```
L(791)
DISPLAY
Transient analysis of a counter-flow heat-exchanger with
allowance for the thermal capacity of the metal.
This Q1 contains PHOTNON USE commands.
ENDDIS
PHOTON USE
p
parphi

msg The computational grid. Note: z = time. Press return for T1
gr y 1
pause
msg T1, 1st-fluid temperature. Note: z = time. Press return for T2
con 1sth y 1 fi;0.05
pause
con off;red
msg T2, 2nd-fluid temperature. Note: z = time. Press return for Tm
con 2ndh y 1 fi;0.05
pause
con off;red
msg Tm, metal temperature. Note: z = time. Press E to end
con metl y 1 fi;0.05
pause
ENDUSE

GROUP 1. Run title
TEXT(791 + Allowance For Metal Capacity
TITLE
User-defined variables:
REAL(CAPM,COEF1O,COEF2O,COEFMO)
CAPM=0.1;COEFMO=CAPM/DELT

In order to accelerate convergence a simple version of the
"partial-elimination algorithm" is employed. This entails
eliminating the late-time metal temperature from the
equations for heat transfer from fluid to metal. Then each
fluid is connected thermally with the other fluid and with
the temperature of the early-time metal. This technique
could be further extended with advantage.

The heat-transfer resistance offered by the metal is
accounted for implicitly in the values which are ascribed
to COEF1 and COEF2.

COEF12=COEF1*COEF2/(COEF1+COEF2+COEFMO)
COEF1O=COEF1*COEFMO/(COEF1+COEF2+COEFMO)
COEF2O=COEF2*COEFMO/(COEF1+COEF2+COEFMO)

Arrange that metal temperature, named METL, occupies
store with index 1 above 2NDH and 2 above 1STH.

SOLVE(C1);NAME(C1)=METL;TERMS(METL,N,N,N,Y,N,N)
FIINIT(METL)=0.5*(T1IN+T2IN)

Repeat the COVALs using COEF12, which has changed
since it was calculated for case 2.
COVAL(NEPLUS,1STH,COEF12,LOCNE)
COVAL(NEMINUS,2NDH,COEF12,LOCNE)

Connect shell fluid with old metal
PATCH(NEO2,VOLUME,1,NX,1,NY,1,NZ,1,LSTEP)
COVAL(NEO2,1STH,COEF1O,LOCNE)

Connect metal with shell fluid
PATCH(NEM2,VOLUME,1,NX,1,NY,1,NZ,1,LSTEP)
COVAL(NEM2,METL,COEF1O,LOCNE)

Connect tube fluid with old metal
PATCH(NEO1,VOLUME,1,NX,1,NY,1,NZ,1,LSTEP)
COVAL(NEO1,2NDH,COEF2O,LOCNE)

Connect metal with tube fluid
PATCH(NEM1,VOLUME,1,NX,1,NY,1,NZ,1,LSTEP)
COVAL(NEM1,METL,COEF2O,LOCNE)

Transient for metal
COVAL(NEOLD,METL,COEFMO,LOCNE)

LSWEEP=10;RESREF(METL)=RESREF(1STH)*0.1

Output
OUTPUT(METL,N,N,Y,Y,Y,Y)
PLOT(PROFILES,METL,T2IN,T1IN)
PLOT(TIMEPLOT,METL,T2IN,T1IN)
NTPRIN=LSTEP/4
```