls heat exchange within the space. It does not include the system equipment itself, such as heat source, distribution system and controller.
The ISO 11855 series addresses an embedded system that is integrated with the building structure. Therefore, the panel system with open air gap, which is not integrated with the building structure, is not covered by this series.
The ISO 11855 series shall be applied to systems using not only water but also other fluids or electricity as a heating or cooling medium.
The object of the ISO 11855 series is to provide criteria to effectively design embedded systems. To do this, it presents comfort criteria for the space served by embedded systems, heat output calculation, dimensioning, dynamic analysis, installation, operation, and control method of embedded systems. SIST EN ISO 11855-2:2015

INTERNATIONAL STANDARD ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 1 Building environment design — Design, dimensioning, installation and control of embedded radiant heating and cooling systems — Part 2: Determination of the design heating and cooling capacity 1 Scope This part of ISO 11855 specifies procedures and conditions to enable the heat flow in water based surface heating and cooling systems to be determined relative to the medium differential temperature for systems. The determination of thermal performance of water based surface heating and cooling systems and their conformity to this part of ISO 11855 is carried out by calculation in accordance with design documents and a model. This should enable a uniform assessment and calculation of water based surface heating and cooling systems. The surface temperature and the temperature uniformity of the heated/cooled surface, nominal heat flow density between water and space, the associated nominal medium differential temperature, and the field of characteristic curves for the relationship between heat flow density and the determining variables are given as the result. This part of ISO 11855 includes a general method based on Finite Difference or Finite Element Methods and simplified calculation methods depending on position of pipes and type of building structure. The ISO 11855 series is applicable to water based embedded surface heating and cooling systems in residential, commercial and industrial buildings. The methods apply to systems integrated into the wall, floor or ceiling construction without any open air gaps. It does not apply to panel systems with open air gaps which are not integrated into the building structure.
The ISO 11855 series also applies, as appropriate, to the use of fluids other than water as a heating or cooling medium. The ISO 11855 series is not applicable for testing of systems. The methods do not apply to heated or chilled ceiling panels or beams. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO 11855-1:2012, Building environment design — Design, dimensioning, installation and control of embedded radiant heating and cooling systems — Part 1: Definition, symbols, and comfort criteria EN 1264-2, Water based surface embedded heating and cooling systems — Part 2: Floor heating: Prove methods for the determination of the thermal output using calculation and test methods SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 2
AA m2 Surface of the occupied area
AF m2 Surface of the heating/cooling surface area
AR m2 Surface of the peripheral area
bu — Calculation factor depending on the pipe spacing
B, BG, B0 W/(m2K) Coefficients depending on the system
D m External diameter of the pipe, including sheathing where used
da m External diameter of the pipe di m Internal diameter of the pipe dM m External diameter of sheathing
cW kJ/(kgK) Specific heat capacity of water
ht W/(m2K) Total heat exchange coefficient (convection + radiation) between surface and space
KH W/(m2K) Equivalent heat transmission coefficient
KWL — Parameter for heat conducting devices
kfin — Parameter for heat conducting devices
kCL — Parameter for heat conducting layer
LWL m Width of heat conducting devices
Lfin m Width of fin (horizontal part of heat conducting device seen as a heating fin)
LR m Length of installed pipes
m — Exponents for determination of characteristic curves
mH kg/s Design heating/cooling medium flow rate
n, nG — Exponents
q W/m2 Heat flux at the surface
qA W/m2 Heat flux in the occupied area
qdes W/m2 Design heat flux
qG W/m2 Limit heat flux qN W/m2 Nominal heat flux qR W/m2 Heat flux in the peripheral area
qu W/m2 Outward heat flux Ro m2K/W Partial inwards heat transmission resistance of surface structure
Ru m2K/W Partial outwards heat transmission resistance of surface structure
R,B m2K/W Thermal resistance of surface covering
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 3 R,ins m2K/W Thermal resistance of thermal insulation
sh m In Type B systems, thickness of thermal insulation from the outward edge of the insulation to the inward edge of the pipes (see Figure 2)
sl m In Type B systems, thickness of thermal insulation from the outward edge of the insulation to the outward edge of the pipes (see Figure 2)
sins m Thickness of thermal insulation sR m Pipe wall thickness su m Thickness of the layer above the pipe sWL m Thickness of heat conducting device S m Thickness of the screed (excluding the pipes in type A systems)
W m Pipe spacing
 W/(m2K) Heat exchange coefficient
s,max °C Maximum surface temperature
s,min °C Minimum surface temperature
i °C Design indoor temperature
m °C Temperature of the heating/cooling medium
R °C Return temperature of heating/cooling medium
V °C Supply temperature of heating/cooling medium
u °C Indoor temperature in an adjacent space
H K Heating/cooling medium differential temperature
H,des K Design heating/cooling medium differential temperature
H,G K Limit of heating/cooling medium differential temperature
N K Nominal heating/cooling medium differential temperature
V K Heating/cooling medium differential supply temperature
V,des K Design heating/cooling medium differential supply temperature
 W/(mK) Thermal conductivity
 K Temperature drop V R  — Conversion factor for temperatures
 — Content by volume of the attachment burrs in the screed
5 Concept of the method to determine the heating and cooling capacity A given type of surface (floor, wall, ceiling) delivers, at a given average surface temperature and indoor temperature (operative temperature i), the same heat flux in any space independent of the type of embedded system. It is therefore possible to establish a basic formula or characteristic curve for cooling and a basic formula or characteristic curve for heating, for each of the type of surfaces (floor, wall, ceiling), independent of the type of embedded system, which is applicable to all heating and cooling surfaces (see Clause 6). Two methods are included in this part of ISO 11855:  simplified calculation methods depending on the type of system (see Clause 7);  Finite Element Method and Finite Difference Method (see Clause 8). SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 4
Figure 1 — Basic characteristic curve for floor heating and ceiling cooling SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 5 For floor heating and ceiling cooling in Figure 1, the heat flow density q is given by: q = 8,92 (S,m i)1,1 (W/m2) (1) where S,m is the average surface temperature in°C; i is the nominal indoor operative temperature in °C. For other types of surface heating and cooling systems, the heat flux q is given by: Wall heating and wall cooling: q = 8 (|s,m i |) (W/m2)
(2) Ceiling heating: q = 6 (|s,m i |) (W/m2)
(3) Floor cooling: q = 7 (|s,m i |) (W/m2)
(4) The heat transfer coefficient is combined convection and radiation. NOTE In many building system simulations using dynamic computer models, the heat transfer is often split up in a convective part (between heated/cooled surface and space air) and a radiant part (between heated/cooled surface and the surrounding surfaces or sources). The radiant heat transfer coefficient may in the normal temperature range 15-30 °C be fixed to 5,5 W/m2K. The convective heat transfer coefficient depends on type of surface, heating or cooling, air velocity (forced convection) or temperature difference between surface and air (natural convection). For using the simplified calculation method in Annex A the characteristic curves present the heat flux as a function of the difference between the heating/cooling medium temperature and the indoor temperature. For the user of Annex A, this means not to do any calculations by directly using values of heat exchange coefficients. Consequently, Annex A does not include values for such an application or special details or equations concerning heat exchange coefficients on heating or cooling surfaces. Thus, the values . of Table A.12 of Annex A are not intended to calculate the heat flux directly. In fact, they are provided exclusively for the conversion of characteristic curves in accordance with Equation (A.32) in Clause A.3. For simplifications these calculations are based on the same heat exchange coefficient for floor cooling and ceiling heating, 6,5 W/m2K. For every surface heating and cooling system, there is a maximum allowable heat flux, the limit heat flux qG. This is determined for a selected design indoor room temperature of i (for heating, often 20 °C and for cooling, often 26 °C) at the maximum or minimum surface temperature F,max and a temperature drop  = 0 K. For the calculations, the centre of the heating or cooling surface area, regardless of the type of system, is used as a reference point for S,max. The average surface temperature, S,m, which determines the heat flow density (refer to the basic characteristic curve) is linked with the maximum or minimum surface temperature: S,m  S,max and. S,m  S,min always applies. The attainable value, S,m, depends not only on the type of system, but also on the operating conditions (temperature drop  = V R, outward heat flow qu and heat resistance of the covering R,B). The following assumptions form the basis for calculation of the heat flux:  heat transfer between the heated or cooled surface and the space occurs in accordance with the basic characteristic curve; SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 6
0,014 m  d  0,022 m 0,01 m  su/e  0,18 7.1 A.2.3 Plane section system
D 2 c)
7.1, A.2.4 In concrete slab
E 4 ST /W  0,3 7.2, B.1 Capillar tubes in concrete surface
F 5 da/W  0,2
7.2, B.2 Wooden constructions, pipes in sub floor or under sub floor, conductive devices G 6 wl  10 surroundingmaterial SWL   0,01
7.2, Annex C
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 7 7.1 Universal single power function The heat flux between embedded pipes (temperature of heating or cooling medium) and the space is calculated by the general equation: imiiqBaH()û (W/m2) (5) where B is a system-dependent coefficient in W/(m2K). This depends on the type of system; ()imiia is the power product, which links the parameters of the structure (surface covering, pipe spacing, pipe diameter and pipe covering). This calculation method is given in Annex A for the following four types of systems:  Type A with pipes embedded in the screed or concrete (see Figure 2 and A.2.2);  Type B with pipes embedded outside the screed (see Figure 2 and A.2.3);  Type C with pipes embedded in the screed (see Figure 2 and A.2.2);  Type D plane section systems (see A.2.4). Figure 2 shows the types as embedded in the floor, but the methods can also be applied for wall and ceiling systems with a corresponding position of the pipes. This method shall only be used for system configurations meeting the boundary conditions listed for the different types of systems in Annex A.
a)
Type A and C Key 1 floor covering 2 weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed) 3 thermal insulation 4 structural bearing SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 8
b)
Type B Key 1 floor covering 2 weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed, wood) 3 heat diffusion devices 4 thermal insulation 5 structural bearing SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 9
c)
Type D Key 1 floor covering R, B 2 weight bearing and thermal diffusion layer (cement screed, anhydrite screed, asphalt screed, timber) 3 thermal insulation 4 structural bearing Figure 2 — System types A, B and C covered by the method in Annex A 7.2 Thermal resistance methods The heat flux between embedded pipes (temperature of heating or cooling medium) and the space or surface is calculated using thermal resistances. The concept is shown in Figure 3. An equivalent resistance, RHC, between the heating or cooling medium to a fictive core (or heat conduction layer) at the position of the pipes is determined. This resistance includes the influence of type of pipe, pipe distance and method of pipe installation (in concrete, wooden construction, etc.). In this way a fictive core temperature is calculated. The heat transfer between this fictive layer and the surfaces, Ri and Re (or space and neighbour space) is calculated using linear resistances (adding of resistance of the layers above and below the heat conductive layer). The equivalent resistance of the heat conductive layer is calculated in different ways depending on the type of system. This calculation method, using the general resistance concept, is given in Annex B for the following two types of systems:  Type E with pipes embedded in massive concrete slabs (see Figure 4 and B.1);  Type F with capillary pipes embedded in a layer at the inside surface (see Figure 5 and B.2). SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 10
Figure 3 — Basic network of thermal resistance
Figure 4 — Pipes embedded in a massive concrete layer, Type E
Figure 5 — Capillary pipes embedded in a layer at the inner surface, Type F SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 11 This calculation method, using the general resistance concept, is shown in Annex C for pipes embedded in wooden floor constructions using heat conducting plates (Figure 6).
Figure 6 — Pipes in wooden constructions, TYPE G The equivalent resistance of the conductive layer may also be determined either by calculation using Finite Element Analysis (FEA) or Finite Difference Methods (FDM) (see Clause 8) or by laboratory testing (as in, for example, EN 1264-2:2008, Annex B). 8 Use of basic calculation programmes 8.1 Basic calculation programmes A numerical analysis by Finite Element Method or by Finite Difference Method shall be conducted in accordance with the state-of-the-art practice and the applicable codes and standards, in such a way that they can readily be verified. The calculation programme used shall be verified according to Annex D. The numerical analysis may be used to calculate the heating and cooling capacity or the equivalent resistances. On basis of the equivalent resistances, the heating and cooling capacity is calculated for different temperature differences between the surface and the room. 8.2 Items to be included in a complete computation documentation The following items are to be included in a complete computation documentation:  representation and documentation of the structure to be analysed, by means of the technical drawings, diagrams and sketches;  indication of the material data used as a basis and the requisite data sources;  description of load cases used as a basis, including substantiation by codes and standards;  description and representation of the numerical model applied, indicating the mathematical and physical basis, for example the element type, the shape functions, number of elements, nodes and degrees of freedom;  name, verification, if available, and origin of the computation programme; SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 12
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 13 Annex A (normative)
Calculation of the heat flux A.1 General The basic calculation is done for reference heating systems (see A.2). For floor heating systems these results apply directly. The method described in A.3 enables the conversion of these results into results for other surfaces in the room (ceiling and wall heating). The method is also applicable for all the cooling surfaces (floor, ceiling, wall cooling). This calculation method [1] is based on the results obtained in A.2.2/A.2.3 and A.2.4. The change in the surface thermal resistance R=(1/) influences the temperature field within the system in the same way as a change in the thermal resistance of the surface covering RB[1]. A.2 Reference heating systems A.2.1 General The heat flux q at a surface is determined by the following parameters:  pipe spacing W;  thickness su and thermal conductivity E of the layer above the pipe;  thermal conduction resistance R,B of covering;  pipe external diameter D = da, including sheathing (D = dM) if necessary and the thermal conductivity of the pipe R and/or the sheathing M. In the case of non-circular pipes, the equivalent diameter of circular pipes having the same circumference is to be calculated (the screed covering shall be used unchanged). The thickness and the thermal conduction resistance of firmly deposited barrier layers up to a thickness of 0,3 mm shall not be taken into consideration. In this case, D = da shall be used;  heat conducting devices, characterized by the value KWL in accordance with A.3;  contact between the pipes and the heat conducting devices or screed, characterized by the factor aK;  the heat-conducting layer of the heating system is thermally decoupled by the thermal insulation from the structural base of the building. The heat flux is proportional to nH(û), where the temperature difference between the heating medium and the room temperature is VRHViRiûIn (A.1) SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 14
is a system-dependent coefficient in W/(m2K). This depends on the type of system; miaii() is a power product which links the parameters of the structure together (see A.2.2, A.2.3 and A.2.4). A distinction shall be made between systems with pipes inside the screed, systems with pipes below the screed and plane section systems. Equation (A.2) applies directly for usual constructions. A.2.2 Systems with pipes inside the screed (type A and type C) For these systems (see Figure A.1), the characteristic curves are calculated by: mmmqBaaaaUWDBWUDûH (A.3) where B = B0 = 6,7 W/m2K The B-values are valid for a thermal conductivity R = R,0 = 0,35 W/(mK) of the pipe and pipe wall thickness sR = sR,0 = (da di)/2 = 0,002 m. For other materials with different heat conductivity or pipe wall thickness or for sheathed pipes, B shall be calculated in accordance with A.2.6. For a heating cement screed with reduced humidity, E = 1,2 W/(mK) shall be used. This value is also applicable to levelling layers. If a different value is used, its validity shall be checked. aB - surface covering factor in accordance with the following equation ,sasRu,0u,0Bu,0BE11 (A.4) where  = 10,8 W/(m2K); u, 0 = 1 W/(mK); SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 15 su, 0 = 0,045 m; R, B is the heat conduction resistance of the floor covering, in m2K/W; E is the heat conductivity of the screed, in W/(mK); w is the pipe spacing factor in accordance with Table A.1; w = f(R,B); U is the covering factor in accordance with Table A.2; U = f(W, R,B); D is the pipe external diameter factor in accordance with Table A.3; D = f(W, R,B). WmW10,075 (A.5) where 0,050 m  W  0,375 m (where W is the pipe spacing); mu = 100(0,045 – su); (A.6) where su  0,010 m (where su is the thickness of the layer above the pipe); mD = 250(D – 0,020) (A.7) applies where 0,008 m  D  0,030 m (where D is the external diameter of the pipe, including sheathing where used) Equations (A.4) to (A.7) are valid for thickness of layer above pipe (inward) 0,065 m  su su*, where: su* = 0,100 m for pipe spacing W  0,200m; su* = 0,5 W for pipe spacing W  0,200 m. The actual spacing W shall be used for calculation of su, also if W 0,375. For su  su*, the equivalent heat transfer coefficient is: ,ssKssK*uuH*uuEH11 (A.8) In Equation (A.8), ,ssK*uuHis the power product from Equation (A.3), calculated for a covering u*s above the pipe. The heat flux is: qKHHû (A.9) For pipe spacing W  0,375 m, the heat flux is approximated by: qqW0,3750,375 (A.10) where q0,375 is the heat flux, calculated for a spacing W = 0,375 m. The limit curves are calculated in accordance with Equation (A.18) (see A.2.5). SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 16
With ()10,44fWW
T pipe spacing factor in accordance with Table A.6; afsTu(/)E U covering factor which is calculated in accordance with the following equation: sasu,0u,0UuE11 (A.12a) where  = 10,8 W/(m2K); u, 0 = 1 W/(mK); su, 0 = 0,045 m; SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 17 D)aWL is the heat conduction device factor in accordance with Table A.8; ; afKWWLWL(,,aK is the correction factor for the contact in accordance with Table A.9; ; afWK()WmW10,075 applies for
where W is the pipe spacing (A.13) mWm0,0500,450The characteristic value KWL is: sbsKWLWLuuEWL0,125 (A.14) where bfWu() according to Table A.7; sWLWL product of the thickness and the thermal conductivity of the heat conducting material; suE is the product of the thickness and the thermal conductivity of the screed. If the width LWL of the heat conducting device is smaller than the pipe spacing W, the value determined for
according to Table A.8 shall be corrected to: aWLLWLWLaaaaLWLWLWWLWLWL23WLWL,WL,WL,0WLWLWL()13,2(/)3,4(/)1,2(/) (A.15) The heat conduction device factors LWaWLWL, and LaWLWL,0 shall be taken from Table A.8. For LWL = W, tables for the characteristic value KWL are directly applicable in accordance with Equation (A.14). For LWL = 0, KWL shall be constituted with sWL = 0. The correction factor for the contact, aK, takes into account the additional heat transmission resistance caused by spot or line contact only between the pipe and the heat conducting device. This depends on the manufacturing tolerances of the pipes and conducting devices as well as on the care taken during installation and is therefore subject to fluctuations in individual cases. Table A.9, therefore, gives average values for . aKThe limit curves are calculated in accordance with Equation (A.18) (see A.2.5). Limitation of the method: Position of pipes Pipe spacing
mWm0,0500,4500,01  su/E  0,0792 A.2.4 Plane section systems The following equation applies to surfaces fully covered with embedded heating or cooling elements (see Figure A.3): mqBaaaWBUWûH (A.16) SIST EN ISO 11855-2:2015

ISO 11855-2:2012(E) 18
ISO 11855-2:2012(E) © ISO 2012 – All rights reserved 19 1,1F,maxioû with Koû9 (A.19) The intersection of the characteristic curve with the limit curve is calculated from: nmiBBaGi11GH,Giû (A.20) The limit curves for type A and C systems, for T  0,375 m, are calculated according to: mqqfWGG;0,375G0,375 (A.21) fH,GH,G;0,375Gûû (A.22) where qG; 0,375 is the limit heat flux, calculated for a spacing W = 0,375 m; H, G; 0,375 is the limit temperature difference between the heating medium and the room, calculated for a spacing W = 0,375 m. and fG1,0 for sWu0,173 sWmqqqeWfmqW2u20(/0,173)G,maxG,maxG,0,375GG,0,3750,3750,375 for sWu0,173 (A.23) where q G,max is the maximum permissible heat flux in accordance with Table A.13, calculated for an isothermal surface temperature distribution using the basic characteristic curve (Figure A.1), with (F, m  i) = (F, max  i). For type B systems, Equations (A.11) and (A.12) apply directly, when the pipe spacing W and the width of the heat diffusion device LWL are the same. For LWL < W, the value of the heat flux qG, LWL = W, calculated in accordance with Equation (A.11), shall be corrected using the following
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