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- .MCD 25000 0
- .CMD SURFACEFORMAT rot=10 tilt=35 vScale=20 size=15,30 hide=n
- .CMD SKETCHFORMAT mag=1.000000,1.000000 center=0.500000,0.500000 size=15,30 box=y
- .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 0.001000000000000
- .CMD MARGIN 0
- .CMD LINELENGTH 78
- .CMD SET PRNCOLWIDTH 8
- .CMD SET PRNPRECISION 4
- .TXT 0 41 1 39
- a1,38,37,37
- Copyright (c) 1990 by Mathsoft, Inc.
- .TXT 2 -41 1 44
- a1,43,78,42
- FREE CONVECTION FROM PLATES AND CYLINDERS
- .TXT 2 0 3 79
- a3,78,78,204
- This document calculates free convection heat-transfer rate from plates and
- cylindrical objects such as tanks and pipes to a fluid such as atmospheric
- air.
- .TXT 4 0 1 50
- a1,49,78,48
- Enter fluid properties at the film temperature:
- .TXT 1 50 2 21
- a2,20,39,37
- specific heat at
- constant pressure
- .TXT 1 -50 1 10
- a1,9,78,8
- density
- .TXT 0 21 1 20
- a1,19,78,18
- dynamic viscosity
- .EQN 2 -21 4 16
- ▌:0.054*lb/ft^3
- .EQN 0 21 3 21
- µ:1.57*10^-5*lb/(ft*s)
- .EQN 0 29 3 17
- Cp:0.24*BTU/(lb*F)
- .TXT 4 0 2 15
- a2,14,78,22
- thermal
- conductivity
- .TXT 1 -50 2 20
- a2,19,31,29
- wall temperature
- (absolute)
- .EQN 0 19 2 22
- T.w:(460+500)*R
- .EQN 2 31 3 21
- KT:0.0197*BTU/(h*ft*F)
- .TXT 1 -50 2 21
- a2,20,39,30
- fluid temperature
- (absolute)
- .EQN 0 19 2 21
- T.a:(460+50)*R
- .TXT 3 39 1 20
- a1,19,37,18
- Press [Ctrl-PgDn]
- .TXT 1 -58 1 46
- a1,45,78,44
- Indicate the type of heat-transfer surface:
- .TXT 2 1 7 48
- a7,47,59,247
- 1 - vertical cylinder
- 2 - horizontal cylinder
- 3 - horizontal heated plate facing upward or
- 3 - horizontal cooled plate facing downward
- 4 - horizontal heated plate facing downward
- 4 - horizontal cooled plate facing upward
- 5 - vertical plate
- .EQN 2 55 1 10
- Sht:2
- .TXT 1 25 1 18
- a1,17,78,16
- Initialization:
- .EQN 0 18 1 11
- L:1*ft
- .EQN 0 14 1 12
- Dp:1*ft
- .EQN 0 13 1 12
- Lc:1*ft
- .EQN 0 13 1 11
- d:1*ft
- .EQN 3 -39 4 18
- ß:2/((T.a+T.w))
- .TXT 2 -100 1 40
- a1,39,78,38
- Enter the appropriate geometric data:
- .TXT 2 0 1 21
- a1,20,59,19
- cylinder: diameter
- .EQN 0 21 1 11
- d:1*ft
- .TXT 0 14 1 9
- a1,8,39,7
- plate:
- .TXT 0 8 2 18
- a2,17,35,26
- characteristic
- dimension
- .EQN 0 17 1 11
- L:5*ft
- .EQN 2 21 1 38
- Lt:if(Sht≈1,Lc,if(Sht≈2,d,L))
- .EQN 0 40 5 35
- GrPr:(g*Cp*ß*(T.w-T.a)*▌^2*Lt^3)/(KT*µ)
- .TXT 1 -111 1 9
- a1,8,68,7
- length
- .EQN 0 11 1 12
- Lc:1*ft
- .TXT 0 22 1 8
- a1,7,39,6
- depth
- .EQN 0 17 1 15
- Dp:0.05*ft
- .TXT 2 21 1 35
- a1,34,78,33
- Grashof-Prandtl numbers product:
- .TXT 1 -32 1 26
- a1,25,26,24
- Press [Ctrl-PgDn] twice
- .EQN 2 67 2 42
- r:if(GrPr>10^4,if(GrPr<10^9,1,2),0)
- .TXT 1 -34 1 26
- a1,25,78,24
- Identifying the regime:
- .EQN 2 34 3 45
- n:if(GrPr>10^4,if(GrPr<10^9,0.25,1/3),0)
- .TXT 1 -34 1 26
- a1,25,78,24
- constant for equations:
- .TXT 4 0 1 42
- a1,41,78,40
- Heat-transfer coefficient (BTU/h ft F):
- .EQN 2 15 4 17
- δT:(T.w-T.a)/(1*F)
- .EQN 1 -15 3 10
- L':Lt/ft
- .EQN 0 38 2 10
- ▐:δT^n
- .EQN 0 15 4 10
- Φ:▐/L'^n
- .EQN 5 -53 2 17
- h'[(1,1):0.29*Φ
- .EQN 0 25 2 17
- h'[(2,1):0.27*Φ
- .EQN 0 24 2 17
- h'[(3,1):0.27*Φ
- .EQN 3 -49 2 17
- h'[(1,2):0.19*▐
- .EQN 0 25 2 17
- h'[(2,2):0.18*▐
- .EQN 0 24 2 17
- h'[(3,2):0.22*▐
- .EQN 3 -49 2 17
- h'[(4,1):0.12*Φ
- .EQN 0 25 2 17
- h'[(5,1):0.29*Φ
- .EQN 0 24 2 17
- h'[(5,2):0.19*▐
- .EQN 3 -49 4 23
- ho:h'[(Sht,r)*BTU/(h*ft^2*F)
- .EQN 1 -27 4 22
- ho=?BTU/(h*ft^2*F)
- .EQN 0 54 1 33
- area:if(Sht≤2,π*d*Lc,Dp*L)
- .TXT 1 -109 1 52
- a1,51,78,50
- The free convection heat-transfer coefficient is:
- .TXT 1 109 1 25
- a1,24,78,23
- Rate of heat-transfer:
- .EQN 0 27 1 19
- Q:area*ho*δT*F
- .EQN 4 -81 3 19
- Q=?BTU/h
- .TXT 1 -55 1 50
- a1,49,78,48
- Rate of heat-transfer from the cylinder/plate:
- .TXT 24 5 1 19
- a1,18,16,17
- UNIT DEFINITIONS
- .TXT 0 24 1 23
- a1,22,25,21
- MKS (SI) unit system
- .TXT 3 -24 1 15
- a1,15,13,14
- I. Base units
- .EQN 1 5 1 8
- m~1L
- .EQN 0 18 1 9
- kg~1M
- .EQN 0 18 1 8
- s~1T
- .EQN 0 18 1 8
- K~1Q
- .TXT 2 -59 1 21
- a1,21,19,20
- II. Angular measure
- .EQN 1 5 1 9
- rad~1
- .EQN 0 18 3 15
- deg~π/180*rad
- .TXT 4 -23 1 28
- a1,28,26,27
- III. Derived units: Length
- .EQN 1 5 1 12
- cm~.01*m
- .EQN 0 18 1 13
- km~1000*m
- .EQN 0 18 1 13
- mm~.001*m
- .EQN 1 -36 1 14
- ft~.3048*m
- .EQN 0 18 1 14
- in~2.54*cm
- .EQN 0 18 1 11
- yd~3*ft
- .EQN 0 18 1 14
- mi~5280*ft
- .TXT 2 -59 1 25
- a1,25,23,24
- IV. Derived units: Mass
- .EQN 1 5 2 14
- gm~10^-3*kg
- .EQN 1 18 1 17
- tonne~1000*kg
- .EQN 0 18 1 19
- lb~453.59247*gm
- .EQN 2 -36 3 9
- oz~lb/16
- .EQN 1 18 1 15
- ton~2000*lb
- .EQN 1 18 1 18
- slug~32.174*lb
- .TXT 2 -41 1 25
- a1,24,22,23
- V. Derived units: Time
- .EQN 1 5 1 15
- minute~60*s
- .EQN 0 18 1 12
- h~3600*s
- .EQN 0 18 1 12
- day~24*h
- .EQN 2 -36 1 16
- year~365*day
- .TXT 2 -5 1 34
- a1,33,31,32
- VI. Derived units: Area, Volume
- .EQN 1 5 2 18
- hectare~10^4*m^2
- .EQN 0 36 2 17
- acre~4840*yd^2
- .TXT 3 -37 1 5
- a1,5,3,4
- ---
- .EQN 1 1 2 13
- L~(.1*m)^3
- .EQN 0 36 2 13
- mL~10^-3*L
- .EQN 2 0 2 22
- fl_oz~29.57353*cm^3
- .EQN 3 0 1 17
- gal~128*fl_oz
- .TXT 2 -41 1 45
- a1,44,42,43
- VII. Derived units: Velocity, Acceleration
- .EQN 1 5 3 10
- mph~mi/h
- .EQN 0 18 3 10
- kph~km/h
- .TXT 4 -19 1 6
- a1,6,4,5
- ----
- .EQN 1 1 4 16
- g~9.80665*m/s^2
- .TXT 1 22 1 27
- a1,27,25,26
- (acceleration of gravity)
- .TXT 4 -27 1 44
- a1,43,41,42
- VIII. Derived units: Force, Energy, Power
- .EQN 1 5 4 11
- N~kg*m/s^2
- .EQN 0 18 2 15
- dyne~10^-5*N
- .EQN 1 23 1 12
- lbf~g*lb
- .TXT 1 -1 1 15
- a1,15,13,14
- (pound force)
- .EQN 2 1 1 12
- kgf~g*kg
- .TXT 1 -1 1 18
- a1,18,16,17
- (kilogram force)
- .TXT 2 -41 1 7
- a1,6,4,5
- ----
- .EQN 1 1 1 9
- J~N*m
- .EQN 0 18 2 14
- erg~10^-7*J
- .EQN 0 23 1 16
- cal~4.1868*J
- .EQN 1 0 1 17
- kcal~1000*cal
- .EQN 1 -41 2 27
- BTU~1.05505585262*10^3*J
- .TXT 3 -1 1 7
- a1,6,4,5
- ----
- .EQN 1 1 3 7
- W~J/s
- .EQN 0 41 3 17
- hp~550*(ft*lbf)/s
- .EQN 1 -23 1 13
- kW~1000*W
- .TXT 2 22 1 23
- a1,23,21,22
- (standard horsepower)
- .TXT 2 -45 1 41
- a1,40,38,39
- IX. Derived units: Pressure, Viscosity
- .EQN 1 5 4 9
- Pa~N/m^2
- .EQN 0 18 4 11
- psi~lbf/in^2
- .EQN 0 18 2 22
- atm~1.01325*10^5*Pa
- .EQN 2 0 2 23
- torr~1.33322*10^2*Pa
- .EQN 2 0 2 24
- in_Hg~3.38638*10^3*Pa
- .TXT 3 -37 1 6
- a1,6,4,5
- ----
- .EQN 1 37 4 14
- St~10^-4*m^2/s
- .EQN 1 -36 1 14
- P~0.1*Pa*s
- .EQN 2 0 1 13
- cP~0.01*P
- .TXT 2 -5 1 17
- a1,16,73,15
- X. Temperature
- .EQN 2 5 1 7
- C~K
- .EQN 0 13 1 11
- F~1.8*C
- .EQN 0 16 1 7
- R~F
-