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PRINCIPLES OF HEATING, VENTILATION AND AIR CONDITIONING with Worked Examples 9562hc_9789814667760_tp.indd Tai ngay!!! Ban co the xoa dong chu nay!!! 9/10/15 3:42 PM May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory This page intentionally left blank PST˙ws PRINCIPLES OF HEATING, VENTILATION AND AIR CONDITIONING with Worked Examples Nihal E Wijeysundera World Scientific NEW JERSEY • LONDON 9562hc_9789814667760_tp.indd • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI • TOKYO 9/10/15 3:42 PM Published by :RUOG6FLHQWL¿F3XEOLVKLQJ&R3WH/WG 7RK7XFN/LQN6LQJDSRUH 86$RI¿FH :DUUHQ6WUHHW6XLWH+DFNHQVDFN1- 8.RI¿FH 6KHOWRQ6WUHHW&RYHQW*DUGHQ/RQGRQ:&+ +( British Library Cataloguing-in-Publication Data $FDWDORJXHUHFRUGIRUWKLVERRNLVDYDLODEOHIURPWKH%ULWLVK/LEUDU\ PRINCIPLES OF HEATING, VENTILATION AND AIR CONDITIONING WITH WORKED EXAMPLES &RS\ULJKWE\:RUOG6FLHQWL¿F3XEOLVKLQJ&R3WH/WG $OOULJKWVUHVHUYHG7KLVERRNRUSDUWVWKHUHRIPD\QRWEHUHSURGXFHGLQDQ\IRUPRUE\DQ\PHDQV HOHFWURQLFRUPHFKDQLFDOLQFOXGLQJSKRWRFRS\LQJUHFRUGLQJRUDQ\LQIRUPDWLRQVWRUDJHDQGUHWULHYDO system now known or to be invented, without written permission from the publisher )RUSKRWRFRS\LQJRIPDWHULDOLQWKLVYROXPHSOHDVHSD\DFRS\LQJIHHWKURXJKWKH&RS\ULJKW&OHDUDQFH &HQWHU,QF5RVHZRRG'ULYH'DQYHUV0$ 86$,QWKLVFDVHSHUPLVVLRQWRSKRWRFRS\ LVQRWUHTXLUHGIURPWKHSXEOLVKHU ,6%1 3ULQWHGLQ6LQJDSRUH Steven - Principles of Heating.indd 24/7/2015 9:15:35 AM Principles of Heating 9562–00a To my grandchildren Emiko Chrisanthi, Sunil Hitoshi, Isabella Anjali, Amali Satomi, and Helina Maya v May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory This page intentionally left blank PST˙ws Principles of Heating 9562–00b Preface Courses in Heating, Ventilation and Air Conditioning (HVAC) are usually offered in departments of mechanical engineering, civil engineering, architecture and building science This book is written mainly with the interests of students and instructors in these departments in mind However, a significant part of the contents may be used in courses such as, thermal systems and heat transfer, especially the worked examples Practicing engineers could use this book to clarify the fundamental principles behind various design procedures recommended in professional handbooks A number of professional societies like the American Society of Heating, Refrigeration and Air Conditioning Engineers (ASHRAE) publish comprehensive handbooks and design guides for use by HVAC engineers These handbooks are updated regularly to include the most recent design procedures, developed through sponsored research projects One of the main challenges for instructors in HVAC courses is to distill the materials available in professional handbooks, to a concise form to be included in regular undergraduate courses This is often a time consuming task because the handbooks are intended for practicing engineers This book tries to make the task easier for instructors by presenting the material in a directly useable format For students the contents should appear as extensions and applications of the material covered in basic courses on thermodynamics, heat transfer and fluid mechanics Every effort is made to include simple derivations for most of the design parameters used in practice, without making the mathematical details unduly complicated For instance, in chapter a simple onedimensional thermal network approach is used to derive the fenestration design parameter called the ‘solar heat gain coefficient (SHGC)’ Likewise, in chapter 10 a lumped-capacity transient thermal model is vii Principles of Heating 9562–00b viii Preface used to clarify the physical meaning of ‘the radiant time series (RTS)’, and its application in cooling load estimation In chapter a ‘vector approach’ is introduced to analyze complex three-dimensional geometrical design problems These situations are encountered in computing incident angles of solar beams on inclined surfaces, and in determining the effectiveness of shading devices like overhangs Included in this book are the most up-to-date empirical models available in the ASHRAE Handbook - 2013 Fundamentals, that are relevant for design In particular, in chapter 9, for computing the solar radiation absorption and transmission in building envelopes, the latest two-parameter model is used to estimate the ‘clear-sky radiation’ at different locations In design oriented courses such as HVAC, it is important for students to understand the fundamentals behind the recommended design procedures Comprehensive worked examples provide an ideal means to present design concepts in a practically useful manner With this objective in mind, about 15 worked examples are included in each chapter, carefully chosen to expose students to diverse design situations encountered in HVAC practice Computations required in worked examples illustrating basic principles are performed using a calculator Worked examples involving more realistic design situations are done using MATLAB programs, included in the book At the end of each chapter there are additional problems for which numerical answers are provided The format of the worked examples and problems is a novel feature of this book For instructors, this should provide a useful source for problems to be included in courses, tutorials and examinations MATLAB programming is now taught routinely in most engineering and science courses Therefore a number of MATLAB codes, for solving HVAC design problems requiring extensive computations, are also included Computer codes are included for the following applications: (i) computation of psychrometric properties, (ii) design of cooling towers, (iii) design of wet-coil heat exchangers, (iv) computation of hourly diffuse and direct solar radiation intensities, (v) computation of sol-air Principles of Heating 9562–00b Preface ix temperature, (vi) estimation of hourly cooling load due to people, lights, roofs, and walls, (vii) design of overhangs, and (viii) design of duct and pipe systems I wish to thank ASHRAE for granting permission to extract representative design data from the ASHRAE Handbook - 2013 Fundamentals, for inclusion in this book I was fortunate to have had the opportunity to teach a number of courses in refrigeration, air conditioning, and thermal systems at the Department of Mechanical Engineering, National University of Singapore (NUS) The notes developed for these courses provided the framework and much of the material for this book I am thankful to my colleagues in the energy and bio-thermal division at NUS, with whom I shared the teaching of these courses, for many valuable discussions on HVAC systems I am thankful to Dr Raisul Islam for fruitful discussions on a number of practical design aspects of chiller systems and their energy efficiency I wish to thank Dr A H Jahangeer for providing valuable technical support on many occasions and Mr Mahipala D Fernando for fruitful discussions on heat pump systems Thanks are due to my sons Duminda and Harindra, and my daughtersin-law Sindhu and Sophia, for their constant encouragement Finally, my heartfelt thanks are given to my wife Kamani for her encouragement and generous support towards the completion of this project Nihal E Wijeysundera May 2, 2013 14:6 BC: 8831 - Probability and Statistical Theory This page intentionally left blank PST˙ws Principles of Heating 9562–13 682 Principles of Heating, Ventilation and Air Conditioning with Worked Examples heat rejection rate in the cooling tower for the different load conditions Neglect any effects due to storage Table E13.15.1 Water-loop heat pump data H/C -Loads (kW) A B C D Zone í14 í14 í12 í10 Zone í9 í9 10 10 Zone í12 í10 12 14 Zone í20 18 15 20 Solution Fig E13.15.1 Water-loop heat pump system As seen in Fig E13.15.1, the heat pumps operating in the heating mode extract heat from the water loop while those in the cooling mode reject heat to the water loop If the net heat supplied to the water loop is positive, the water loop temperature will increase steadily and eventually exceed the limiting value of 35°C When this happens water in the loop is sent through the cooling tower to maintain the loop temperature at 35°C as shown in Fig 13.11 The reverse occurs if there is a net heat out flow from the loop, in which case, the loop temperature will steadily decrease and eventually drop below the limiting value of 15°C The water is then sent through a water heater to maintain the temperature at 15°C For each of the load conditions listed in Table E13.15.1, we shall first determine whether the net heat flow to the loop is positive or negative For condition A, all four heat pumps are in the heating mode and are therefore extracting heat from the water loop The heat extraction rate by a heat pump is given by Principles of Heating 9562–13 Building Energy Estimating and Modeling Methods ܳ௨௧ ൌ ܳ ቀͳ െ ଵ 683 ቁ The equilibrium temperature of the water loop is 15°C The heating mode COP is 4.5 The total heating load ܳ ൌ ͳͶ ͻ ͳʹ ʹͲ ൌ ͷͷ kW The rate of heat removal from the water loop is ܳ௨௧ ൌ ͷͷ ቀͳ െ ଵ ቁ ൌ ͶʹǤͺ kW ସǤହ Therefore the furnace has to supply heat at the rate 42.8 kW to maintain the water temperature at 15°C The electrical energy supply rate to the heat pumps is ܹ ൌ ହହ ସǤହ ൌ ͳʹǤʹ kW For condition B, zones 1, and are heated and zone is cooled by the respective heat pumps The heat extraction rate by heat pumps 1, and from the water loop is given by ܳ௨௧ ൌ ͵͵ ቀͳ െ ଵ (E13.15.1) ቁ The rate of heat rejection to the water loop by heat pump is given by: ܳ ൌ ܳ ቀͳ ଵ ቁ ൌ ͳͺ ቀͳ ଵ (E13.15.2) ቁ The net heat extraction rate from the water loop is ܳǡ௧ ൌ ͵͵ ቀͳ െ ଵ ቁ െ ͳͺ ቀͳ ଵ ቁ (E13.15.3) We shall use Eq (E13.15.3) to determine the equilibrium temperature of the water loop by substituting the COP values at the two limiting temperatures of 15°C and 35°C For 15°C, and 35°C the net rates of heat out flow are 5.55 kW, 6.2 kW respectively Hence it is clear that due to continuous heat extraction, the water loop temperature will decrease steadily and eventually reach 15°C The furnace has to supply heat at the rate 5.55 kW to maintain the water temperature at 15°C The total electrical energy supply rate to the heat pumps is given by Principles of Heating 9562–13 684 Principles of Heating, Ventilation and Air Conditioning with Worked Examples ܹ ൌ ଷଷ ସǤହ ଵ଼ ൌ ͻǤͶͷ kW ଼Ǥହ For condition C, zones and are heated and zones and are cooled by the respective heat pumps The total heat extraction rate by heat pumps and from the water loop is given by ܳ௨௧ ൌ ʹʹ ቀͳ െ ଵ (E13.15.3a) ቁ The total rate of heat rejection to the water loop by heat pumps and is given by ܳ ൌ ʹ ቀͳ ଵ (E13.15.4) ቁ Hence the net heat extraction rate from the water loop is ܳǡ௧ ൌ ʹʹ ቀͳ െ ଵ ቁ െ ʹ ቀͳ ଵ ቁ (E13.15.5) We shall use Eq (E13.15.5) to determine the equilibrium temperature of the water loop by substituting the COP values at the two limiting temperatures of 15°C and 35°C For 15°C, and 35°C the net rates of heat inflow are 13 kW, 15.1 kW respectively Therefore it is clear that due to continuous heat inflow, the water loop temperature will increase steadily and eventually reach 35°C The cooling tower has to remove heat at the rate 15.1 kW to maintain the water temperature at 35°C The total electrical energy supply rate to the heat pumps is given by ܹ ൌ ଶଶ ଽ ଶ ଷǤହ ൌ ͳͲǤʹ kW For condition D, zone is heated and zones 2, and are cooled by the respective heat pumps The total heat extraction rate by heat pump from the water loop is given by ܳ௨௧ ൌ ͳͲ ቀͳ െ ଵ ቁ (E13.15.6) The total rate of heat rejection to the water loop by heat pumps 2, and is given by ܳ ൌ ͶͶ ቀͳ ଵ ቁ (E13.15.7) Principles of Heating 9562–13 Building Energy Estimating and Modeling Methods 685 The net heat extraction rate from the water loop is ܳǡ௧ ൌ ͳͲ ቀͳ െ ଵ ቁ െ ͶͶ ቀͳ ଵ (E13.15.8) ቁ We shall use Eq (E13.15.8) to determine the equilibrium temperature of the water loop by substituting the COP values at the two limiting temperatures of 15°C and 35°C For 15°C, and 35°C the net rates of heat inflow are 41 kW, and 47.7 kW respectively Hence it is clear that due to continuous heat inflow, the water loop temperature will increase steadily and eventually reach 35°C The cooling tower has to remove heat at the rate 47.7 kW to maintain the water temperature at 35°C The total electrical energy supply rate to the heat pumps is given by ܹ ൌ ଵ ଽ ଶ ଷǤହ ൌ ͺǤͺ kW An extension of the above analysis is included in problem 13.12 below Problems P13.1 A building with an effective heat conductance – UA of 0.68 kW °Cí1 is occupied for 14 hours from 7h to 20h and unoccupied during the rest of the day The rates of internal heat gain during the occupied and unoccupied periods are 2.85 kW and 0.9 kW respectively The corresponding indoor temperatures are 22°C and 16°C respectively The building is heated using a fuel-fired furnace of capacity 14 kW and rated efficiency 88% The part-load degradation factor of the furnace is 0.25 The hourly ambient temperatures for a particular day are given in Table P13.1.1 Calculate (i) the balance temperatures, and (ii) the energy input to the furnace, during the occupied and unoccupied periods Plot the energy flow rates versus temperature curves [Answers: (i) 17.8°C, 14.68°C, (ii) 96.6 kWh, 100.2 kWh] Table P13.1.1 Hourly ambient temperatures Hour TA °C Hour TA °C 13 14 2 14 15 15 15 16 13 17 12 18 11.5 19 10 20 21 10 7.7 22 11 9.5 23 12 12 24 Principles of Heating 9562–13 686 Principles of Heating, Ventilation and Air Conditioning with Worked Examples P13.2 The building described in problem 13.1 is to be heated using a heat pump whose capacity Qcap (kW), and COP vary with ambient temperature ta (°C) according to the equations: ܳ ൌ ͲǤͶݐ ͲǤͲͲͳͷݐ ଶ ܱܲܥൌ ʹǤͳ ͲǤͲͺݐ ͲǤͲͲ͵ͷݐ ଶ The conditions for the occupied and unoccupied periods are the same as in problem 13.1 The degradation factor due to cycling of the heat pump is 0.25 Calculate (i) the heat pump balance temperatures, (ii) the electrical energy input to the heat pump, and (iii) the auxiliary energy input required, for the occupied and unoccupied periods Plot the energy flow rates versus temperature curves [Answers: (i) 4.53°C, 2.72°C, (ii) 56.7 kWh, 34.8 kWh, (iii) 0.7 kWh, 4.28 kWh] P13.3 The rated capacity and COP of an air conditioner are 75 tons and 3.5 respectively It is used to cool a building whose hourly cooling loads are given in Table P13.3.1 The degradation coefficient for part-load operation of the air conditioner is 0.25 Estimate (i) the hourly energy input rate to the air conditioner, (ii) the total energy input, and (iii) the average COP [Answers: (ii) 1014 kWh, 3.15] Table P13.3.1 Hourly cooling loads Hour Ql, kW Hour Ql, kW Hour Ql, kW Hour Ql, kW 65 73 13 225 19 188 62 92 14 230 20 170 58 101 15 220 21 142 55 10 133 16 211 22 119 60 11 160 17 206 23 96 60 12 188 18 197 24 82 P13.4 The monthly average ambient temperatures for Vancouver are given in Table P13.4.1[1] (i) Using the MATLAB code in Appendix A13.1 or otherwise, calculate the bin data for Vancouver (ii) Calculate the degree–days for base temperatures of 18.3°C and 12°C Principles of Heating 9562–13 Building Energy Estimating and Modeling Methods 687 [Answer: use the MATLAB code in Appendix A13.1 and compare degree–day data with data in Ref [1]] P13.4.1 Monthly average temperatures for Vancouver from Ref [1] Month Tam °C Month Tam °C January 4.2 July 17.9 February 4.9 August 18 March 6.8 Sept 15 April 9.5 October 10.4 May 12.8 Nov 6.6 June 15.6 Dec 3.9 P13.5 A fuel-fired furnace of rated capacity of 30 kW and efficiency 90% is used to heat a house in Vancouver (see problem 13.4) The balance temperature for the house is 18.3°C (i) Calculate the yearly energy input to the furnace using the bin method, (a) neglecting the performance degradation due to cycling, and (b) assuming a degradation coefficient of 0.25 (ii) Use the degree–day method to estimate the yearly energy input to the furnace (iii) Obtain the answers to (a) and (b) if the balance temperature decreases to 12°C due to design changes [Answers: (i) (a) 176 GJ, (b) 216GJ, (ii) 176GJ, (iii) (a) 76GJ, (b) 95GJ] P13.6 The full-load capacity and COP of an air conditioner are 25 tons and 3.5 respectively The part-load degradation factor is 0.3 The air conditioner is installed in a building whose cooling load varies from kW to 85 kW (i) Plot a graph of the power input to the air conditioner versus the cooling load (ii) If two such air conditioners are to be operated in an optimal manner in a building whose cooling load varies from 10 kW to 170 kW, plot the variation of the power input to the chillers with the cooling load [Answer: see worked examples 13.9 and 13.10] P13.7 The building in worked example 13.10 is to be cooled using chillers A, B, C and D with capacities of 750 kW, 1500 kW, 1500 kW, and 3500 kW respectively The variation of the COP of the chillers A, B and C with load fraction is given by: ܿሺ݂ ሻ ൌ െͺǤͷͷ݂ ଷ ͳͳǤ݂ ଶ െ ͲǤͶ͵݂ ͵Ǥͺ The variation of the COP of chiller D with load fraction is given by: Principles of Heating 9562–13 688 Principles of Heating, Ventilation and Air Conditioning with Worked Examples ܿሺ݂ ሻ ൌ ͳͳǤʹ݂ ଷ െ ʹͺǤͳ݂ ଶ ʹͳǤͲ݂ ʹǤʹ The chillers are to be operated in an optimal manner to satisfy the hourly cooling load given Table E13.10.1 Calculate (i) the hourly input of electrical energy to the chillers, (ii) the total electrical energy input, and (iii) the average COP of the cooling system [Answers: simulate different combinations and compare the total energy inputs] P13.8 A building has a constant cooling load of 180 kW It is cooled by a chiller system where the condenser heat is rejected to the atmosphere through a cooling tower The variation of the COP of the chiller with the ambient wet-bulb temperature is well represented by the equation ܱܲܥൌ Ǥͺ െ ͲǤͳ͵ݐ௪ ͲǤͲͲͳͷݐ௪ ଶ The seasonal bin data for the local wet-bulb temperature is given in Table P13.8.1 Estimate (i) the seasonal energy input to the chiller, (ii) the average COP, and (ii) the total heat rejected in the cooling tower [Answers: (i) 600 GJ, (ii) 5.02, (iii) 3611 GJ] Table P13.8.1 Bin data for wet-bulb temperature twb, °C N-bin 11 675 12.9 680 15.5 795 18.2 995 21 1010 23.5 480 26.5 12 P13.9 A building has an effective heat conductance – UA of 0.78 kW °Cí1 From Monday to Friday, it is occupied for 14 hours from 7h to 20h, and unoccupied during the rest of the day The building is unoccupied during Saturday and Sunday The rates of internal heat gain during the occupied and unoccupied periods are 3.2 kW and 1.1 kW respectively The corresponding indoor temperatures are 21°C and 16°C respectively The building is heated using a fuel-fired furnace of capacity 30 kW and rated efficiency 88% The part-load degradation factor is 0.25 The bin data for three hour-groups for the location are given in Table E13.13.1 Calculate (i) the balance temperatures for the occupied and unoccupied periods, and (ii) the annual energy input to the furnace during the occupied and unoccupied periods [Answers: (i) 16.9°C, 14.6°C, (ii) 27.9 MWh, 36.8 MWh] Principles of Heating 9562–13 Building Energy Estimating and Modeling Methods 689 P13.10 A building in Vancouver is heated with a heat pump whose capacity Qcap (kW), and COP vary with ambient temperature Ta (°C), according to the following equations: ଶ ܳ ൌ ͵ͳǤ͵ͺ ͳǤܶ ͲǤͲʹܶ ܱܲܥൌ ʹǤʹ ͲǤͲͺʹܶ ͲǤͲͲ͵ܶ ଶ The UA-value of the building is 0.62 kW°Cí1 and the indoor temperature is 22°C The rate of internal heat gain of the building is 2.6 kW The part-load degradation coefficient of the heat pump is 0.25 Estimate (i) the annual electrical energy input to the heat pump, (ii) the annual energy input to the auxiliary heat source, and (iii) the average COP [Answers: (i) 65.7GJ, (ii) 0.15 GJ, (iii) 2.27] P13.11 A house in Vancouver has an effective UA-value of 1.3 kW°Cí1 It is heated using a ground-source heat pump, of capacity 25 kW and average COP 3.5 The average ground temperature for heat absorption by the heat pump is 7.2°C The internal heat gains and the indoor temperature of the house are 5.4 kW and 22°C respectively The degradation coefficient due to cycling of the heat pump is 0.25 Calculate (i) heat pump balance temperature, (ii) the heating load, the heat supplied by the heat pump and the auxiliary energy source, (iii) the electrical energy input to the heat pump, and (iv) the average COP Sketch the energy flow rates versus ambient temperature graphs [Answers: (i) í1.38°C, (ii) 315 GJ, 311.7 GJ, 3.2GJ, (iii) 98.8 GJ, (iv) 3.15] P13.12 A water-loop heat pump system is used to heat and cool a building with zones (see Fig E13.15.1) If the water temperature in the loop falls below 15°C, a gas-fired furnace in the loop is activated to maintain the temperature of the water at 15°C If the temperature rises above 35°C, the water is sent through a cooling tower which maintains the water temperature at 35°C (See Fig 13.11.) The heating and cooling mode COPs of the heat pumps are well represented by the equations: ߝ ൌ ͲǤʹݐ௪ െ ͳ Principles of Heating 9562–13 690 Principles of Heating, Ventilation and Air Conditioning with Worked Examples ߝ ൌ Ǥʹͷ െ ͲǤͳͷ ୵ where tw (°C) is the temperature of the water loop The cooling (positive) and heating (negative) loads of the zones for four different time periods are given in Table P13.12.1 Calculate (i) the total energy input rate to the heat pumps, (ii) the heat input rate to the furnace, and (iii) the heat rejection rate in the cooling tower, for the different load conditions Neglect any effects due to storage [Answers: (A) 31.7 kW, kW, kW, (B) 24.4 kW, kW, kW, (C) 43.3 kW, kW, 103.3 kW, (D) 44 kW, 16 kW, kW] Table P13.12.1 Water-loop heat pump data H/C -Loads (kW) A B C D Zone í30 í20 í20 í30 Zone í30 í20 25 í25 Zone 10 30 25 í25 Zone 20 20 30 20 P13.13 Analyze the WLHP system in worked example 13.13 including a water storage tank of volume 2m3, if each time period is hours References ASHRAE Handbook - 2013 Fundamentals, American Society of Heating, Refrigeration and Air Conditioning Engineers, Atlanta, 2013 Erbs, D G., Klein, S A and Beckman, W A., ‘Estimation of degree–days and ambient temperature bin data from monthly– average temperatures’ ASHRAE Journal, 25(6), 1983 Kuehn, Thomas H., Ramsey, James W and Threlkeld, James L., Thermal Environmental Engineering, 3rd edition, Prentice-Hall, Inc., New Jersey, 1998 Mitchell, John W and Braun, James E., Principles of Heating, Ventilation and Air Conditioning in Buildings John Wiley and Sons, Inc., New York, 2013 Stoecker, Wilbert F., Design of Thermal Systems, International Edition, McGraw-Hill Book Company, London, 1989 Principles of Heating 9562–13 Building Energy Estimating and Modeling Methods 691 Stoecker, Wilbert F and Jones, Jerold W., Refrigeration and Air Conditioning, International Edition, McGraw-Hill Book Company, London, 1982 Appendix A13.1 - MATLAB Code for Bin Data and Degree–Days % computation of yearly bin data for ambient temperature % uses computed bin data to calculate the degree–days tbas=[-27.5,-25,-22.5,-20,-17.5,-15,-12.5,-10,-7.5,-5,-2.5,0,2.5, 5,7.5,10,12.5,15,17.5,20,22.5,25,27.5,30,32.5,35]; % mean temperature of each bin, 26 bins in all for i=1:26 tbou(i)=tbas(i)-1.25; % boundary temperatures of bins, C end tbou(27)=35+1.25 % monthly average ambient temperatures, C; data for Toronto tma=[-4.7,-4.5,0.4,7.2,13.4,18.9,21.6,20.7,16.4,9.7,3.9,-2] % number of days of the 12 months - Jan to Dec nd=[31,28,31,30,31,30,31,31,30,31,30,31]; tyav=sum(tma)/12; % yearly average temperature, C sum2=0; for i=1:12 sum2=sum2+((tma(i)-tyav)^2)/12; end sigy=sum2^0.5; % standard deviation of daily ambient temperatures for j=1:12 stdm=1.451-0.0290*tma(j)+0.0369*sigy; % correlation for monthly average standard deviation for i=1:27 hp(i)=(tbou(i)-tma(j))/(stdm*(nd(j)^0.5)); % H-parameter qf(i)=(1+exp(-3.396*hp(i)))^(-1); % cumulative fraction of number of hours below T-base aaq(i,j)=qf(i); % monthly cumulative fractions, j = month, i = bin-number end end Principles of Heating 9562–13 692 Principles of Heating, Ventilation and Air Conditioning with Worked Examples for j=1:12 for i=1:26 nhr(i,j)=(aaq(i+1,j)-aaq(i,j))*nd(j)*24 % monthly bin data , j = month , i= bin end end % compute yearly bin data in hours for 26 - different bins for i=1:26 sumy=0; for k=1:12 sumy=sumy+nhr(i,k); end ynhr(i)=sumy % number of hours per year in bin number, i end % compute monthly heating degree–days for the 12 months using % computed bin data tbala=22 % input balance temperature of building for i=1:12 sumdd=0; for k=1:26 sumdd=sumdd+nhr(k,i)*(tbala-tbas(k))/24; if tbas(k)>=tbala break end end yndd( i)=sumdd % number of degree–days end Principles of Heating 9562–99 Index cooling load estimation, 447, 459, 478 absorption cycles, 84, 87 conduction time factors, 472, 476 absorption of solar radiation, 406 heat balance method, 468 fenestrations, 411 opaque surfaces, 406 radiant time series, 471, 476 adiabatic saturation, 126 cooling tower performance, 230 air distribution, 529, 539 cooling towers, 229, 646 air washers, 224 analysis, 230, 232 air-source heat pumps, 9, 82, 643 approach, 233 air–water mixtures, 119, 121 range, 234 simplified model, 232 angle of incidence, 400 counter-flow heat exchangers, 267 beam radiation, 396, 400 cross-flow heat exchangers, 267, 275 below grade heat transfer, 351 cycling of furnaces, 642 degradation coefficient, 642 bin method, 638 black surface, 35 Darcy–Weisbach equation, 532, 593 bypass systems, 166, 177 degree of saturation, 121 Carnot refrigeration cycle, 66 dehumidification, 163, 285 centrifugal compressors, 81, 539 design of pipe networks, 601 centrifugal pumps, 596, 598 diffuse radiation, 396 clear-sky model, 404 diffusion coefficient, 219, 363 coefficient of performance - COP, 67 direct-return systems, 602 Colebrook's equation, 532, 594 direct-contact processes, 217, 221 condensers, 272 direction of solar beam, 397 condition line, 165, 170, 176, 290 dual-duct systems, 181 conduction, 20, 463 duct design methods, 546 equal friction method, 547 cylindrical systems, 26 static regain method, 549 internal heat generation, 28 dynamic losses in fittings, 534, 595 conduction time factors, 472, 474 equivalent length, 595 cooling coils, 165, 176, 285 693 Principles of Heating 9562–99 694 Index effective temperature, 455 heat transfer correlations, 32, 34 effectiveness–NTU design method, 270 heat transfer from human body, 452 efficiency of finned surfaces, 278, 282 MET units, 452 emissive power, 37 metabolic heat generation, 453, 460 energy estimation methods, 633, 638 enthalpy of moist air, 123 heating and cooling degree-days, 634 balance temperature, 636 enthalpy potential, 221, 224 heating load estimation, 340, 477 equation of time, 400 heating load, 447, 477, 478 evaporative cooling, 169 hour angle, 399 evaporators, 272 humidification, 168 humidifiers, 224 fan characteristics, 541 fan efficiency, 541 efficiency, 228 NTU, 228 fan laws, 542 humidity ratio, 121 fan–duct interaction, 543 HVAC system types, 4-9 Fick's law, 218, 362 indoor air quality, 457 fin-tube heat exchangers, 282, 286 ventilation rate, 459 forced convection, 30 Fourier's law, 20, 26 indoor design conditions, 455 free convection, 33 infiltration, 355 friction chart, 533, 594 heating load, 355 gas-filled cavities, 346 flow rates, 356, 360 fenestrations, 348 stack effect, 357 overall heat transfer coefficient, wind effect, 359 349 generation of bin data, 638 mechanical effect, 359 internal heat gains, 459 grade-level heat transfer, 355 equipment, 461 gray surface, 37, 39 lighting, 460 people, 459 head loss in pipes, 593 friction chart, 594 Kirchoff's law, 38 heat balance method, 468, 478 heat exchanger types, 267 Lewis number, 129, 165, 223 heat pump balance point, 644 lithium bromide–water systems, 86, 87 heat pump cycles, 9, 82, 643 LMTD design method, 267, 270 heat transfer coefficient, 31, 34 Principles of Heating 9562–99 Index 695 mass convection, 220 reflected radiation, 405 mass diffusion, 218 reflection, 37 mass transfer coefficient, 221 refrigerants, 76 mixing process, 160 refrigeration ton,74 modes of heat transfer, 17 reheat systems, 176, 180 moisture transfer, 361 relative humidity, 121 permeability, 363 reverse-return systems, 602 multi-chiller systems, 651 reversible heat pumps, 9, 82, 643 multilayered structures, 21, 340 rotary compressors, 81 isothermal plane method, 342 parallel flow method, 341 sensible cooling, 162 zone method, 343 sensible heat ratio, 134 multi-zone systems, 180 sensible heating, 162 series resistances, 22 net positive suction head (NPSH), 598 shading of fenestrations, 417 simulation methods, 649 operative temperature, 453 central HVAC system, 7, 79, 650 optimization of duct systems, 551 simultaneous heat and mass transfer, outdoor design conditions, 450 221, 231 single-zone systems, 174 parallel resistances, 23 solar altitude angle, 398 pressure loss, 532, 593 solar azimuth angle, 399 fittings, 534, 595 solar declination, 399 straight ducts, 532, 593 solar heat gain coefficient (SHGC), 415 protractors of chart, 134, 135 solar radiation fundamentals, 396 psychrometric chart, 129, 135 sol-air temperature, 407 psychrometric processes, 159 solar time, 399 pump curve, 598 standard longitude, 399 flow control, 600 standard refrigeration cycle, 68 system–pump interaction, 599 standard time, 399 radiant time factors, 472, 473 radiation exchange, 38 thermal comfort, 452 clo unit, 454 radiation heat transfer coefficient, 347 thermal networks, 21, 340 radiation heat transfer, 34 thermal resistance, 21 reciprocating compressors, 80 three-heat-reservoir model, 85 Principles of Heating 9562–99 696 Index total head, 592 energy equation, 592 total pressure distribution, 530 hydronic systems, 593 transient heat transfer, 19, 463 water-loop heat pumps, 10, 83, 654 lumped capacitance model, 465 wet-bulb temperature, 126, 128 transfer function method, 464 wet-coil heat exchangers, 266, 283 transmittance of radiation, 409 multilayered fenestrations, 410 two-stage cycles, 74 analysis, 284, 285 numerical models, 288 physical processes, 284 Wien's law, 36 vapor compression cycle, 72, 74 variable air volume systems, 183 variable occupancy, 647 zone air distribution, 552, 555 air diffusion performance index, 554 water distribution systems, 591 diffusers, 555