Back Calculation of Airside Coefficient from Design Conditions
As was the case with watertowater heat exchangers discussed in Chapter 16, the airside convection heat transfer coefficient for the AWHX may be found for the noncondensing normal mode of operation from vendor data to eliminate the need for hotside heat transfer correlations specific to the geometry and configuration of the HX. Table 17.4
TABLE 17.4
Design Basis or Test Conditions for Normal Noncondensing Mode of Operation
Total service water flow rate 

Service water flow rate per coil 

Entering water temperature 

Exiting water temperature 

Average water temperature 

Tubeside thermal conductivity 

Tubeside absolute viscosity 

Tubeside specific heat 

Tubeside density 

Tubeside temperature rise 

Tubeside heat transfer rate 

Entering air drybulb temperature 

Exiting air drybulb temperature 

Average air drybulb temperature 

Hotside thermal conductivity 

Hotside absolute viscosity 

Hotside specific heat 

LMTD correction factor 

Tubeside flow rate per coil 

Face velocity out of air side 

Relative humidity 

Total atmospheric pressure 
presents a list of the required design basis parameters for operating in the normal, noncondensing mode to be able to back calculate the airside coefficient of heat transfer.
The design fouling resistance on the air side and the tube side are specified based on the tube and fin materials and the corresponding resistances to heat transfer.
The overall heat transfer coefficient at design conditions, U_{design}, is calculated for the normal noncondensing mode of operation in Table 17.5.
The tubeside convection coefficient may be computed from the Petukhov correlation as in Chapter 16 (Table 17.6).
TABLE 17.5
Verification of U_{design} for Normal Noncondensing Mode of Operation
Greater terminal temperature difference 
(17.33) 

Lesser terminal temperature difference 
(17.34) 

Log mean temperature difference 
(17.35) 

Effective mean temperature difference 
(17.36) 

Design overall heat transfer coefficient 
(17.37) 
TABLE 17.6
TubeSide Convection Coefficient
Mass flow rate/tube 
(17.38) 

Volumetric flowrate/tube 
(17.39) 

Tube area 
(17.40) 

Tube velocity 
(17.41) 

Prandtl number 
(17.42) 

Reynolds number 
(17.43) 

Fanning friction factor 
(17.44) 

Nusselt number 
(17.45) 

Tubeside film coefficient 
(17.46) 
The hotside convection coefficient may be computed as follows: where and
and k, is the tube material thermal conductivity.
Calculation of Airside Mass Flow Rate and Heat Transfer
The airside volumetric flow is converted to mass flow using the ideal gas laws, and the airside heat transfer rate is calculated as shown in Table 17.7.
TABLE 17.7
AirSide Mass Flow Rate and Heat Transfer
Volumetric flow rate 
(17.50) 

Saturation pressure at T_{h}, 
(17.51) 

Partial pressure of the water vapor in the air 
(17.52) 

Partial pressure of the air^{3} 
(17.53) 

Humidity ratio^{2} 
(17.54) 

Mass flow rate of air^{4}^{5} 
(17.55) 

Mass of the water vapor 
(17.56) 

Total mass flow rate on the air side 
(17.57) 

Specific heat of moist air^{1} 
(17.5S) 

Density of air 
(17.59) 

Hotside flow measurement per coil 
(17.60) 

Airside heat transfer rate 
(17.61) 
Note: 1. c_{p}._{m} and c_{p}._{m}, are the specific heats of dry air and water vapor, respectively.
 2. m„ and m_{a} are the molecular weights of water and air, respectively.
 3. P„ is the pressure of the air.
 4. V is the volumetric flow rate.
 5. R is the gas constant, and T + 460 is the temperature of the air in “Rankinc.
Calculation of Airside Coefficient at Test Conditions
The value for h_{h} on the air side based on the test conditions may be computed based on a correlation by Taborek.^{1} If one assumes that the actual value for h_{h} is a function of some ideal value for the airside thermal conductivity for pure crossflow, then
where J_{T} is a correction factor that is a function of the various leakage and bypass paths and, therefore, remains constant for a given HX.
Therefore,
and
Reference 3 suggests the following correlation for AWHX:
Substituting,
Computing “Apparent” Fouling Resistance
Therefore, the total “apparent” fouling resistance as determined by the test may be computed as follows:
Calculating Heat Transfer Rate at Reference Design Basis Accident Conditions
The overall heat transfer coefficient at the design basis limiting conditions, U*, may be expressed as follows:
where A* is calculated as in the case of the design and test conditions (see Section 16.8). Therefore,
It should be noted that the above analysis is applicable only if condensation is not occurring during the AWHX test. The calculation of U* is not valid for accident conditions when water is being condensed from saturated air as a result of a pipe rupture. Such analyses are the purview of the nuclear steam supply system (NSSS) provider based on proprietary tests.
Uncertainty
The method for calculating the uncertainties contained herein is the same as in Section 16.9. However, the uncertainty of the “apparent” fouling as it applies to AWHX deserves additional emphasis.
Fouling resistance measured during a test is defined as follows:
As may be seen from the equations above, the uncertainty of the fouling resistance is a function of the uncertainties of U,_{esp} h,„ and h_{c}. The sensitivity coefficients, в, and uncertainty of the fouling are determined numerically by perturbing each parameter plus and minus by the amount of the uncertainty to determine the impact on the fouling
The sensitivity coefficients are
and
The overall coefficient of heat transfer indicated by the test conditions, U_{test}, may be calculated as follows:
The uncertainty of U_{tes}, may be determined by first calculating the sensitivity coefficients for the variables Q_{ave} and EMTD. The area, A, is assumed to be constant.
The weighted average heat transfer rate and the uncertainty of the average heat transfer rate may be calculated as follows:
One may calculate the uncertainty of the EMTD as a function of the uncertainties of the temperatures measured. In addition, Example K.l in Reference 4 includes additional uncertainty to account for the uncertainty associated with possible variation in the HX fouling by assuming a Biot number of 0.5 for a watertowater HX (see Appendix G of Reference 4).
Defining
An additional uncertainty in the EMTD of 2% is assumed for incomplete mixing in the HX.
The sensitivity coefficients for EMTD to temperature as found in Appendix В of Reference 4 may be computed as follows:
The sensitivity coefficients for the variation in fouling and incomplete mixing are 1.0.
The hotstream and coldstream heat transfer rates may now be calculated as follows:
For the heat transfer rate, Q, the independent variables are the mass flow rate, the specific heat, and the inlet and outlet temperatures. The overall uncertainty of the heat transfer rate is the root mean square of the sum of the uncertainty contributions. For example, the uncertainty of Q_{c} would be as follows:
Table B.2 of Reference 4 shows the resulting equations for the sensitivity coefficient for each independent variable:
References
 1. Thomas, L. C., Heat Transfer Professional Version, Prentice Hall. Englewood Cliffs, NJ. 1993, p. 739.
 2. Gardner, K. A., Fin Efficiency of Extended Surfaces, Transactions of the ASME, vol. 67, 1945. p. 621.
 3. ASME PTC 301991, Air Cooled Heat Exchangers, American Society of Mechanical Engineers, 1991.
 4. ASME PTC 12.52000, Single Phase Heat Exchangers, American Society of Mechanical Engineers, September, 2000.