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- .MCD 20000 0
- .CMD PLOTFORMAT logs=0,0 subdivs=1,1 size=5,15 type=l
- .CMD FORMAT rd=d ct=10 im=i et=3 zt=15 pr=3 mass length time charge
- .CMD SET ORIGIN 0
- .CMD SET TOL 0.001000
- .CMD MARGIN 0
- .CMD LINELENGTH 78
- .CMD SET PRNCOLWIDTH 8
- .CMD SET PRNPRECISION 4
- .TXT 1 1 1 44
- a1,44,42,43
- HEAT TRANSFER -- FLAT WALL WITH TWO LAYERS
- .TXT 2 2 1 27
- a1,27,25,26
- First, define unit system
- .EQN 2 6 1 9
- ft~1L
- .EQN 0 11 3 9
- in~ft/12
- .EQN 0 12 1 10
- sec~1T
- .EQN 0 13 1 9
- lb~1M
- .TXT 0 10 1 15
- a1,15,13,14
- (pounds mass)
- .EQN 2 -23 1 15
- hr~3600*sec
- .EQN 2 -23 4 17
- g~32.174*ft/sec^2
- .EQN 0 23 1 12
- lbf~lb*g
- .EQN 0 20 3 21
- Btu~20.031*ft*lbf/sec
- .EQN 3 -20 1 20
- J~0.07376*ft*lbf
- .EQN 1 -23 3 9
- W~J/sec
- .EQN 1 23 1 10
- degF~1
- .TXT 0 18 3 26
- a3,26,24,68
- (for convenience, define
- Fahrenheit degree as
- dimensionless unit)
- .EQN 5 -41 4 28
- σ~1.713*10^-9*Btu/(ft^2*hr*degF)
- .TXT 1 31 1 29
- a1,29,27,28
- (Stefan-Boltzmann constant)
- .TXT 4 -37 1 24
- a1,24,22,23
- Parameters of problem:
- .EQN 2 6 2 16
- Area:25*ft^2
- .TXT 1 24 1 15
- a1,15,13,14
- ... wall area
- .TXT 2 -25 2 27
- a2,27,25,53
- First layer of wall: wood
- -------------------------
- .EQN 3 7 1 14
- t1:.25*in
- .TXT 0 28 1 15
- a1,15,13,14
- ... thickness
- .EQN 2 -28 4 23
- h1:4.1*Btu/(hr*ft^2*degF)
- .TXT 1 28 1 30
- a1,30,28,29
- ... inside convection coeff.
- .EQN 4 -28 3 23
- k1:0.06*Btu/(hr*ft*degF)
- .TXT 1 28 1 36
- a1,36,34,35
- ... conductive coefficient of wood
- .EQN 3 -28 1 15
- T0:75*degF
- .TXT 0 28 1 32
- a1,32,30,31
- ... maximum inside temperature
- .TXT 2 -35 2 44
- a2,44,42,87
- Second layer of wall: rock-wool insulation
- ------------------------------------------
- .EQN 3 7 1 14
- t2:.25*in
- .TXT 0 28 1 15
- a1,15,13,14
- ... thickness
- .EQN 2 -28 4 24
- h2:21.8*Btu/(hr*ft^2*degF)
- .TXT 3 28 1 31
- a1,31,29,30
- ... outside convection coeff.
- .EQN 2 -28 3 24
- k2:0.017*Btu/(hr*ft*degF)
- .TXT 1 28 2 31
- a2,31,29,45
- ... conductive coefficient of
- rock-wool
- .EQN 3 -28 1 16
- T4:-20*degF
- .TXT 0 28 1 33
- a1,33,31,32
- ... minimum outside temperature
- .TXT 2 -40 1 21
- a1,21,19,20
- Compute resistances
- .EQN 2 7 3 16
- Rh1:1/(h1*Area)
- .TXT 1 30 2 28
- a2,28,26,47
- ... convective resistance,
- inside surface
- .EQN 3 -30 3 16
- Rk1:t1/(k1*Area)
- .TXT 1 30 2 28
- a2,28,26,45
- ... conductive resistance,
- inside layer
- .EQN 3 -30 3 16
- Rk2:t2/(k2*Area)
- .TXT 1 30 2 28
- a2,28,26,46
- ... conductive resistance,
- outside layer
- .EQN 3 -30 3 16
- Rh2:1/(h2*Area)
- .TXT 1 30 2 28
- a2,28,26,46
- ... convective resistance,
- outside layer
- .EQN 4 -30 1 31
- Rtot:Rh1+Rk1+Rk2+Rh2
- .TXT 0 30 1 22
- a1,22,20,21
- ... total resistance
- .TXT 2 -40 1 25
- a1,25,23,24
- Heat flow, temperatures
- .EQN 2 4 3 14
- Q:(T0-T4)/Rtot
- .EQN 0 22 3 19
- Q=?Btu/hr
- .TXT 1 21 3 26
- a3,26,24,67
- ... heat flow at time of
- maximum temperature
- difference
- .EQN 4 -21 1 14
- T0=?degF
- .TXT 0 21 1 32
- a1,32,30,31
- ... inside temperature (given)
- .EQN 2 -44 1 18
- T1:T0-Q*Rh1
- .EQN 0 23 1 18
- T1=?degF
- .TXT 0 21 1 32
- a1,32,30,31
- ... temperature of inside wall
- .EQN 2 -44 1 18
- T2:T1-Q*Rk1
- .EQN 0 23 1 18
- T2=?degF
- .TXT 0 21 1 32
- a1,32,30,31
- ... temperature between layers
- .EQN 2 -44 1 18
- T3:T2-Q*Rk2
- .EQN 0 23 1 18
- T3=?degF
- .TXT 0 21 1 33
- a1,33,31,32
- ... temperature of outside wall
- .EQN 2 -21 1 15
- T4=?degF
- .TXT 0 21 1 33
- a1,33,31,32
- ... outside temperature (given)
-