```
PHOTON USE
AUTOPLOT
file
phi 5

cl
msg LAMINAR PLANE COUETTE FLOW
msg Prandtl number = 1 Eckert number =5
msg Velocity (W1) profile
msg Blue line --- PHOENICS solution
msg crosses ---   analytical solution
da 1 w1;da 1 w1a
col3 1;blb4 2
msg press  to continue
pause
cl

msg Prandtl number = 1 Eckert number =5
msg Temperature (H1) profile
msg Blue line --- PHOENICS solution
msg crosses ---   analytical solution
da 1 h1;da 1 h1a
col3 1;blb4 2
msg press  to end

pause
end
END_USE
DISPLAY

GROUP 1. Run title and other preliminaries
TEXT(1D Lam Couette Flow And Heat Trans
TITLE

DISPLAY
The case considered is laminar Couette flow between
infinite parallel plane plates with heat transfer. The
upper plate moves horizontally, while the lower plate
remains stationary. The lower and upper plates are kept
at uniform temperatures Tbot and Ttop, respectively.
This problem is of practical interest in journal-bearing
technology.
ENDDIS

The dimensionless equations to be solved are:

d/dy (dw/dy) = 0

(1/Pr) d/dy (dT/dy) + E (dw/dy)**2 = 0

where y  = y/yin
w  = w/wtop
T  = (T-Tbot)/(Ttop-Tbot)
Pr = cp*rho*enul/k
E  = wtop**2/(cp*(Ttop-Tbot))

Here, E is the Eckert number and the product E*Pr represents
the ratio of heat generation due to friction to the heat
transferred due to conduction.

The dimensionless analytical solutions are:

w = y

T = y*(1.+0.5*E*Pr*(1.-y))

The temperature distribution consists of a linear term
and a term which depends on the ratio E*Pr. The solution
properties of this equation as a function of E*Pr has
been discussed in detail by H.Schlicting, 'Boundary Layer
Theory', Chapter XIV, 4th Edition, McGraw Hill, (1960).

REAL(YIN,WTOP);YIN=1.0;WTOP=1.0
GROUP 2. Transience; time-step specification
** set parab=t to activate spot & residual
monitoring print out as a function of lithyd
PARAB=T;CARTES=T
GROUP 4. Y-direction grid specification
NY=50;GRDPWR(Y,NY,YIN,1.0)
GROUP 7. Variables stored, solved & named
SOLVE(W1,H1);STORE(W1A,H1A)
GROUP 8. Terms (in differential equations) & devices
TERMS(W1,N,N,P,P,P,P)
TERMS(H1,P,N,P,P,P,P)
GROUP 9. Properties of the medium (or media)
RHO1=1.0;ENUT=0.;ENUL=1.0
REAL(ECKERT);PRNDTL(H1)=1.0;ECKERT=5.0
HUNIT=ECKERT
GROUP 11. Initialization of variable or porosity fields
** compute analytical solutions
REAL(WA,GR,TA);INTEGER(JJM1)
DO JJ=1,NY
+PATCH(IN:JJ:,INIVAL,1,NX,JJ,JJ,1,NZ,1,1)
+GR=0.5*YFRAC(JJ)
IF(JJ.NE.1) THEN
+JJM1=JJ-1
+GR=YFRAC(JJM1)+0.5*(YFRAC(JJ)-YFRAC(JJM1))
ENDIF
+GR=GR*YVLAST
+WA=GR
+TA=GR*(1.+0.5*ECKERT*PRNDTL(H1)*(1.-GR))
+INIT(IN:JJ:,W1A,ZERO,WA)
+INIT(IN:JJ:,H1A,ZERO,TA)
ENDDO
GROUP 13. Boundary conditions and special sources
PATCH(WALLTOP,NWALL,1,NX,NY,NY,1,NZ,1,1)
COVAL(WALLTOP,W1,1.0,WTOP)
COVAL(WALLTOP,H1,1.0/PRNDTL(H1),1.0)
PATCH(WALLBOT,SWALL,1,NX,1,1,1,NZ,1,1)
COVAL(WALLBOT,W1,1.0,0.0)
COVAL(WALLBOT,H1,1.0/PRNDTL(H1),0.0)

GROUP 15. Termination of sweeps
LSWEEP=1;LITHYD=10
GROUP 22. Spot-value print-out
IYMON=NY;TSTSWP=-1
GROUP 23. Field print-out and plot control
NPLT=1;NYPRIN=1;NZPRIN=1
GROUP 24. Dumps for restarts
```