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GROUP 1. Run title and other preliminaries
PHOTON USE
AUTOPLOT
file
phi 5

cl
msg MHD PLANE CHANNEL FLOW
msg Hartmann number = 10 Reynolds number =100
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

msg press  to end
pause
end
END_USE
DISPLAY

TEXT(1D Laminar MHD Channel Flow
TITLE

DISPLAY
This problem concerns the steady fully-developed laminar
flow of an incompressible electrically-conducting fluid
in the positive z-direction of a plane channel. A uniform
magnetic field By is imposed normal to the walls and a
current jx is induced in the fluid in the x-direction,
together with a magnetic field Bz in the z-direction. The
problem neglects end effects, secondary flows, Hall effect
and ion-slip phenomena.
ENDDIS

The dimensionless momentum equation to be solved is:

dp/dz + d/dy(dw/dy)/Re + Ha*Ha(K-w)/Re = 0

where y =y/yin
z =z/yin
w =w/win
p=p/(rho*win**2)
Re=win*yin/enul
Ha=sig*(By*yin)**2/(rho1*enul)
K =Ex/(win*By)

Here, yin is the channel half width (m), By is
the imposed magnetic flux density in the +ve y
direction (volt.s/m**2), sig is the electric
conductivity (ohm/m) and Ex is electric field
intensity in the +ve x-direction (volt/m).

The Hartmann number Ha represents the ratio of
the electromagnetic forces to the viscous forces.

The voltage ratio K is the ratio of the voltage
to the open-circuit voltage. If K=0, this corresponds
to a short-circuit condition. When K=1 the net current
flow is zero, which is known as the open-circuit
condition. This is the classical Hartmann problem.
Further, if K < 1 the channel will act as a MHD pump,
whereas if K > 1 the channel will act as a flowmeter.

The analytical solution to this problem has been
presented in 'Engineering Magnetohydrodynamics',
Chapter 10, G.W.Sutton and A.Sherman, McGraw Hill,
(1965).

REAL(YIN,HIN,WIN);YIN=1.0;WIN=1.0
GROUP 2. Transience; time-step specification
CARTES=T
GROUP 4. Y-direction grid specification
NY=40;GRDPWR(Y,NY,YIN,1.)
GROUP 5. Z-direction grid specification
ZWLAST=0.1
GROUP 7. Variables stored, solved & named
SOLVE(W1);STORE(W1A)
GROUP 8. Terms (in differential equations) & devices
TERMS(W1,N,N,P,P,P,P)
GROUP 9. Properties of the medium (or media)
RHO1=1.;ENUT=0.
REAL(REY,FLOWIN);REY=100.;ENUL=1./REY
REAL(HA,KVOLT);HA=10.0;KVOLT=1.0
HA
KVOLT
REY
GROUP 11. Initialization of variable or porosity fields
FIINIT(W1)=WIN
** compute analytical solutions
REAL(WA,GR,HAY);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;HAY=GR*HA
+WA=HA*(COSH(HA)-COSH(HAY))/(HA*COSH(HA)-SINH(HA))
+INIT(IN:JJ:,W1A,ZERO,WA)
ENDDO
GROUP 13. Boundary conditions and special sources
PATCH(WALL,NWALL,1,NX,NY,NY,1,NZ,1,1)
COVAL(WALL,W1,1.0,0.0)
** activate fully-developed pressure-drop calculation
FDFSOL=T;USOURC=T
FLOWIN=RHO1*WIN*YIN
PATCH(FDFW1DP,VOLUME,1,NX,1,NY,1,NZ,1,1)
COVAL(FDFW1DP,W1,FLOWIN,GRND1)

PATCH(MHDFOR,VOLUME,1,NX,1,NY,1,NZ,1,1)
COVAL(MHDFOR,W1,HA*HA/REY,KVOLT)

GROUP 15. Termination of sweeps
LSWEEP=5;LITHYD=8
GROUP 16. Termination of iterations
RESREF(W1)=1.E-12*WIN*YIN
GROUP 17. Under-relaxation devices
REAL(DTF);DTF=10.0*ZWLAST/WIN
RELAX(W1,FALSDT,DTF)
GROUP 19. Data communicated by satellite to GROUND
FLOWIN=RHO1*WIN*YIN
GROUP 22. Spot-value print-out
IYMON=NY;TSTSWP=-1
GROUP 23. Field print-out and plot control
NPLT=1;NYPRIN=1;NZPRIN=1;NTPRIN=2
GROUP 24. Dumps for restarts
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