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

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1 Load Calculaions Hea Balance Mehod - Theory Prof. Jeffrey D. Spiler School of Mechanical and Aerospace Engineering, Oklahoma Sae Universiy

2 Tonigh The hea balance mehod heory The hea balance mehod applicaion Demonsraion Overview of he RTS mehod and oher simplified mehods Srenghs, weaknesses and limiaions of simplified mehods.

3 Abbreviaions MPS 171 refers o he exbook (McQuison, Parker and Spiler, 5 h Ediion) p. 171 ASHRAE HOF refers o he 2001 ASHRAE Handbook of Fundamenals, page 30.40

4 Imporan Announcemen Afer insalling sofware from CD-ROM, download laes version from web sie: hp://

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6 Imporan Definiions Zone: room(s) for which loads are de d assumed o have uniform emperaure. (i.e. conrolled by a single hermosa and for muliple rooms, hey should all have similar load profiles.) Boundaries are slighly vague, depending on mehod usually drawn a inside surface of walls, windows, ceiling, floor, bu includes hea sorage of building maerials.

7 Imporan Definiions Hea Gains: Insananeous rae of hea ransfer or hea gain ino he zone. Includes convecive and radiaive hea ransfer. (Hea may be conduced o zone boundary, bu is hen conveced or radiaed ino zone.) Cooling load: hea ransfer rae required o mainain consan zone air emperaure Hea exracion rae: acual hea ransfer rae of sysem, wih zone air emperaure changing (e.g., due o hermosa seback, limied sysem capaciy or proporional conrol)

8 Hea Gain, Cooling Load, Hea Exracion Rae Insananeous hea gain Convecive componen Insananeous cooling load Hea exracion by equipmen Radiaive componen Furnishings, srucure, variable hea sorage Convecion (wih ime-delay)

9 Overview Discuss hea balance mehod firs all oher mehods are approximaions of he hea balance mehod, or approximaions of approximaions (e.g. he CLTD/SCL/CLF mehod approximaes he ransfer funcion mehod, which approximaes he hea balance mehod)

10 Hea Balance Mehod Based on hea balances for exerior zone surfaces, inerior zone surfaces, and zone air. Assures conservaion of energy (which is no guaraneed for approximae mehods). Pardon he equaions!

11 ABSORBED INCIDENT SOLAR CONVECTION TO OUTSIDE AIR LW RADIATION OUTSIDE FACE HEAT BALANCE THROUGH THE WALL CONDUCTION SW RADIATION FROM LIGHTS INSIDE FACE HEAT BALANCE LW RADIATION FROM INTERNAL SOURCES TRANSMITTED SOLAR CONVECTION TO ZONE AIR LW RADIATION EXCHANGE WITH OTHER SURFACES INFILTRATION VENTILATION EXHAUST AIR AIR HEAT BALANCE CONVECTION FROM INTERNAL SOURCES HVAC SYSTEM AIR

12 Hea balance - zone surface q" solar,ou, q" solar,in, q" convecion,ou, q" conducion,ou, q" conducion,in, q" convecion,in, o q" radiaion,in, i q" radiaion,ou, os, Wall is, Exerior surface Inerior surface

13 q q Transien conducion hea ransfer conducion ransfer funcions Nz Ny Nq " conducion, in, = Zois, Znis, nδ Yoos, Ynos, nδ Φnq" conducion, in, nδ n= 1 n= 1 n= 1 Ny Nx Nq " conducion, ou, = Yo is, Ynis, nδ X oos, X nos, nδ Φnq" conducion, ou, nδ n= 1 n= 1 n= 1 H = Ny Y Nx X ou, n is, nδ n os, nδ n " conducion, ou, nδ n= 1 n= 1 n= 1 " conducion, ou, = Yo is, X oos, H ou, Nq q Φ q

14 Exerior Surface Hea Balance, ou, = solar, ou, q radiaion, ou, q convecion, ou, q conducion q q = solar, ou, αg q convecion, ou, = hc ( o os, q radiaion ou, = hr, g ( g os, ) hr sky( sky os,, ) ) os, = Y o is, H ou, X o αg h c h h c r g o h h r g r sky g h r sky sky

15 Hea Balance - Fenesraion q" solar,ou, q" solar,in, q" convecion,ou, R c q" convecion,in, o os, is, i q" radiaion,in, q" radiaion,ou, R r Exerior pane Window Inerior pane

16 Inerior surface hea balance Similar o exerior surface, accouns for Radiaion hea ransfer beween surfaces wih deailed model (e.g. MRT/balance) Solar radiaion ransmied hrough windows, absorbed ono inerior surfaces Radiaion hea ransfer from inernal equipmen, lighing, and people Convecive hea ransfer from zone air.

17 Hea Balance Zone Air A j q" convecion,in, A j q" convecion,in, qinfilraion/venilaion qsysem q inernal,conv, is, A j q" convecion,in, i Aj q" convecion,in,

18 Hea Balance Zone Air Air emperaure is assumed uniform hroughou space. (This is someimes called he well-sirred model.) Because of his, air leaving he space does no affec he energy balance direcly. Radiaion only affecs surface hea-balances - air is assumed o be non-paricipaing media

19 Hea Balance Zone Air q& Can be formulaed o solve for cooling load direcly, assuming zone air emperaure is consan N sysem =, Ajhc, i, j ( is, j = 1 i ) m& a,infilraion c p ( o i ) q& inernal,conv,

20 Hea Balance Zone Air Or, can be formulaed o solve for zone emperaure when here is no sysem conribuion (e.g., where space emperaure is allowed o floa): i = N j= 1 A h j c, i, j ( is, N j= 1 ) m& A h j c, i, j a,infilraion m& c p o a,infilraion q& c p inernal,conv,

21 Hea Balance Zone Air Or, can be formulaed o solve for zone air emperaure when he sysem is on: p a,infilraion j i c N j j inernal,conv, o p a,infilraion j is j i c N j j i c m A h b q c m A h a & & & = = =,, 1,,,, 1 ) (

22 Hea Balance Zone Air Relies on a piecewise linear represenaion of sysem capaciy q sys =abt z Qsys (W) 6000 Heaing () / Cooling (-) Zone Air Temperaure (C)

23 Simple Seady-Sae Example of Hea Balance for a Roof (1) Consider a horizonal roof a 36 N, 84 W: June 21, 1 p.m. CDT, 317 Bu/hr-f 2 oal inciden solar radiaion, α=0.8 No hermal mass; U=0.2 Bu/hr-f 2 (surface-osurface) Ouside air dry bulb emperaure = 85 F Wind speed = 12 mph, h c =1.896 Bu/hr-f 2 F Sky emperaure = 74.2 F; h r,sky =1.183 Bu/hrf 2 F Inside surface emperaure, is = 72 F conrived is,h c,h r,sky ypically no known a priori

24 Seady-sae Example (2) q" solar q" convecion,ou q" conducion 85 F o os is 72 F q" radiaion,ou Wall T sky 74.2 F Exerior surface Inerior surface

25 Seady-sae Example (3) q solar q convecion,ou q radiaion,ou =q conducion ) ( ) ( ) ( is os o sky r os o c U h h G = α U h h U h h G r c is sky r o c os = ) ( ) ( ) ( α In oher words, a weighed average.

26 Seady-Sae Example (4) os = 0.8(317) 1.896(85) 1.183(74.2) os = F 0.2(72) q conducion = U ( os is ) = 0.2( ) =17.1 Bu/(hr-f 2 )

27 Quesions?