Cooling Towers
Where : G = 0.1524 m ( 0.50 ft )
Equations 12 through 15 inclusive can be iterated for different values of L and N s to find an acceptable tube length ( L ), bundle width ( W b
) and number of bundles
( N s
) for the application .
Conclusion The above method , while simple , provides the user with a quick and reasonably accurate way to thermally size a set of plume abatement coils given a defined set of conditions . The author hopes users of this calculation method find it useful for budget designs . Future articles are being considered for additional tube sizes ( OD ), pitches ( Pt & Pl ), tube side fouling factors ( f ) as well as a calculation of air side and tube side pressure drops .
References
1 . W . M . Kays , A . L . London : Compact Heat Exchangers , Third Edition , McGraw-Hill Book Company , New York , 1984
2 . F . P . Incropera , D . P . De Witt : Fundamentals of Heat and Mass Transfer , Third Edition , John Wiley and Sons , New York , 1990
3 . The Basics of Air-Cooled Heat Exchangers , Hudson Products Corporation , Texas , 2007
Sample calculation
Size a plume abatement coil for the following conditions :
T ai
= 5.0 C ( 41.0 F )
T ao
= 15.6 C ( 60.0 F )
M a
= 1,216,966 kg / hr ( 2,682,194 lb / hr )
cp a
= 1013.1 J / kg C ( 0.242 Btu / lb F )
Th i
= 23.9 C ( 75.0 F )
Th o
= 21.8 C ( 71.2 F )
cp h
= 4,245.2 J / kg C ( 1.014 Btu / lb F ) OD = 25.4 mm ( 1.00 in ) t = 0.89 mm ( 0.035 in ) Pt = 63.5 mm ( 2.50 in ) L = 6.93 m ( 22.75 ft ) U = 2,381,330 J / hr sqm C ( 116.5 Btu hr sqft F )
N s
= 8 bundles
Solve for the required heat duty as expressed in equation 1 :
Q a
= M a cp a
( T ai
– T ao )
Q a
= ( 1,216,966 kg / hr )( 1013.1 J / kg C )( 15.6 C – 5.0 C )
Q a
= 13,035,173,549 J / hr
Solve for the hot side mass flow as expressed in equation 3 assuming a 2.1 C difference between the hot fluid inlet and outlet temperatures :
M h
= Q / ( cp h ( T hi
– T ho ))
M h
= 13,035,173,549 J / hr / ( 4,245.2 J / kg C ( 23.9 C – 21.8 C ))
M h
= 1,454,492 kg / hr
Calculate the heat transfer effectiveness per equation 8 : E = Q / Q max E = 13,035,173,549 J / hr / 23,289,327,412 J / hr E = 0.560
Determining the value of NTU per Figure 6 with E = 0.560 and C r
= 0.200 you get an NTU value of 0.90 . Now , from equation 10 we can calculate the bare tube surface area using the overall heat transfer coefficient provided in Table 1 :
A = NTU C min
/ U A = ( 0.90 )( 1,232,964,392 J / hr C / 2,381,331 J / hr sqm C ) A = 466.0 sqm Determine the number of tube rows in the bundle from equation 11 and Table 2 :
N z
= [( T hi
-T ho
)/( T hi
-T ci
)]( U c / U )
N z
= [( 23.9 C – 21.8 C )/( 23.9 C -5.0 C )]( 2,044,061 / 2,381,331 J / hr sqm C )
N z
= 0.096 From Table 2 , N = 4 rows .
The total number of tubes in the bundle can now be determined by equation 12 :
N t
= A / [( pi )( OD / w )( L )]
N t
= 466.0 sqm / [( 3.1416 )( 25.4 mm / 1000 mm / 1 m ) ( 6.93 m )]
N t
= 842.1 tubes rounded down to 842 tubes
Calculate the heat capacity for both the hot fluid and air per equations 4 and 5 :
C h
= M h cp h
= Q /( T hi
– T ho )
C h
= 13,035,173,549 J / hr /( 23.9 C – 21.8 C )
C h
= 6,174,555,892 J / hr C
C a
= M a cp a
= Q / ( T ai
– T ao )
C a
= 13,035,173,549 J / hr / ( 15.6 C – 5.0 C )
C a
= 1,232,964,392 J / hr C
Calculate the heat capacity ratio per equation 6 with
C min
= C a and C max
= C h :
C r
= C min / C max
C r
= 1,232,964,392 J / hr C / 6,178,079,644 J / hr C
C r
= 0.200
Calculate the maximum heat transfer rate per equation 7 :
Q max
= C min ( T hi
– T ai )
Q max
= 1,232,964,392 J / hr C ( 23.9 C – 5.0 C )
Q max
= 23,289,327,412 J / hr
Based on the number of rows being 4 , the number of tubes per row of the exchanger can be determined by equation 13 :
N r
= N t / N
N r
= 842 / 4
N r
= 210.5 rounded up to 211 tubes .
From here , the overall width of the heat exchanger surface can be determined by equation 14 as follows :
W = N r
( P t
/ w ) W = 211 ( 63.5 mm / 1000 mm / m ) W = 13.4 m
The approximate width of an individual bundle can be determined from equation 15 as follows :
W b
= ( W / N s ) + G
W b
= ( 13.4 m / 8 bundles ) + 0.1524 m
W b
= 1.82 m / bundle
24 Heat Exchanger World October 2022 www . heat-exchanger-world . com