bessel
DESCRIPTION
excelTRANSCRIPT
04/17/2023 document.xls
UNSTEADY STATE HEATING WITH HOT WATER
4/17/2023 Kern, p627
Input data
Heat-up time h 4
Overall HTC Btu/h sq.ft °F U 38 Wt x Sp.ht
Heated fluid heat capacity Btu Mc 6206 = 6206 1
Heating fluid heat capacity Btu/h WC 15000 = 15000 1
Starting batch temperature °F t1 70
Ending batch temperature °F t2 160
Heating fluid inlet temp °F T1 185
Heat transfer area A sq.ft 67.81229
K 1.18743
LHS ln(T1-t1/T1-t2) 1.526056 solve for these two
RHS WC*(K-1)*t/Mc/K 1.526055 rows being equal
04/17/2023 document.xls
Time to heat a tank with steam at constant temperature
Tank volume gal 7200 Heat-up time hr 4.75
Density pcf 62.4 Max heat transfer rate Btu/h 900000
Specific heat Btu/lbF 1
Coil HTC Btu/sf.lb.F 45
Coil area sf 100
Start temp F 80
End temp F 140
Steam temp F 280
Page
Transient heating coefficients
from AIChE 1931 p311 - 'The drying of porous solids - diffusion calculations' by A.B.Newman
Enter data in yellow cells, and run solver.
Bessel roots 1 2
root 2.4048 5.5201
squared 5.783063 30.4715
Container dia 2r in 3
Container ht 2l in 4.22
Specific ht Cp Btu/lbF 1
Thermal cond k Btu/hsfF/f 0.25
Density s lb/cuf 62.4
Time t min 4
Diffusivity D k/Cps 0.004006
Radial kt/r^2 1.066667
Longit kt/l^2 0.539071
Coefficients
A' 0.003964
R' 0.001448
Temp start To F 270
Temp surface Ti F 185
End average Tav F 185.0005 Assuming negligible surface resistance
Including surface resistance
Outside HTC h Btu/hsfF 50
Radial mr k/rh 0.04 Int sol #NAME? #NAME?
Longit ml k/lh 0.028436 Int sol #NAME? #NAME?
Char # rad w 2.310798 5.306801 first and second roots
Char # long u 2.337504 5.366504 needed if x<0.2
X radial 0.017094
X longit 0.008639
a radial #NAME? #NAME? first term only
a longit #NAME? #NAME?
Y #NAME?
Temp centre F #NAME?
A B C D E F G1
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from AIChE 1931 p311 - 'The drying of porous solids - diffusion calculations' by A.B.Newman
3 4 pi^2
8.654 11.792 9.869604
74.89172 139.0513
Assuming negligible surface resistance
first term only
H I J1
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