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1. Lengths Temps Heating cooling Flows and pressure loss Loop System Surface RT Ti Te Req AT Ln La Ltot To Ts Tr nr Type Material rel C CI Wrm chim mj m ic c Panel 1617 s192 Tiles 8 12 mm ES 72 38 1 2 Panel 1617 s192 Parquet 15 mm paper felt PE foil 3 20 0 60 7 2 70 72 47 ls None x None Es 1 4 None UY None E hs None LT None Es 1 6 None x None Ww 1 7 None L None Ed 1 8 None UT None E3 Ho None L None idl 1 10 None LY None w z a a z Max opt temp 47 C Fluid type Water Pipe roughness PEX pipes 0 007 mm 62 C choose Figure 7 A common supply temperature has manifold By giving the maximum supply temperature all heating requirements will be fulfilled Here the value of 47 C is given and all calculated values for the loops are shown We find out the following e In column T the fulfilled requirements are displayed For the wood floor the required 60 W m are supplied However since the supply water temperature is higher than the optimal for the tiled floor the current status will be able to fulfil 96 W m7 This loop will need a thermostat to reduce heat emission Alternatively the design temperature drop in column J can be increased e The column in U shows the new total requirement Since the heat loss calc2. Material data Material data Morene Material data Material data 2 ORRIO Rr no W m2xK Figure 5 Snapshot of two tables used for calculating the thermal resistance of constructions underneath the panels Going back to the worksheet Manifold1 the R value is entered in column E In the next column F the design indoor temperature is to be given Column G is for the design temperature that is below or surrounds the construction underneath the floor heating system This may be an indoor temperature if the construction is an intermediate floor that separates one apartment from the other It may be the mean outdoor temperature of the heating season if the construction is a slab on ground In other words it is not evident that the temperature that is entered in this column is the design outdoor temperature In the next column the heating or cooling requirement at design conditions has to be given to the program This value is usually calculated on basis of heat losses due to transmission U values and thermal bridges U A iw lt 1 T T and ventilation 0 33 n V T T and divided by the heated floor area In case of heating the value is positive In the case of cooling the value is negative The design temperature drop AT is entered in column J Commonly the temperature drop is given values between 5 10 C In Floor p
3. Di Arial ho A 1 pR ft text Fe a Klistra g Fm CEEE k d atera Cellforma oga Ta Format in t o D fim Sok och markera Urkiipp_ 5 Justering Tal Format Celler Redigering x x S kerhetsvarning Makron har inaktiverats Alternativ 5 fe JB c r 1FIGKI JMLMINAPOIRAT UL VNX Y 2 AA ABJACA 4 4 AG a A 1 E Project iv l 3 4 5 6 7 8 x Ls System Surface Rt Ti nr T Material fre C None Ly None gt 4 2 None v None x 9 None ix None y 10 14 JNone 7 None o 11 None v none 12 1 6 None None x 13 None none x 14 1 8 None iw None v 15 None Ly None x 16 1 10 None None v 17 18 Fluid type Water ibd 19 Pipe roughness PEX pipes 0 007 mm x 2 M 4 b1 Manifoldi RT J E goo y TE Er A ar r GY Microsoft Excel a EEC Figure 1 The red d ellipse marks where the computer s warning on macros activation may appear Activate the use of macros since the scroll menus in the program are use macros The Excel file that you have obtained can be used as a master file meaning that you should save the file without having data in it When you wish to use the file for calculations re name the file so that you can save the changes and yo
4. Ti Te Req AT Ln La Ltot To Ts Tr Req Tot Pow Ap Kv dp furng Vol 6 nr T Material rer c c ur c ff m m m c ec scl wire wim kw kPa vmin mn mbar it 7 None Ly None v 8 f1 2 None none x 9 None None Ly 2 10 14 None z None x 11 None none Fr 12 4 6 None tr None B 13 None None x 14 1 8 None Cr none lx 15 None m None x 16 1 10 None Lx None X 3 17 E Max opt tem oc 18 Fluid type Water Ea 19 Pipe roughness PEX pipes 0 007 mm x 20 21 22 23 M4 Hil Manifold1 RT m Kiar Eg gy a phase change p Ei im pro Jan Akander Ou 1 Inkorgen Micro Design prg Mie Microsoft Excel Se WA 164 Foure 3 Project T can be entered in the white zone on the top of the worksheet The colours of the program have a certain meaning In cells that are marked yellow you can enter or change numbers Cells that have other colours cannot be changed The first column is called Loop column B in the Excel file This column allows the loop numbers to be changed The default setting is manifold nr loop nr for example 1 3 means the third loop on manifold 1 You can change to other numbers or expressions in this column If you wish to insert other symbols than numbers you may need to place quote marks around the symbols for example 1 A rather than just 1 A In the second column t
5. slice of the floor construction which is studied at a distance x from the loop s inlet and having the thickness dx and the width s the pipe spacing the heat flow occurring upward here denoted by the small heat flow 6 through the floor surface is 5D 0 x w 1 1 amp 8 x 0 w 1 2 The total heat flow through the pipe which compensates for the upward and downward heat flows passes through the thermal resistance R This thermal 14 resistance accounts for the construction including the systems ability to conduct heat sideways However it is defined on basis of the floor surface area i e per square meter flooring The law of energy conservation gives that AD x FD x 5D x w 1 3 So that aD x 0 x 0 0 x 0 W 1 4 The heat transfer 6M from the bulk water temperature in the pipe to the star circuits temperature 0 x passes through R according to the following AD x 0 x 8 x w 1 5 By solving for 0 x equation 5 will give that 8 8 9 28 ec je s dx Insertion of the expression for 6 x in equation 1 4 will render the following ZOE 4 2 AR RL R R SD x ei w 1 7 1 a R R However the heat that is transmitted through R comes from water in the pipe that equation is losing temperature over the distance dx The change in temperature is denoted by d0 and is n
6. Contact Manager gt Nes nue IR i LJ st ng z 2 Excel atternatiy X Avsluta Excel Wl 16 1 10 None J None eS Ss se S 17 E 18 Fluid type Water w 19 Pipe roughness PEX pipes 0 007 mm 20 21 22 23 4 floor 25 Version 3 0 May 2013 narh Manifold1 RT J Klar a phase change p 2 Tan Akander Ou D Design pro Mic osoft Ex SV lt 8 Wa 165 figure 2 Making a anew file i in 1 which your data will be saved Now it s time to enter information and input data in the worksheet On the top part of the worksheet you may enter the project ID for example customer name quotation number or other information that is important etc as marked in Figure 3 Floore design master_v30 Microsoft Excel Start Infoga Sidlayout Formler Data Granska Visa x Rs ariar ho gt Aa EP Radibiyt text Fj ii Kista Fx u vtr es e o g vik d Formatera Cellformat Infoga Ta Format orte S k och 3 ai o te 2 tt markera ET 4 el ERE g Tecken Justering Tal Format Celler Redigering x S kerhetsvarning Makron har inaktiverats Alternativ D2 v fe eal ZB Cc LD FIG JNLIM NMP Q IRRT U VNX Y Z AA ABACK AE AF AG AH Ag 1 A aD l 3 4 Flows and pressure loss 5 jk System Surface RT
7. User manual Design program in Excel for Floor panel products Manual version 1 0 for Excel program version 3 2 released in May 2014 floore Requirements The design program requires a certain amount of input data so that correct output data can be calculated The calculations are done for one manifold at a time with ten loops per manifold The program is made in Microsoft Excel and should be compatible with other platforms All decimals are given as commas The input data are the following for each loop 1 System type in other words the panel type and pipe 2 Flooring materials that are placed above the panels 3 Thermal resistance of the sub floor 4 Design indoor temperature of the zone 5 Design outdoor temperature or zone below the sub floor 6 Design temperature drop of the water in the loop 7 The heating requirement of the room zone based on heated floor area 8 Pipe lengths split up in parts that actively emit heat and non emitting parts Getting started When the Excel program is opened you will have be warned about allowing macros to be used A security warning sign is shown giving you the alternative to either protect the computer from harmful codes or to activate the content Choose to activate the contents the macros are codes for the scroll lists provided in the program A THE Floore design master_v30 Microsoft Excel Start Infoga Sidlayout Formler Data Granska Visa x
8. ction Integration of equation 9 given that the loop has the length L and the design temperature drop A along the loops distance gives the total power that the loop emits here expressed by equation 1 12 Mike ROS SaaS w 1 12 pw s R R RL 6 Ow R R Ogu z Ov The outlet temperature 0 out can be substituted with the expression 0 A The power of the upward heat flow is s L A0 D w 1 13 R R ae r it DR In 0 Ow R ps O aw And of the downward heat flow is L AO g s w 1 14 R AL ER 6 0w R O a n l out Equation 13 can be used to determine the supply temperature 6 in given that the desired upward power output is or density of heat flow q s L and the maximum temperature drop A0 along the loop is chosen The supply temperature is then 0 0 5e Ce 1 15 17 The density of heat flow heat flux g is calculated from the heating requirement at design conditions qu D design S L according to the following equation qj d design U 0 6 W m 1 16 where the U value of the floor ground construction in essence is U x W m K 1 17 This U value can be estimated by use of EN ISO 13370 2007 Thermal performance of buildings Heat transfer via the ground Calculation methods Note that D lt in other words that the sum of heat emitted upward design and downward are larger than the
9. e _ None Fluid type Water 62 Pipe roughness PEX pipes 0 007 mm ix C choose Figure 9 The only difference in input is the panel thickness The optimal temperatures increase with panel thickness As seen in Figure 9 the optimal supply temperature increases with the thickness of the panel which seems to be in contradiction to the function of increased thermal insulation However there is one aspect that has not been considered here and that is the influence of the increased insulation on the heating requirement which in this case is the same 60 W m The thermal insulation of the various panels is shown in Table 1 Observe that the pipe size and spacing have influence on the insulation value obviously increased pipe size decreases the insulation performance Table 1 Panel type and estimated thermal resistance of each panel Panel type Thermal resistance m K W Panel 1213 s192 0 192 Panel 1213 s120 0 102 Panel 1225 s192 0 672 Panel 1250 s192 1 440 Panel 1617 s192 0 242 Panel 1625 s192 0 609 Panel 1650 s192 1 410 Now if the original construction has the thermal resistance Ry 3 00 m K W this value will increase if extra insulation is placed on it Also the heating requirement will reduce since the transmission loss through the floor will be reduced The changes due to the insertion of panels are displayed in Table 2 10 Table 2 Cha
10. e amount of turns of the valve from initially shut position that is needed to constrict flow 2 5 turns means that the valve is fully open At the bottom part of the display highlighted in green the parameters for the whole system manifold and all loops are displayed Some comments on the panels A tricky part in design work is to understand the role of the insulation capability of the various panels Since these perform as insulating materials the heating requirement will reduce in accordance to the insulation capacity of the panel that will be installed Let s have a look at an example all parameters are the same except for the panel type that will be used Figure 9 shows the input where the heating requirement is set to be the same independently of what type of panel is used Lengths Temps Heating cooling Flows and pressure loss Loop System Surface RT Ti Te Req AT Ln La Ltot To Ts nr Type Material La C ciwe ciim mjm cle Panel 16175192 Tiles 8 12 mm 20 15 60 72 37 1 2_ Panel 1625 5192 _ Tiles 8 12 mm 3 20 151 60 7 2 70 72 38 Panel 1650 s192 Tiles 8 12 mm Ww 72 39 1 4 None None ES lis None CA None Es 1 6 None None Hz None a None j 1 8 None _ None Es Ho None _ None 1 10 Non
11. egative when the temperature drops along the loop The relationship between heat flow and temperature drop is ID x M c p d0 x w 1 8 15 where M is the mass flow rate of water in the pipe and c is the specific heat pw capacity of water In combination with equation 1 3 the temperature drop is dependent on the internal and external temperatures as seen in Figure 1 2 as well as the thermal resistances Insertion of equation 1 8 into equation 1 7 gives after some tidying up that d0 x s dx 1 9 RR 6 R R l 0 x M c w i A R R F R R R P R R Special attention is given to the term which here is named 0 here defined as R R lan re F c 1 10 R R R R The general solution of the integral of equation 9 is given as SX RR 8 M c Vekv e 0 x 0 0 ec 1 11 n Temp Distance Figure 1 2 Temperature drop of the water during the distance dx The drop is due to heat emission to the internal and external environment 16 Equation 1 11 shows that at the inlet of the loop x 0 the temperature is 0 If the loop is endless x 00 the temperature becomes In principle is the temperature that is obtained in the plane of the pipe when the system is turned off This is the case where the heat transfer is one dimensional directed from the indoor environment and downward through the entire floor constru
12. el 1617 s192 _X Laminate 8 mm paper felt PE foil Lm 4 2 Panel 1625 s192 Laminate 8 mm paper felt PE foil Es Panel 1650 s192 Laminate 8 mm paper felt PE foil Le 1 4 None Lx None Y None _ None j 1 6 None _7 None Lx None _7 None bd 1 8 None None EA None oT None Le 1 10 None az None T Fluid type Water Z Pipe roughness PEX pipes 0 007 mm a 10 6 kPa 24 4 liters 11 The results show that the thicker panels give a substantially reduced total heating requirement called Tot column U and also seen in Pow column V The difference in requirement is simply due to that the ground losses are less with the thicker panels Please note that all values that are shown and also the inserted supply temperature do not show decimal values and may appear irregular when rounded off to the nearest integer 12 APPENDIX 1 Floor design program model Aim This report presents the model that is used in Floor s design program The model considers upward heat dissipation downward losses including the loss due to that the floor is heated by the system and system temperatures The temperature drop along a loop is estimated with an exponential function A star circuit model Underlying assumptions in the model are the following e The model uses a steady state approach e The temperatures of the internal and external environments are uniform co
13. he type of system used can be chosen from a scroll menu column C in the Excel file There is a variety of systems each having different pipe spacing pipe dimensions and panel thickness Usually the same type of panel is used in a project The names of the panels follow a certain pattern These are called Panels and are followed by four numbers The first two numbers indicate the external diameter of the pipe and the latter two numbers represent the height of the panel the measures are in millimetres The last four characters represent the pipe spacing also in millimetres So when the following panel is shown Panel 1625 s192 it means that a 16 mm pipe is used with a spacing of 192 mm and that the panel is 25 mm high In the same manner Panel 1213 s192 is the thin panel building 13 mm in height and has a 12 mm pipe with the spacing 192 mm A third column column D in the Excel file has a scroll menu for the choice of material layers that are put onto the floor heating panel In a project various zones in the building can have different materials Note that the surface materials have a large influence on the water temperatures A value of the thermal resistance of the sub floor must be entered in the fourth column E in the Excel file This parameter is called Ry and has the unit m K W If the U value of the floor construction is known the thermal resistance is the inverse of the U value If the U value is not known there i
14. heating requirement of zone The reason is that a heat loss calculation at design conditions that yields does not consider the design fact that the floor construction is actively heated By heating the construction an extra heat loss is generated This heat loss is quantified by the following equation such that leira TT Ag ie a Z w m 1 18 ral gh Iar fol in e R Opu B Ov or AO q extra U 0 a 0 1 19 R e R ER ln 6 Ow R Our En Ov Determining the thermal resistances of the star circuit The resistances in the star network model can be obtained by two means e To perform heat power and temperature measurements e And or to perform simulations of two dimensional heat flow in constructions with integrated heat sources As measurements require immense resources simulations are faster and easier to analyse However simulations may not be reliable since a number of assumptions 18 have to be performed The most effective method is to combine measurements and simulations The working steps used here are the following e Perform measurements on a limited amount of pre defined cases Measurements involve monitoring supplied power and temperatures under controlled environmental conditions e Analyse measurement data to validate simulation models e Perform simulations for a large number of cases based on the experience and validated models from the measurements This procedure is common Experie
15. ign pr Mie amp Micros a s lt 6 WAE 1645 Figure 4 The iEndche t RT for calculation of floor construction thermal resistance can be accessed by clicking on RT at the bottom left side of the Excel interface The R values are in this case calculated according to standard EN ISO 13370 2007 Thermal performance of buildings Heat transfer via the ground Calculations methods it is possible to calculate the thermal resistance for e Intermediate floors suspended floors between storeys e Slab on ground e Cellars e Crawl spaces The input required is the thickness of various material layers and occasionally the geometry of the foundation of the building please see Figure 5 When the R value is established see the dark blue field on the right hand side of the display that value can be entered in the previous worksheet Intermediate floor Thickness Choose material layer Resistance m m2xK W Material data Material data Material data Material data Material data Material data Material data Alaala lilaa Material data Slab on ground Thickness Material layers in construction Resistance Joint between wall and slab m excluding the ground m xK W Choose thermal bridge type ix Input length m _ 0 Material data za Input width m 0 J Material data Material data w 0 W mxK Material data
16. ipe Calculated heat flow surface surface surface from numeric model 1 C 0 C Adiabatic D W 0 C 0 C TEG and W Adiabat Pipe surface boundary LL Lower surface boundary gt s 2 Upper surface boundary Adiabat Figure 1 4 The boundary conditions of a typical model of a floor heated construction When the calculations have been performed the sets of equations as listed below will give the thermal resistances provided that p and have been calculated according to the boundary conditions expressed in Table 1 1 i s 2 e2 P D D 1 P D R eal s 2 e i2 P D P D D 0 m K W 1 20 m K W 1 21 m K W 1 22 21 References Akander J Lacour C Mao G and Johannesson G 1994 Ett elbaserat golvv rmesystem Matningar och berdkningsmodeller Dept of Building Technology KTH Stockholm Sweden In Swedish Blomberg T 1996 Heat condution in two and three dimensions Computer modelling of building physics applications Report TVBH 1008 Dept of Building Physics LTH Lund Sweden EN ISO 13370 2007 Thermal performance of buildings Heat transfer via the ground Calculations methods European Committee of Standardisation CEN Brussels Belgium
17. nce from a field trial and finite difference models for a constant power cable for the Floor co system are available from the Marma project Akander et al 1994 By using verified models simulations can be used for multiple types of floor constructions and flooring materials The results are used to adapt the parameters of the star model for effective use The important parameters to calculate are R and R The resistance under the floor heating system R can be estimated by using U value calculations as specified by EN ISO 13370 1998 heat loss to the ground or for intermediate floors with traditional one dimensional U value calculations Finite difference modelling When modelling in finite differences work is facilitated if a representative part portion of the actual system is considered see for example Blomberg 1996 Floor heating systems are repetitive in layout so it is more resourceful to select a small section instead of modelling the entire volume in which the floor heating system is installed The only exception for this is in areas that may contain thermal bridges such as joints between suspended floors and external walls where the degree of insulation locally in the wall is small or non existent In floor heating applications two dimensional heat transfer programs are sufficient for effective and accurate modelling The choice of which part of the system that is considered to be representative is dependent on the symmetr
18. nge in values due to the panels Panel type New Rr New dreq m K W W m Panel 1617 s192 3 242 59 1 Panel 1625 s192 3 609 58 0 Panel 1650 s192 4 410 56 3 The nominal heating requirement in the example is 60 W m Within this requirement the heat loss through the floor construction is included This loss can be estimated through the equation Ti Te floor Rr 1 In our case this corresponds to keep in mind totally 60 W m floor Ce 11 7 W m 2 Since the value of Rr in Equation 1 will increase the total heating requirement by means of Equation 2 will decrease as shown in Table 2 Usually for the thin panels 1213 and 1617 it is not practically justified to make the corrections since the thermal insulation of these panels are basically negligible Insertion of the new values in the calculation procedure is illustrated in Figure 10 Here the choice of the supply temperature is also inserted since this value is common for all solutions the supply temperature is important to fulfil heating requirement above the floor whereas ground heat losses are compensated by increased water flow in the loop The results become logical after correction of the heating requirement Lengths Temps Heating cooling Flows and pressure loss Loop System Surface nr Type Material Pan
19. nstant in time and in space e The heating requirement is uniform in the zone The following input is needed for the model to give results e The heating requirement of the zone transmission and ventilation loss calculated on basis of heated floor area e Design temperature drop along the loop e Design internal and external environment temperatures e The thermal resistance of the floor construction below the floor heating system The model is based on a thermal resistance star circuit as displayed in Figur 1 1 Temperatures are represented by the symbol thermal resistances by R and heat flows by Index i stands for internal environment index e for external environment this may be the annual mean ground temperature or a calculated crawlspace temperature or temperature of a heated zone and index s for source in this case the water temperature Star circuit temperature 0 is a representative temperature of the plane where the pipes are situated and has no direct relevance as a design parameter it is more a model parameter 13 Since the temperature of the water decreases whilst travelling in the pipe it is important to account for which source temperature is considered Therefore this temperature will be a function of the distance from pipe inlet here represented by x 0 e Figure 1 1 The star shaped thermal resistance network representing the flow paths of heat in the floor construction For a
20. rojects 7 C is often chosen at design conditions Again in case of heating the value is positive and is negative for cooling Finally pipe lengths are given in the last two columns L and M Ln in column Lis part of the pipe that does not emit energy A default value of 2 m is used representing where the pipe leaves the floor and is connected to the manifold This part does not participate in the heat balance of the building but generates a pressure loss In column M the length of the pipe that actively emits or absorbs heat is to be inserted With this done the necessary input for a loop is completed Let s look at an example of what comes next In Figure 6 the thin system with panel 1617 s192 is used in two loops One loop is covered with tiles and the other with 15 mm parquet The rest of the input data is the same for the two loops When the values have been entered there appears a number for each loop in column P This is the optimum supply temperature for the loop based on the input data In this case the wood floor will require 47 C while the tile floor only needs 38 C to fulfil the same requirement When connected to the same manifold we have to choose a common supply temperature for both loops Therefore you find on row 19 the text Choose supply temp and in red choose If a supply temperature is not chosen no results are displayed in the table
21. s in the program a spread sheet that helps to calculate the R value if the size of the building and the material types and thickness are given please see Figure 4 on how this is accessed Floore design master_v30 Microsoft Excel Start Infoga Sidlayout Formler Data Granska Visa x B a Arial ho i ch B i ca a A Klistra Fr x u an A in F 2j Centrera ove e 23 gt lt 0 200 ko Formatera Cel foga a Format Sorte Sok och m t gt z wy t markera Urklipp Tecken Justering Tal Format Celler Redigering S kerhetsvarning Makron har inaktiverats Alternativ D2 M f E 4B c BL E FIGE LU EL MIN KP IQIRET LUI VNXx IY Z AATABIACH A AF AG AH A y 1 a Project ID 3 4 5 6 7 8 Flows and pressure loss Le System Surface Rt Ti Ky dp furng Vol nr T Material Inst c Umin m n _mbar lit None Ly None B 4 2 none none 7 None x None x 1 10 f1 4 None one 11 None none x 12 1 6 None w None z 13 None v None 44 1 8 None Ly None 62 15 None Ly None x 16 1 10 None x None 7 17 18 Fluid type Water z 19 Pipe roughness PEX pipes 0 007 mm si phase change ps 5 Startsida Hogek O Inkorgen Micro Ey Des
22. ulations do not include losses from systems being floor heating convectors radiators etc the fact that the floor is deliberately heated will cause an extra heat loss The difference in heat loss between column U and T is the extra heat loss that is generated by the system e Column V shows the entire power that is emitted by the loop Lengths Temps Heating cooling Flows and pressure loss Loop System Surface RT Ti Te Req AT Ln La Ltot To Ts Tr nr Type Material KW C CIWm Cm mji mf Ce Panel 1617 s192 Tiles 8 12 mm az 72 38 47 1 2 Panel 1617 s192 Parquet 15 mm paper felt PE foll 3 20 0 60 7 2 70 72 47147 None x None Es 1 4 None UY None Es None LT None 1 6 None x None Es None L None Es 1 8 None CT None E3 ha None L None j Woj None LY None 2 ra s 5 ES Max opt temp 47 C Fluid type Water es Pipe roughness PEX pipes 0 007 mm ww is displayed in the table The table also displays the pressure drop in the loops column X and the flow column Y The amount of water that is needed in each loop is displayed in column AC If a Floor manifold is used the output data in columns Z AA and AB can be used to adjust flows in the loops Primarily column AB shows th
23. ur data The simplest way is to press on the Office button and in the pop up menu choose the Save As alternative and then the Macro activated Excel Worksheet please see Figure 2 In this way the Excel file is saved in a format that allows you to work with the files menus in the future Rename the file and proceed to work with your project Floore design master_v30 Microsoft Excel O ae Spara en kopia av dokumentet kj TEE Excer arbetsbok ES Ls a En Spara filen som en Excel arbetsbok Bree korsstyrd atera Cellformat Infoga Ta Format s Sok och 4 Oppna terir om tabell ort z 7 markera Tal Format Celler Redigering m k 2 LIN KP QIR T U L VNX Y Z AA AB ACK AE AF AG AH A amp Bin r Excet arbetsbok i N Spara som jal ww Spara arbetsboken i binarfilformat optimerat for snabb inl sning och sparning i x GoD suivut i meets TE Ten e S iH para en kopia av arbetsboken som r hel kompatibel med Excel 97 2003 Flows and pressure loss A Forerea gt GX OpenDocument kaikyibiad L Kep tumi Vol Gai Spara arbetsboken i ODF format Open Document f m vein mh mbar i Format ig Skicka 5 PDF eller XPS f 5 Publicera en kopia av arbetsboken som en PDF D pubicera Ki eller XPS fi Andra format 1 MK ppna dialogrutan Spara som om du vill v lja bland 1 Business
24. y of the isotherms in the construction Commonly this is found within the distance of a half spacing distance way from the pipes as shown in figure 1 3 19 Figure 1 3 Cross section of a floor construction with a surface mounted floor heating system where pipe spacing has the value s The dark frame depicts an area with isotherms that is symmetric with neighbouring pipes The dashed frame shows the symmetric area for the considered cable The area within the dashed frame is entered as a model in the finite difference program Required data are material geometry material layer thickness material thermal conductivity and suitable boundary conditions Two calculations have to be performed per construction and system type in which the boundary conditions are varied For the upper surface the interior surface thermal resistance has to be given a value In practical calculations a value of 0 09 0 10 m K W can be used More exact values are given by an equation in EN 1264 The boundary conditions are illustrated in Figure 4 with values specified in Table 1 1 for the two calculations Adiabatic surface means that there is no heat exchange with the surroundings no heat passes the surface 20 Table 1 1 Combinations of boundary conditions to calculate thermal resistances of the star network The heat flow densities are defined as positive in the flow direction as viewed in Figure 1 Case Upper Lower P
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