chimneys thermal and fluid dynamic calculation methods...en 13384-1 edition: 2019-09-01 chimneys —...

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ÖNORM Edition: 2019-09-01 Chimneys — Thermal and fluid dynamic calculation methods Part 1: Chimneys serving one heating appliance Abgasanlagen — Wärme- und strömungstechnische Berechnungs- verfahren — Teil 1: Abgasanlagen mit einer Feuerstätte Conduits de fumée — Méthodes de calcul thermo-aéraulique — Partie 1: Conduits de fumée ne desservant qu'un seul appareil Publisher and printing Austrian Standards International Standardization and Innovation Heinestraße 38, 1020 Wien Copyright © Austrian Standards International 2019 All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means – electronic, mechanical and photocopying or any other data carrier – without prior permission! E-Mail: [email protected] Internet: www.austrian-standards.at/terms-of-use Sale and distribution of national and foreign standards and technical regulations via Austrian Standards plus GmbH Heinestraße 38, 1020 Wien E-Mail: [email protected] Internet: www.austrian-standards.at Webshop: www.austrian-standards.at/webshop Tel.: +43 1 213 00-300 Fax: +43 1 213 00-355 ICS 91.060.40 Identical (IDT) with EN 13384-1:2015+A1:2019-07 Supersedes ÖNORM EN 13384-1:2015-05 responsible Committee 187 Chimneys AS+ Shop 12.09.2019 This is a preview of "ONORM EN 13384-1:201...". Click here to purchase the full version from the ANSI store.

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Page 1: Chimneys Thermal and fluid dynamic calculation methods...EN 13384-1 Edition: 2019-09-01 Chimneys — Thermal and fluid dynamic calculation methods Part 1: Chimneys serving one heating

ÖNORM

EN 13384-1

Edition: 2019-09-01

Chimneys — Thermal and fluid dynamic calculation methods

Part 1: Chimneys serving one heating appliance

Abgasanlagen — Wärme- und strömungstechnische Berechnungs-verfahren — Teil 1: Abgasanlagen mit einer Feuerstätte

Conduits de fumée — Méthodes de calcul thermo-aéraulique — Partie 1: Conduits de fumée ne desservant qu'un seul appareil

Publisher and printing Austrian Standards International Standardization and Innovation Heinestraße 38, 1020 Wien

Copyright © Austrian Standards International 2019 All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means – electronic, mechanical and photocopying or any other data carrier – without prior permission! E-Mail: [email protected] Internet: www.austrian-standards.at/terms-of-use

Sale and distribution of national and foreign standards and technical regulations via Austrian Standards plus GmbH Heinestraße 38, 1020 Wien E-Mail: [email protected] Internet: www.austrian-standards.at Webshop: www.austrian-standards.at/webshop Tel.: +43 1 213 00-300 Fax: +43 1 213 00-355

ICS 91.060.40 Identical (IDT) with EN 13384-1:2015+A1:2019-07 Supersedes ÖNORM EN 13384-1:2015-05 responsible Committee 187 Chimneys

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This is a preview of "ONORM EN 13384-1:201...". Click here to purchase the full version from the ANSI store.

Page 2: Chimneys Thermal and fluid dynamic calculation methods...EN 13384-1 Edition: 2019-09-01 Chimneys — Thermal and fluid dynamic calculation methods Part 1: Chimneys serving one heating

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This is a preview of "ONORM EN 13384-1:201...". Click here to purchase the full version from the ANSI store.

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Contents 0ÁÇÅ

European foreword ....................................................................................................................................................... 5

1 Scope .................................................................................................................................................................... 7

2 Normative references .................................................................................................................................... 7

3 Terms and definitions ................................................................................................................................... 7

4 Symbols and abbreviations ...................................................................................................................... 12

5 Calculation method for non-balanced flue chimneys ..................................................................... 17 5.1 General principles ........................................................................................................................................ 17 5.2 Pressure requirements .............................................................................................................................. 17 5.2.1 Negative pressure chimneys .................................................................................................................... 17 5.2.2 Positive pressure chimneys...................................................................................................................... 18 5.3 Temperature requirement ....................................................................................................................... 19 5.4 Calculation procedure ................................................................................................................................ 19 5.5 Flue gas data characterising the !combustion" appliance ................................................. 20 5.5.1 General ............................................................................................................................................................. 20 5.5.2 !Flue gas mass flow and combustion air mass flow .................................................................... 205.5.3 Flue gas temperature .................................................................................................................................. 21 5.5.4 Minimum draught for the !combustion" appliance (PW) for negative pressure

chimney ........................................................................................................................................................... 22 5.5.5 Maximum draught for the !combustion" appliance (PWmax) for negative

pressure chimney ......................................................................................................................................... 23 5.5.6 Maximum differential pressure of the !combustion" appliance (PWO) for

positive pressure chimney ........................................................................................................................ 23 5.5.7 Minimum differential pressure of the !combustion" appliance (PWOmin) for

positive pressure chimney ........................................................................................................................ 23 5.6 Characteristic data for the calculation ................................................................................................. 23 5.6.1 General ............................................................................................................................................................. 23 5.6.2 Mean value for roughness (r) .................................................................................................................. 23 5.6.3 Thermal resistance (1/Λ) .......................................................................................................................... 23 5.7 Basic values for the calculation ............................................................................................................... 24 5.7.1 Air temperatures .......................................................................................................................................... 24 5.7.2 External air pressure (pL) ......................................................................................................................... 26 5.7.3 Gas constant ................................................................................................................................................... 26 5.7.4 $ÅÎÓÉÔÙ ÏÆ ÔÈÅ ÅØÔÅÒÎÁÌ ÁÉÒ (ρL) .................................................................................................................... 26 5.7.5 Specific heat capacity of the flue gas (cp) ............................................................................................. 27 5.7.6 Condensing temperature (Tsp) ................................................................................................................ 27 5.7.7 Correction factor for temperature instability (SH) ........................................................................... 27 5.7.8 Flow safety coefficient (SE) ........................................................................................................................ 27 5.8 Determination of the temperatures ...................................................................................................... 27 5.8.1 General ............................................................................................................................................................. 27 5.8.2 Calculation of the coefficient of cooling (K) ........................................................................................ 28 5.8.3 Coefficient of heat transmission (kb) ..................................................................................................... 28 5.9 Determination of the density of the flue gas and the velocity of the flue gas ......................... 31 5.9.1 Density of the flue gas (ρm) ....................................................................................................................... 31 5.9.2 Velocity of the flue gas (wm) ..................................................................................................................... 31

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5.10 Determination of the pressures .............................................................................................................. 31 5.10.1 Pressure at the flue gas inlet into the chimney .................................................................................. 31 5.10.2 Theoretical draught available due to chimney effect (PH) ............................................................. 32 5.10.3 Pressure resistance of the chimney (PR) .............................................................................................. 33 5.10.4 Wind velocity pressure (PL) ...................................................................................................................... 34 5.11 Minimum draught required at the flue gas inlet into the chimney and maximum

allowed draught (PZe and PZemax) and maximum and minimum differential pressure at the flue gas inlet into the chimney (PZOe and PZOemin) .................................................................. 35

5.11.1 General ............................................................................................................................................................. 35 5.11.2 Minimum and maximum draught for the !combustion" appliance (PW and

PWmax) and maximum and minimum differential pressure of the !combustion"

appliance (PWO and PWOmin) ........................................................................................................................ 36 5.11.3 Effective pressure resistance of the connecting flue pipe (PFV) ................................................... 36 5.11.4 Pressure resistance of the air supply (PB) ........................................................................................... 37 5.12 Calculation of the inner wall temperature at the chimney outlet (Tiob) .................................... 38

6 Secondary air for negative pressure chimneys ................................................................................. 40 6.1 General ............................................................................................................................................................. 40 6.2 Calculation method ...................................................................................................................................... 40 6.3 Basic values for the calculation of secondary air .............................................................................. 40 6.3.1 General ............................................................................................................................................................. 40 6.3.2 Mixing calculations ...................................................................................................................................... 40 6.4 Pressures ......................................................................................................................................................... 41 6.4.1 Pressure resistance for the air supply with secondary air (PBNL) ............................................... 41 6.4.2 Draught required for the secondary air devices (PNL) ..................................................................... 43 6.4.3 Pressure resistance for that part of the connecting flue pipe before the secondary air

device (PFV1) .................................................................................................................................................... 44 6.4.4 Pressure requirement with secondary air .......................................................................................... 44 6.5 Temperature requirement with secondary air ................................................................................. 44

7 Calculation method for balanced flue chimneys ............................................................................... 45 7.1 General principles ........................................................................................................................................ 45 7.2 Pressure requirements ............................................................................................................................... 46 7.3 Temperature requirements ...................................................................................................................... 46 7.4 Calculation procedure ................................................................................................................................. 46 7.5 Flue gas data characterizing the !combustion" appliance .................................................. 47 7.6 Characteristic data for the calculation .................................................................................................. 47 7.7 Basic values for the calculation ............................................................................................................... 47 7.7.1 Air temperatures .......................................................................................................................................... 47 7.7.2 Other basic values ........................................................................................................................................ 48 7.8 Determination of the temperatures ....................................................................................................... 48 7.8.1 Non-concentric (separate) ducts............................................................................................................. 48 7.8.2 Concentric ducts – calculation based on a correction factor for heat radiation .................... 49 7.8.3 Concentric ducts – calculation based on calculated heat radiation ........................................... 64 7.8.4 Mean temperatures for pressure calculation ..................................................................................... 68 7.9 Determination of densities and velocities ........................................................................................... 69 7.9.1 Density and velocity of the flue gas ........................................................................................................ 69 7.9.2 Density and velocity of the !combustion" air ........................................................................... 69 7.10 Determination of pressures ...................................................................................................................... 70 7.10.1 Pressure at the flue gas inlet into the chimney .................................................................................. 70 7.10.2 Theoretical draught due to chimney effect in the chimney segment (PH) ............................... 70 7.10.3 Pressure resistance in the chimney segment (PR) ............................................................................ 70 7.10.4 Wind velocity pressure (PL) ...................................................................................................................... 70

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7.11 Minimum draught required at the flue gas inlet into the chimney and maximum allowed draught (PZe and PZemax) and maximum and minimum differential pressure at the flue gas inlet into the chimney (PZOe and PZOemin) .................................................................. 71

7.11.1 General ............................................................................................................................................................. 71 7.11.2 Minimum and maximum draught for the !combustion" appliance (PW and

PWmax) and maximum and minimum differential pressure of the !combustion"

appliance (PWO and PWOmin) ........................................................................................................................ 71 7.11.3 Effective pressure resistance of the connection pipe (PFV) ........................................................... 71 7.11.4 Pressure resistance of the air supply .................................................................................................... 71 7.12 Calculation of the inner wall temperature at the chimney outlet (Tiob) ................................... 74

8 Consideration of the condensation heat of the flue gas water vapour ..................................... 75 8.1 General ............................................................................................................................................................. 75 8.2 Onset of condensation ................................................................................................................................ 75 8.3 Calculation of the flue gas temperature at the outlet of a chimney segment with

condensation (j ≥ NsegK) ........................................................................................................................... 78

9 Consideration of chimney fans ................................................................................................................ 83 9.1 General ............................................................................................................................................................. 83 9.2 Inline fans ....................................................................................................................................................... 84 9.3 Exhaust fans ................................................................................................................................................... 85

Annex A ɉÉÎÆÏÒÍÁÔÉÖÅɊ Calculation of thermal resistance ............................................................................ 86

Annex B ɉÉÎÆÏÒÍÁÔÉÖÅɊ Tables ................................................................................................................................. 87

Annex C ɉÉÎÆÏÒÍÁÔÉÖÅɊ Chimney outlet with regard to adjacent buildings ........................................... 104

Annex D ɉÉÎÆÏÒÍÁÔÉÖÅɊ Determination of the gas constant R considering the condensation ........ 105

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European foreword

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4ÈÉÓ ÄÏÃÕÍÅÎÔ ÈÁÓ ÂÅÅÎ ÐÒÅÐÁÒÅÄ ÕÎÄÅÒ Á ÍÁÎÄÁÔÅ ÇÉÖÅÎ ÔÏ #%. ÂÙ ÔÈÅ %ÕÒÏÐÅÁÎ #ÏÍÍÉÓÓÉÏÎ ÁÎÄ ÔÈÅ %ÕÒÏÐÅÁÎ &ÒÅÅ 4ÒÁÄÅ !ÓÓÏÃÉÁÔÉÏÎȢ

4ÈÅ ÓÔÁÒÔ ÁÎÄ ÆÉÎÉÓÈ ÏÆ ÔÅØÔ ÉÎÔÒÏÄÕÃÅÄ ÏÒ ÁÌÔÅÒÅÄ ÂÙ ÁÍÅÎÄÍÅÎÔ ÉÓ ÉÎÄÉÃÁÔÅÄ ÉÎ ÔÈÅ ÔÅØÔ ÂÙ ÔÁÇÓ !"Ȣ

4ÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄ Ȱ#ÈÉÍÎÅÙÓ ɂ 4ÈÅÒÍÁÌ ÁÎÄ ÆÌÕÉÄ ÄÙÎÁÍÉÃ ÃÁÌÃÕÌÁÔÉÏÎ ÍÅÔÈÏÄÓȱ ÃÏÎÓÉÓÔÓ ÏÆ ÔÈÒÅÅ 0ÁÒÔÓȡ

ɂ 0ÁÒÔ ρȡ #ÈÉÍÎÅÙÓ ÓÅÒÖÉÎÇ ÏÎÅ ÃÏÍÂÕÓÔÉÏÎ ÁÐÐÌÉÁÎÃÅ

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ɂ 0ÁÒÔ ςȡ #ÈÉÍÎÅÙÓ ÓÅÒÖÉÎÇ ÍÏÒÅ ÔÈÁÎ ÏÎÅ ÃÏÍÂÕÓÔÉÏÎ ÁÐÐÌÉÁÎÃÅ

ɂ 0ÁÒÔ σȡ -ÅÔÈÏÄÓ ÆÏÒ ÔÈÅ ÄÅÖÅÌÏÐÍÅÎÔ ÏÆ ÄÉÁÇÒÁÍÓ ÁÎÄ ÔÁÂÌÅÓ ÆÏÒ ÃÈÉÍÎÅÙÓ ÓÅÒÖÉÎÇ ÏÎÅ ÈÅÁÔÉÎÇ ÁÐÐÌÉÁÎÃÅ

!ÃÃÏÒÄÉÎÇ ÔÏ ÔÈÅ #%.Ȥ#%.%,%# )ÎÔÅÒÎÁÌ 2ÅÇÕÌÁÔÉÏÎÓȟ ÔÈÅ ÎÁÔÉÏÎÁÌ ÓÔÁÎÄÁÒÄÓ ÏÒÇÁÎÉÓÁÔÉÏÎÓ ÏÆ ÔÈÅ ÆÏÌÌÏ×ÉÎÇ ÃÏÕÎÔÒÉÅÓ ÁÒÅ ÂÏÕÎÄ ÔÏ ÉÍÐÌÅÍÅÎÔ ÔÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄȡ !ÕÓÔÒÉÁȟ "ÅÌÇÉÕÍȟ "ÕÌÇÁÒÉÁȟ #ÒÏÁÔÉÁȟ #ÙÐÒÕÓȟ #ÚÅÃÈ 2ÅÐÕÂÌÉÃȟ $ÅÎÍÁÒËȟ %ÓÔÏÎÉÁȟ &ÉÎÌÁÎÄȟ &ÏÒÍÅÒ 9ÕÇÏÓÌÁÖ 2ÅÐÕÂÌÉà ÏÆ -ÁÃÅÄÏÎÉÁȟ &ÒÁÎÃÅȟ 'ÅÒÍÁÎÙȟ 'ÒÅÅÃÅȟ (ÕÎÇÁÒÙȟ )ÃÅÌÁÎÄȟ )ÒÅÌÁÎÄȟ )ÔÁÌÙȟ ,ÁÔÖÉÁȟ ,ÉÔÈÕÁÎÉÁȟ ,ÕØÅÍÂÏÕÒÇȟ -ÁÌÔÁȟ .ÅÔÈÅÒÌÁÎÄÓȟ .ÏÒ×ÁÙȟ 0ÏÌÁÎÄȟ 0ÏÒÔÕÇÁÌȟ 2ÏÍÁÎÉÁȟ 3ÅÒÂÉÁȟ 3ÌÏÖÁËÉÁȟ 3ÌÏÖÅÎÉÁȟ 3ÐÁÉÎȟ 3×ÅÄÅÎȟ 3×ÉÔÚÅÒÌÁÎÄȟ 4ÕÒËÅÙ ÁÎÄ ÔÈÅ 5ÎÉÔÅÄ +ÉÎÇÄÏÍȢ

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1 Scope

4ÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄ ÓÐÅÃÉÆÉÅÓ ÍÅÔÈÏÄÓ ÆÏÒ ÔÈÅ ÃÁÌÃÕÌÁÔÉÏÎ ÏÆ ÔÈÅ ÔÈÅÒÍÁÌ ÁÎÄ ÆÌÕÉÄ ÄÙÎÁÍÉÃ ÃÈÁÒÁÃÔÅÒÉÓÔÉÃÓ ÏÆ ÃÈÉÍÎÅÙÓ ÓÅÒÖÉÎÇ ÏÎÅ !ÃÏÍÂÕÓÔÉÏÎ" ÁÐÐÌÉÁÎÃÅȢ

4ÈÅ ÍÅÔÈÏÄÓ ÉÎ ÔÈÉÓ ÐÁÒÔ ÏÆ ÔÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄ ÁÒÅ ÁÐÐÌÉÃÁÂÌÅ ÔÏ ÎÅÇÁÔÉÖÅ ÏÒ ÐÏÓÉÔÉÖÅ ÐÒÅÓÓÕÒÅ ÃÈÉÍÎÅÙÓ ×ÉÔÈ ×ÅÔ ÏÒ ÄÒÙ ÏÐÅÒÁÔÉÎÇ ÃÏÎÄÉÔÉÏÎÓȢ )Ô ÉÓ ÖÁÌÉÄ ÆÏÒ ÃÈÉÍÎÅÙÓ ×ÉÔÈ !ÃÏÍÂÕÓÔÉÏÎ" ÁÐÐÌÉÁÎÃÅÓ ÆÏÒ ÆÕÅÌÓ ÓÕÂÊÅÃÔ ÔÏ ÔÈÅ ËÎÏ×ÌÅÄÇÅ ÏÆ ÔÈÅ ÆÌÕÅ ÇÁÓ ÃÈÁÒÁÃÔÅÒÉÓÔÉÃÓ ×ÈÉÃÈ ÁÒÅ ÎÅÅÄÅÄ ÆÏÒ ÔÈÅ ÃÁÌÃÕÌÁÔÉÏÎȢ

4ÈÅ ÍÅÔÈÏÄÓ ÉÎ ÔÈÉÓ ÐÁÒÔ ÏÆ ÔÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄ ÁÒÅ ÁÐÐÌÉÃÁÂÌÅ ÔÏ ÃÈÉÍÎÅÙÓ ×ÉÔÈ ÏÎÅ ÉÎÌÅÔ ÃÏÎÎÅÃÔÅÄ ×ÉÔÈ ÏÎÅ ÁÐÐÌÉÁÎÃÅȢ 4ÈÅ ÍÅÔÈÏÄÓ ÉÎ 0ÁÒÔ ς ÏÆ ÔÈÉÓ %ÕÒÏÐÅÁÎ 3ÔÁÎÄÁÒÄ ÁÒÅ ÁÐÐÌÉÃÁÂÌÅ ÔÏ ÃÈÉÍÎÅÙÓ ×ÉÔÈ ÍÕÌÔÉÐÌÅ ÉÎÌÅÔÓ ÁÎÄ ÏÎÅ ÉÎÌÅÔ ×ÉÔÈ ÍÕÌÔÉÐÌÅ ÁÐÐÌÉÁÎÃÅÓȢ 0ÁÒÔ σ ÄÅÓÃÒÉÂÅÓ ÍÅÔÈÏÄÓ ÆÏÒ ÔÈÅ ÄÅÖÅÌÏÐÍÅÎÔ ÏÆ ÄÉÁÇÒÁÍÓ ÁÎÄ ÔÁÂÌÅÓ ÆÏÒ ÃÈÉÍÎÅÙÓ ÓÅÒÖÉÎÇ ÏÎÅ !ÃÏÍÂÕÓÔÉÏÎ" ÁÐÐÌÉÁÎÃÅȢ

2 Normative references

!4ÈÅ ÆÏÌÌÏ×ÉÎÇ ÄÏÃÕÍÅÎÔÓ ÁÒÅ ÒÅÆÅÒÒÅÄ ÔÏ ÉÎ ÔÈÅ ÔÅØÔ ÉÎ ÓÕÃÈ Á ×ÁÙ ÔÈÁÔ ÓÏÍÅ ÏÒ ÁÌÌ ÏÆ ÔÈÅÉÒ ÃÏÎÔÅÎÔÃÏÎÓÔÉÔÕÔÅÓ ÒÅÑÕÉÒÅÍÅÎÔÓ ÏÆ ÔÈÉÓ ÄÏÃÕÍÅÎÔȢ &ÏÒ ÄÁÔÅÄ ÒÅÆÅÒÅÎÃÅÓȟ ÏÎÌÙ ÔÈÅ ÅÄÉÔÉÏÎ ÃÉÔÅÄ ÁÐÐÌÉÅÓȢ &ÏÒÕÎÄÁÔÅÄ ÒÅÆÅÒÅÎÃÅÓȟ ÔÈÅ ÌÁÔÅÓÔ ÅÄÉÔÉÏÎ ÏÆ ÔÈÅ ÒÅÆÅÒÅÎÃÅÄ ÄÏÃÕÍÅÎÔ ɉÉÎÃÌÕÄÉÎÇ ÁÎÙ ÁÍÅÎÄÍÅÎÔÓɊÁÐÐÌÉÅÓȢ"

%. ρττσȟ Chimneys — General requirements

%. ρψυφȤρȟ Chimneys — Requirements for metal chimneys — Part 1: System chimney products

%. ρψυωȟ Chimneys — Metal chimneys — Test methods

%. ρσυπςȟ Chimneys — Requirements and test methods for clay/ceramic flue terminals

%. ρυςψχȤρȡςππχϹ!ρȡςπρπȟ Chimneys — Design, installation and commissioning of chimneys —Part 1: Chimneys for non-roomsealed heating appliances

ÐÒ%. ρφτχυȤςȟ Chimneys - Accessories — Part 2: Chimney fans - Requirements and test methods

#%.Ⱦ42 ρχτωȟ European scheme for the classification of gas appliances according to the method of evacuation of the combustion products (types)

3 Terms and definitions

&ÏÒ ÔÈÅ ÐÕÒÐÏÓÅÓ ÏÆ ÔÈÉÓ ÄÏÃÕÍÅÎÔȟ ÔÈÅ ÔÅÒÍÓ ÁÎÄ ÄÅÆÉÎÉÔÉÏÎÓ ÇÉÖÅÎ ÉÎ %. ρττσ ÁÎÄ ÔÈÅ ÆÏÌÌÏ×ÉÎÇ ÁÐÐÌÙȢ

!)3/ ÁÎÄ )%# ÍÁÉÎÔÁÉÎ ÔÅÒÍÉÎÏÌÏÇÉÃÁÌ ÄÁÔÁÂÁÓÅÓ ÆÏÒ ÕÓÅ ÉÎ ÓÔÁÎÄÁÒÄÉÚÁÔÉÏÎ ÁÔ ÔÈÅ ÆÏÌÌÏ×ÉÎÇ ÁÄÄÒÅÓÓÅÓȡ

Ɇ )%# %ÌÅÃÔÒÏÐÅÄÉÁȡ ÁÖÁÉÌÁÂÌÅ ÁÔ ÈÔÔÐȡȾȾ×××ȢÅÌÅÃÔÒÏÐÅÄÉÁȢÏÒÇȾ

Ɇ )3/ /ÎÌÉÎÅ ÂÒÏ×ÓÉÎÇ ÐÌÁÔÆÏÒÍȡ ÁÖÁÉÌÁÂÌÅ ÁÔ ÈÔÔÐȡȾȾ×××ȢÉÓÏȢÏÒÇȾÏÂÐ"

3.1 heat output Q

ÁÍÏÕÎÔ ÏÆ ÈÅÁÔ ÐÒÏÄÕÃÅÄ ÂÙ Á !ÃÏÍÂÕÓÔÉÏÎ" ÁÐÐÌÉÁÎÃÅ ÐÅÒ ÕÎÉÔ ÏÆ ÔÉÍÅ

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