```
TALK=T;RUN(1,1)
PHOTON USE
p

up z;vec x 1 sh;pau;clear
con p1 x 1 fi;.01;pau;clear
con tem1 x 1 fi;.01;pau;cl
ENDUSE
DISPLAY
The problem considered is laminar free convection of air
between a pair of parallel, vertically-mounted flat plates of
length H. These plates are maintained either at uniform
heat fluxes (UHF) qw or uniform wall temperatures (UWT) tw.

The solution domain has one plane of symmetry at the centre
of the gap B between the two plates. The external pressure
is the same at both the top and bottom of the plate, so the
flow is driven entirely by buoyancy forces.

The Boussinesq assumption is made in the simulations, and the
flow is characterised by the Grashof number GrB and the
gap-to-length ratio B/H.

The solution domain comprises the gap between the
two channel plates, as well as the free environment upstream
and downstream of the channel.

For economy, the solution domain may be restricted to the gap
alone, although this approach is less accurate for developing
flow because of the empirical representation of total pressure
losses at the channel inlet and outlet.

The practical application of free convection in vertical
channels may be found in the electronics and telecommunications
industry.

The flow is fully developed if GrB*(B/H) < 1 for a UWT
condition, and when GrB*(B/H) < 100 for a UHF condition (see
Aung, Int.J. Heat Mass Transfer, Vol.15,p1577, 1972).

Developing flow has been considered by Aung et al, Int.J.Heat
Mass Transfer, Vol.15, p2293, 1972 & Morrone et al, Int.J.Heat
Mass Transfer, Vol.40, No.5, p993, 1997).

The dimensionless equations solved are:

dW/dZ + dV/dY = 0 ;
W*dZ/dZ + V*dV/dY =  d/dY(dW/dY) + d/dZ(dW/dZ)
- dP/DZ + GrB*T
W*dT/dZ + V*dT/dY =  (1./Pr)*d/dY(dT/dY)
+ (1./Pr)*d/dZ(dT/dZ)
where

Z  = z/B ; Y = y/B ; W = w*B/enul ; V = v*B/enul
P  = (p-p,ref)*(B**2)/(rho*enul**2)
T  = k*(t-tref)/(qw*B)  ; Pr = rho*enul*cp/k
GrB = g*beta*qw*B**4/(k*enul**2)

This Q1 may be used to run 6 cases which are documented in
the literature. The results are summarised below in terms of
the dimensionless volumetric flow rate PSI(=wbulk*B/enul):

Developing Flow (UHF)
---------------------
phoenics        phoenics
reduced domain   full domain    Morrone
GrH=1.E5 B/H=0.5      19.0            27.0         30.0
GrH=1.E4 B/H=0.8      12.5            19.0         21.5

Fully-Developed Flow
--------------------
phoenics             Aung
reduced & full domain
GrB=1.E2  B/H=0.04 (UWT)         8.16              8.33
GrB=1.E2  B/H=0.04 (UHF)        14.80             17.13

where GrH=GrB*(H/B)**4a n The dimensionless volumetric flow
rate produced by PHOENICS can be obtained from the RESULT file
by taking TWICE the printed NETT source of R1 at INLET.

ENDDIS
************************************************************
Group 1. Run Title and Number
************************************************************
************************************************************

TEXT(Free Convection Between Vertical Plates )

************************************************************
************************************************************

IRUNN = 1 ;LIBREF = 254
************************************************************
Group 2. Time dependence
************************************************************
Group 3. X-Direction Grid Spacing
CARTES = T
NX = 1
XULAST =1.
XFRAC(1)=1.
************************************************************
Group 4. Y-Direction Grid Spacing
NY = 55
YVLAST =1.5
YFRAC(1)=0.050764 ;YFRAC(2)=0.088385
YFRAC(3)=0.122251 ;YFRAC(4)=0.153888
YFRAC(5)=0.183964 ;YFRAC(6)=0.212852
YFRAC(7)=0.240788 ;YFRAC(8)=0.267935
YFRAC(9)=0.294409 ;YFRAC(10)=0.3203
YFRAC(11)=0.345677 ;YFRAC(12)=0.370597
YFRAC(13)=0.395104 ;YFRAC(14)=0.419237
YFRAC(15)=0.443027 ;YFRAC(16)=0.466501
YFRAC(17)=0.489684 ;YFRAC(18)=0.512595
YFRAC(19)=0.535254 ;YFRAC(20)=0.557674
YFRAC(21)=0.579872 ;YFRAC(22)=0.601859
YFRAC(23)=0.623647 ;YFRAC(24)=0.645247
YFRAC(25)=0.666667 ;YFRAC(26)=0.672294
YFRAC(27)=0.679596 ;YFRAC(28)=0.687699
YFRAC(29)=0.69637 ;YFRAC(30)=0.70549
YFRAC(31)=0.714985 ;YFRAC(32)=0.724803
YFRAC(33)=0.734907 ;YFRAC(34)=0.745267
YFRAC(35)=0.75586 ;YFRAC(36)=0.766668
YFRAC(37)=0.777674 ;YFRAC(38)=0.788865
YFRAC(39)=0.80023 ;YFRAC(40)=0.811758
YFRAC(41)=0.823442 ;YFRAC(42)=0.835272
YFRAC(43)=0.847243 ;YFRAC(44)=0.859347
YFRAC(45)=0.87158 ;YFRAC(46)=0.883935
YFRAC(47)=0.896409 ;YFRAC(48)=0.908996
YFRAC(49)=0.921694 ;YFRAC(50)=0.934498
YFRAC(51)=0.947405 ;YFRAC(52)=0.960411
YFRAC(53)=0.973514 ;YFRAC(54)=0.986712
YFRAC(55)=1.
************************************************************
Group 5. Z-Direction Grid Spacing
PARAB = F
NZ = 65
ZWLAST =3.75
ZFRAC(1)=0.030343 ;ZFRAC(3)=0.073072
ZFRAC(5)=0.109959 ;ZFRAC(7)=0.143924
ZFRAC(9)=0.175974 ;ZFRAC(11)=0.206618
ZFRAC(13)=0.236162 ;ZFRAC(15)=0.264806
ZFRAC(17)=0.292694 ;ZFRAC(19)=0.319932
ZFRAC(21)=0.339798 ;ZFRAC(23)=0.357493
ZFRAC(25)=0.37793 ;ZFRAC(27)=0.400115
ZFRAC(29)=0.423621 ;ZFRAC(31)=0.448204
ZFRAC(33)=0.473702 ;ZFRAC(35)=0.5
ZFRAC(37)=0.526298 ;ZFRAC(39)=0.551796
ZFRAC(41)=0.576379 ;ZFRAC(43)=0.599885
ZFRAC(45)=0.62207 ;ZFRAC(47)=0.642507
ZFRAC(49)=0.660202 ;ZFRAC(51)=0.669213
ZFRAC(53)=0.685063 ;ZFRAC(55)=0.712805
ZFRAC(57)=0.751212 ;ZFRAC(59)=0.799575
ZFRAC(61)=0.857398 ;ZFRAC(63)=0.924306
ZFRAC(65)=1.
************************************************************
Group 6. Body-Fitted Coordinates
************************************************************
Group 7. Variables: STOREd,SOLVEd,NAMEd
ONEPHS = T
NAME(1)=P1 ;NAME(5)=V1
NAME(7)=W1 ;NAME(148)=PRPS
NAME(150)=TEM1
* Y in SOLUTN argument list denotes:
* 1-stored 2-solved 3-whole-field
* 4-point-by-point 5-explicit 6-harmonic averaging
SOLUTN(P1,Y,Y,Y,N,N,Y)
SOLUTN(V1,Y,Y,N,N,N,N)
SOLUTN(W1,Y,Y,N,N,N,N)
SOLUTN(PRPS,Y,N,N,N,N,Y)
SOLUTN(TEM1,Y,Y,Y,N,N,N)
PRPS = 148
************************************************************
Group 8. Terms & Devices
* Y in TERMS argument list denotes:
* 1-built-in source 2-convection 3-diffusion 4-transient
* 5-first phase variable 6-interphase transport
TERMS(P1,Y,Y,Y,N,Y,Y)
TERMS(V1,Y,Y,Y,Y,Y,Y)
TERMS(W1,Y,Y,Y,Y,Y,Y)
TERMS(TEM1,N,Y,Y,N,Y,N)
DIFCUT =0. ;ZDIFAC =1.
GALA = F ;ADDDIF = F
ISOLX = -1 ;ISOLY = -1 ;ISOLZ = -1
************************************************************
Group 9. Properties used if PRPS is not
stored, and where PRPS = -1.0 if it is!
RHO1 =1. ;TMP1 =0.
EL1 =0.
TSURR =0. ;TEMP0 =0.
PRESS0 =0.
DVO1DT =4096. ;DRH1DP =0.
EMISS =0. ;SCATT =0.
ENUL =1. ;ENUT =0.
PRNDTL(V1)=1. ;PRNDTL(W1)=1.
PRNDTL(TEM1)=-1.408451
PRT(V1)=1. ;PRT(W1)=1.
PRT(TEM1)=1.
CP1 =1. ;CP2 =1.
************************************************************
Group 10.Inter-Phase Transfer Processes
************************************************************
Group 11.Initial field variables (PHIs)
FIINIT(P1)=1.0E-10 ;FIINIT(V1)=1.0E-10
FIINIT(W1)=0. ;FIINIT(PRPS)=-1.
FIINIT(TEM1)=0.

PATCH(PLATE ,INIVAL, 1, 1, 1, 25, 21, 50, 1, 1)
INIT(PLATE ,PRPS,0. ,198. )
FSWEEP = 1
NAMFI =CHAM
************************************************************
Group 12. Patchwise adjustment of terms
Patches for this group are printed with those
for Group 13.
Their names begin either with GP12 or &
************************************************************
Group 13. Boundary & Special Sources

PATCH(HOCS ,CELL , 0, 0, 0, 0, 0, 0, 1, 1)
COVAL(HOCS ,V1 , FIXFLU , GRND1 )
COVAL(HOCS ,W1 , FIXFLU , GRND1 )

PATCH(INLET ,LOW , 1, 1, 1, 55, 1, 1, 1, 1)
COVAL(INLET ,P1 ,100. ,0. )
COVAL(INLET ,TEM1,0. ,0. )

PATCH(HEATFLUX,SWALL , 1, 1, 26, 26, 21, 50, 1, 1)
COVAL(HEATFLUX,TEM1, FIXFLU ,1. )

PATCH(EXIT ,HIGH , 1, 1, 1, 55, 65, 65, 1, 1)
COVAL(EXIT ,P1 ,100. ,0. )
COVAL(EXIT ,TEM1,0. ,0. )

PATCH(FREEBH ,SOUTH , 1, 1, 1, 1, 51, 65, 1, 1)
COVAL(FREEBH ,P1 ,100. ,0. )
COVAL(FREEBH ,TEM1,0. ,0. )

PATCH(BUOY ,PHASEM, 1, 1, 1, 55, 1, 65, 1, 1)
COVAL(BUOY ,W1 , FIXFLU , GRND3 )
XCYCLE = F
EGWF = T
WALLCO = GRND2
BUOYA =0. ; BUOYB =0.
BUOYC =-1.
************************************************************
Group 14. Downstream Pressure For PARAB
************************************************************
Group 15. Terminate Sweeps
LSWEEP = 800 ;ISWC1 = 1
LITHYD = 1 ;LITFLX = 1 ;LITC = 1 ;ITHC1 = 1
SELREF = T
RESFAC =1.0E-04
************************************************************
Group 16. Terminate Iterations
LITER(P1)=50 ;LITER(V1)=10
LITER(W1)=10 ;LITER(TEM1)=50
ENDIT(P1)=GRND1 ;ENDIT(V1)=1.0E-03
ENDIT(W1)=1.0E-03 ;ENDIT(TEM1)=1.0E-03
************************************************************
Group 17. Relaxation
RELAX(P1,LINRLX,1.)
RELAX(V1,FALSDT,3.493856)
RELAX(W1,FALSDT,3.493856)
RELAX(PRPS,LINRLX,1.)
RELAX(TEM1,FALSDT,1.0E+09)
OVRRLX =0.
EXPERT = F ;NNORSL = F
************************************************************
Group 18. Limits
VARMAX(P1)=1.0E+10 ;VARMIN(P1)=-1.0E+10
VARMAX(V1)=1.0E+06 ;VARMIN(V1)=-1.0E+06
VARMAX(W1)=1.0E+06 ;VARMIN(W1)=-1.0E+06
VARMAX(PRPS)=1.0E+10 ;VARMIN(PRPS)=-1.0E+10
VARMAX(TEM1)=1.0E+10 ;VARMIN(TEM1)=-1.0E+10
************************************************************
Group 19. Data transmitted to GROUND
PARSOL = F
ISG62 = 1
SPEDAT(SET,SCHEME,INLCS005,I,1)
SPEDAT(SET,SCHEME,INLCS007,I,1)
SPEDAT(SET,GXMONI,PLOTALL,L,T)
SPEDAT(SET,MATERIAL,198,L,T)
************************************************************
Group 20. Preliminary Printout
DISTIL = T ;NULLPR = F
NDST = 0
DSTTOL =1.0E-02
EX(P1)=125.400002 ;EX(V1)=1.595
EX(W1)=9.028 ;EX(PRPS)=0.7902
EX(TEM1)=0.04486
************************************************************
Group 21. Print-out of Variables
INIFLD = F ;SUBWGR = F
* Y in OUTPUT argument list denotes:
* 1-field 2-correction-eq. monitor 3-selective dumping
* 4-whole-field residual 5-spot-value table 6-residual table
OUTPUT(P1,Y,N,Y,Y,Y,Y)
OUTPUT(V1,Y,N,Y,Y,Y,Y)
OUTPUT(W1,Y,N,Y,Y,Y,Y)
OUTPUT(PRPS,Y,N,Y,N,N,N)
OUTPUT(TEM1,Y,N,Y,Y,Y,Y)
************************************************************
Group 22. Monitor Print-Out
IXMON = 1 ;IYMON = 54 ;IZMON = 64
NPRMON = 100000 ;NPRMNT = 1 ;TSTSWP = -1
UWATCH = T ;USTEER = T
HIGHLO = F
************************************************************
Group 23.Field Print-Out & Plot Control
NPRINT = 100000 ;NUMCLS = 5
NYPRIN = -1 ;IYPRF = 1 ;IYPRL = 10000
NZPRIN = 2 ;IZPRF = 1 ;IZPRL = 10000
XZPR = F ;YZPR = F
IPLTF = 1 ;IPLTL = -1 ;NPLT = 10
ISWPRF = 1 ;ISWPRL = 100000
ITABL = 3 ;IPROF = 1
ABSIZ =0.5 ;ORSIZ =0.4
NTZPRF = 1 ;NCOLPF = 50
ICHR = 2 ;NCOLCO = 45 ;NROWCO = 20
No PATCHes yet used for this Group
************************************************************
Group 24. Dumps For Restarts
SAVE = T ;NOWIPE = F
NSAVE =CHAM
STOP
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