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Simplied Approach to Estimating Tube side Heat Transfer Coefficients V.Ganapathy

For boiler design purposes,where the fluids are generally in turbulent flow region,the following equation may be used to determine the tube side heat transfer coefficient.

 NU=0.023Re0.8 Pr0.4               (1)

where
Nusselt number NU=hd/12k
Reynolds number Re=15.2Wd/m
Prandtl number Pr=mCp/k
h=tube side heat transfer coefficient,Btu/ft2hF
d=tube inner diameter,in
W=flow rate per tube,lb/h
k=thermal conductivity,Btu/fthF
Cp=specific heat,Btu/lbF
m=viscosity,lb/fth
The fluid properties are estimated at the average fluid temperature
Substituting the above expressions into the equation (1) and simplifying we have:

h = 2.44W0.8 C/d1.8

where C=(Cp/m)0.4k0.6

Computation of C requires reference to fluid properties and hence can be tedious.C has been computed by the author for various fluids and for good engineering estimates,the equations/data shown below may be used.
C values for Saturated,Superheated steam 
pressure,psia 100 500 1000 2000
sat steam 0.244 0.417 0.490 0.900
400 F 0.271
500 0.273 0.360
600 0.281 0.322 0.413
700 0.291 0.316 0.358 0.520
800 0.305 0.320 0.345 0.420
900 0.317 0.327 0.347 0.394
1000 F 0.325 0.340 0.353 0.386

Example: Determine the tube side heat transfer coefficient when 5000 lb/h of superheated steam at 1000 psia and 800 F flows inside a superheater tube of inner diameter 1.75 in.
Solution: C =0.345
h =2.44 x50000.8x0.345/1.751.8 = 271 Btu/ft2hF
C values for air,flue gases at atmospheric pressure 
temp,F 200 400 600 800 1000 1200
C 0.162 0.172 0.180 0.187 0.194 0.205
For flue gases,increase C by about 5 to 10 % depending on % water vapor.Or if flue gas analysis is available,use the method discussed below to estimate mixture properties. The "Programs for Steam Plant Engineers" software(see Homepage) includes a program to determine gas mixture properties at atmospheric pressure given the gas analysis. For effect of gas pressure on C,see author's Steam Plant calculations Manual book.
Example:200 lb/h of air at 800 F and at atmospheric pressure flows inside a tube of inner diameter 1.75 in. Determine h.
Soluton: C=0.187. h =2.44x0.187x2000.8/1.751.8 =11.55 Btu/ft2hF
C for compressed water
 C =10-1.318+.214 ln(t)
where t= water temperature,F
Example:In a boiler economizer,8000 lb/h water at 500 psia,300 F flows in a tube of inner dia 1.7 in. Determine h.
Solution: h=2.44x80000.8 x10-1.318+.214ln(300)/1.71.8 =995 Btu/ft2hF
ESTIMATING GAS MIXTURE PROPERTIES
Determine specific heat,viscosity and thermal conductivity of a flue gas mixture at atmospheric pressure have the following data:

    Table:  data of gas properties
  gas % volume  Cp  m   k MW
 N2   80  0.286  0.108  0.03  28
 O2  12  0.270  0.125  0.043  32
 SO2   8  0.210  0.105  0.040  64
The following equations may be used to determine mixture properties given induvidual gas data:
 mm= Syimi (MWi)0.5/ Syi (MWi)0.5 
 km=Syiki (MWi)0.33  / Syi (MWi)0.33
  Cpm= SyiCpi MW /Syi MW
mm =mixture viscosity,lb/fth
km=mixture thermal conductivity,Btu/fthF
Cpm=mixture specific heat,Btu/lbF
MW =molecular weight
subscript i refers to induvidual gas and m for mixture; y refers to volumetric fraction of each gas.

Solution:

Cpm =0.286x0.8x28+0.27x0.12x32+0.21x0.08x64/(0.8x28+0.12x32+0.08x64) =0.272 Btu/lbF
 mm = 0.108x280.5x0.8+0.125x320.5x0.12+0.105x640.5x0.08/(0.8x280.5+0.12x320.5+0.08x640.5)=0.109 lb/fth
 km = 0.03x280.33x0.8+0.043x320.33x0.12+0.04x640.33x0.08/(0.8x280.33+0.12x320.33+0.08x640.33)=0.032 Btu/fthF

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