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Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering, Oklahoma State University

Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

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Page 1: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Load CalculationsHeat Balance Method - Theory

Prof. Jeffrey D. SpitlerSchool of Mechanical and Aerospace Engineering, Oklahoma State University

Page 2: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Tonight

The heat balance method – theoryThe heat balance method – applicationDemonstrationOverview of the RTS method and other simplified methodsStrengths, weaknesses and limitations of simplified methods.

Page 3: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Abbreviations

“MPS 171” refers to the textbook (McQuiston, Parker and Spitler, 5th

Edition) p. 171“ASHRAE HOF 30.40” refers to the 2001 ASHRAE Handbook of Fundamentals, page 30.40

Page 4: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Important Announcement

After installing software from CD-ROM, download latest version from web site:http://www.mae.okstate.edu/hvac

Page 5: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,
Page 6: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Important Definitions

Zone: room(s) for which loads are det’dassumed to have uniform temperature. (i.e. controlled by a single thermostat and for multiple rooms, they should all have similar load profiles.) Boundaries are slightly vague, depending on method – usually drawn at inside surface of walls, windows, ceiling, floor, but includes heat storage of building materials.

Page 7: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Important Definitions

Heat Gains: Instantaneous rate of heat transfer or heat gain into the zone. Includes convective and radiative heat transfer. (Heat may be conducted to zone boundary, but is then convected or radiated into zone.)Cooling load: heat transfer rate required to maintain constant zone air temperatureHeat extraction rate: actual heat transfer rate of system, with zone air temperature changing (e.g., due to thermostat setback, limited system capacity or proportional control)

Page 8: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Gain, Cooling Load, Heat Extraction Rate

Instantaneousheat gain

Furnishings,structure,

variable heatstorage

Instantaneouscooling load

Convective component

Radiativecomponent

Convection(with time-delay)

Heat extractionby equipment

Page 9: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Overview

Discuss “heat balance method” first –all other methods are approximations of the heat balance method, or approximations of approximations (e.g. the CLTD/SCL/CLF method approximates the transfer function method, which approximates the heat balance method)

Page 10: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance Method

Based on heat balances for exterior zone surfaces, interior zone surfaces, and zone air. Assures conservation of energy (which is not guaranteed for approximate methods).Pardon the equations!

Page 11: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

ABSORBEDINCIDENT

SOLAR

CONVECTIONTO OUTSIDE

AIR

LWRADIATION

OUTSIDE FACEHEAT BALANCE

THROUGH THEWALL CONDUCTION

INSIDE FACEHEAT BALANCE

SW RADIATIONFROM LIGHTS

LW RADIATIONFROM INTERNAL

SOURCES

TRANSMITTEDSOLAR CONVECTION

TO ZONEAIR

LW RADIATIONEXCHANGE WITH

OTHERSURFACES

AIR HEATBALANCE

INFILTRATIONVENTILATIONEXHAUST AIR

CONVECTION FROM INTERNAL

SOURCES

HVAC SYSTEMAIR

Page 12: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat balance - zone surface

Wall

Interiorsurface

Exteriorsurface

q"solar,out,j,θ

q"convection,out,j,θ

q" radiat

ion,ou

t,j,θ

q"conduction,out,j,θ q"conduction,in,j,θ q"convection,in,j,θ

q"radiation,in,j,θ

totos,j,θ

tis,j,θ

ti

q" solar

,in,j,θ

Page 13: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Transient conduction heat transfer – conduction transfer functions

∑∑ ∑=

−= =

−− Φ+++−−=Nq

nnjinconductionn

Nz

n

Ny

nnjosnjosonjisnjisojinconduction qtYtYtZtZq

1,,,

1 1,,,,,,,,,,, "" δθδθθδθθθ

∑ ∑∑= =

−−−=

Φ+++−−=Nx

n

Nq

nnjoutconductionnnjosnjosonjis

Ny

nnjisojoutconduction qtXtXtYtYq

1 1,,,,,,,,,

1,,,,, "" δθδθθδθθθ

∑ ∑∑= =

−−−=

Φ++−=Nx

n

Nq

nnjoutconductionnnjosnnjis

Ny

nnjout qtXtYH

1 1,,,,,,,

1,, " δθδθδθθ

θθθθ ,,,,,,,,," joutjosojisojoutconduction HtXtYq ++−=

Page 14: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Exterior Surface Heat Balance

θ,,, joutconductionq ′′ θ,,, joutsolarq ′′= θ,,, joutconvectionq ′′+θ,,, joutradiationq ′′+

tjoutsolar Gq αθ =′′ ,,,

)( ,,,,, θθ josocjoutconvection tthq −=′′

)()( ,,,,,,,, θθθ josskyskyrjosggrjoutradiation tthtthq −+−=′′ −

skyrgrco

skyskyrggroctjoutjisojos hhhX

thththGHtYt

−−

−−

+++++++−

=αθθ

θ,,,,

,,

Page 15: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance - Fenestration

Window InteriorpaneExterior

pane

q"solar,out,j,θ

q"convection,out,j,θ

q" radiation,out,j,θ

q"convection,in,j,θ

q"radiation,in,j,θ

to tos,j,θ tis,j,θ ti

q"solar,in,j,θ

Rc

Rr

Page 16: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Interior surface heat balance

Similar to exterior surface, accounts for Radiation heat transfer between surfaces with detailed model (e.g. MRT/balance)Solar radiation transmitted through windows, absorbed onto interior surfacesRadiation heat transfer from internal equipment, lighting, and peopleConvective heat transfer from zone air.

Page 17: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone Air

ti

Ajq"convection,in,j,θtis,j,θ

Ajq"convection,in,j,θ

A jq"convection,in,j,θ

Aj q"convection,in,j,θ

q infiltration/ventilation

q systemq

internal,conv,θ

Page 18: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone Air

Air temperature is assumed uniform throughout space. (This is sometimes called the well-stirred model.)Because of this, air leaving the space does not affect the energy balance directly.Radiation only affects surface heat-balances -air is assumed to be non-participating media

Page 19: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone Air

Can be formulated to solve for cooling load directly, assuming zone air temperature is constant

onv,θinternal,cioptiona,infiltraijisjic

N

jjsystem qttcmtthAq &&& −−−−−= ∑

=

)()( ,,,,1

, θθ

Page 20: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone Air

Or, can be formulated to solve for zone temperature when there is no system contribution (e.g., where space temperature is allowed to float):

ptiona,infiltrajic

N

jj

onv,θinternal,coptiona,infiltrajisjic

N

jj

i

cmhA

qtcmthAt

&

&&

+

++=

=

=

,,1

,,,,1

)( θ

Page 21: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone Air

Or, can be formulated to solve for zone air temperature when the system is on:

ptiona,infiltrajic

N

jj

onv,θinternal,coptiona,infiltrajisjic

N

jj

i

cmhAb

qtcmthAat

&

&&

++−

+++=

=

=

,,1

,,,,1

)( θ

Page 22: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Heat Balance – Zone AirRelies on a piecewise linear representation of system capacity qsys=a+bTz

Qsys (W)

-10000-8000-6000-4000-2000

0200040006000

10.0 15.0 20.0 25.0 30.0

Zone Air Temperature (C)

Hea

ting

(+) /

Coo

ling

(-)

Page 23: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Simple Steady-State Example of Heat Balance for a Roof (1)

Consider a horizontal roof at 36°N, 84°W:June 21, 1 p.m. CDT, 317 Btu/hr-ft2 total incident solar radiation, α=0.8No thermal mass; U=0.2 Btu/hr-ft2 (surface-to-surface)Outside air dry bulb temperature = 85°FWind speed = 12 mph, hc=1.896 Btu/hr-ft2°FSky temperature = 74.2°F; hr,sky=1.183 Btu/hr-ft2°FInside surface temperature, tis= 72°F“contrived” – tis, hc , hr,sky typically not known a priori

Page 24: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Steady-state Example (2)

Wall

Interiorsurface

Exteriorsurface

q"solar

q"convection,out

q" radiat

ion,ou

tto tos

tis72 F

q"conduction

85 F

Tsky74.2 F

Page 25: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Steady-state Example (3)

q”solar+q”convection,out +q”radiation,out=q”conduction

)()()( isososkyrosoct ttUtthtthG −=−+−+α

UhhtUththG

trc

isskyroctos ++

+++=

)()()(α

In other words, a weighted average.

Page 26: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Steady-State Example (4)

2.0183.1896.1)72(2.0)2.74(183.1)85(896.1)317(8.0

+++++

=ost

Ftos °= 65.157

)7265.157(2.0)(−=

−=′′ isosconduction ttUq

=17.1 Btu/(hr-ft2)

Page 27: Load Calculations Heat Balance Method - Theory Calculations 1 HB... · Load Calculations Heat Balance Method - Theory Prof. Jeffrey D. Spitler School of Mechanical and Aerospace Engineering,

Questions?