NU=0.023Re^0.8 Pr^0.4               (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 = 2.44W^0.8 C/d^1.8

where C=(Cp/m)^0.4k^0.6

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 x5000^0.8x0.345/1.75^1.8 = 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 =2.44x0.187x200^0.8/1.75^1.8 =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=2.44x8000^0.8 x10^{-1.318+.214ln(300)}/1.7^1.8 =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:
 m_m= Sy_im_i (MW_i)^0.5/ Sy_i (MW_i)^0.5 
 k_m=Sy_ik_i (MW_i)^0.33  / Sy_i (MW_i)^0.33
  C_pm= Sy_iC_pi MW_i  /Sy_i MW_i 
m_{m =mixture viscosity,lb/fth}
k_{m=mixture thermal conductivity,Btu/fthF}
C_{pm=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}
 m_{m =} 0.108x28^0.5x0.8+0.125x32^0.5x0.12+0.105x64^0.5x0.08/(0.8x28^0.5+0.12x32^0.5+0.08x64^0.5)=0.109 lb/fth
 k_{m =} 0.03x28^0.33x0.8+0.043x32^0.33x0.12+0.04x64^0.33x0.08/(0.8x28^0.33+0.12x32^0.33+0.08x64^0.33)=0.032 Btu/fthF

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