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Air cooled heat exchanger design : step by step calculation guide

How to design an air heat exchanger ?

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Section summary
Introduction to air cooled heat exchangers
Step by step design of an air cooled heat exchanger
Step by step example calculation of an air cooled heat exchanger
Free air cooled heat exchanger design calculator Excel

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This page is giving a calculation method to design step by step air heat exchangers.

Introduction to air cooled heat exchangers

Air cooled heat exchangers are appealing as they are using a free resource to cool down a process fluid : air. They are typically installed in water network, air conditioning systems or pneumatic conveying (as aftercoolers).

They are typically made of finned tubes into which the process fluid to cool is circulated, and a fan which is forcing the cooling air through the heat exchanger.

1. STEP 1 : Assume the heat exchanger geometry

There are different standard geometries for air cooled heat exchangers. The geometries are related to a compromise in between cost of construction and efficiency of the heat exchanger. The following table is giving typical design [Chopey] :

	Face velocity (FV)
	8 fins / inch (315 fins / m) 2.375 inch pitch (0.0603 m)		10 fins / inch (394 fins / m) 2.375 inch pitch (0.0603 m)		10 fins / inch (394 fins / m) 2.5 inch pitch (0.0635 m)
Number of rows	ft/min	m/s	ft/min	m/s	ft/min	m/s
3	650	3.3	625	3.18	700	3.56
4	615	3.12	600	3.05	660	3.35
5	585	2.97	575	2.92	625	3.18
6	560	2.84	550	2.79	600	3.05

The Engineer designing the air cooled heat exchanger is assuming a geometry. The pitch is dependent on the heat transfer coefficient on the inside of the tubes. If it is likely to be high and greater than the heat transfer coefficient on the air side, then a 2.5 inch pitch is preferred, 2.375 on the contrary.

2. STEP 2 : Gather the data required for the design

The following data must be gathered in order to perform the calculation :

Sizing data of the heat exchanger

• The material of construction of the tubes and the thermal conductivity of the material
• The tubes inside and outside diameters
• A geometry assumed from the table above

Process operation parameters :

• Temperature of the cooling air
• Flowrate of the fluid to cool down
• Inlet temperature of the fluid to cool down
• Target (outlet) temperature of the fluid to cool down
• The heat exchange coefficient on the tubes side

3. STEP 3 : Calculate the air side heat transfer coefficient

The following formula is applied to calculate the air side heat transfer coefficient, depending on the density of fins on the tubes :

With :

h_a = heat exchange coefficient on air side (BTU/h.ft².F)
FV = face velocity (see table 1) (ft/min)

4. STEP 4 : Calculate the conduction coefficient through the tube

The heat transfer coefficient through the tube can be calculated with the following equation :

h_w = 2*λ_w/(D_o-D_i)

With :

h_w = heat transfer coefficient through the tube material (BTU/h.ft².F)
λ_w = thermal conductivity of the tube material (BTU/h.ft².F)
D_o = outside diameter of the tube (in)
D_i = inside diameter of the tube (in)

5. STEP 5 : Calculate the overall heat transfer coefficient

The overall heat transfer coefficient can be calculated with the following formula :

With :

U = overall heat transfer coefficient (BTU/h.ft².F)
h_a = heat transfer coefficient on the air side (BTU/h.ft².F)
h_i = heat transfer coefficient on the tube side (BTU/h.ft².F)
h_w = conduction heat transfer coefficient (BTU/h.ft².F)
h_s = fouling coefficient  (BTU/h.ft².F)

6. STEP 6 : Estimate the air outlet temperature

The following table can be used to estimate the air outlet temperature :

	Outlet air temperature, c
Process inlet temperature, c	U=50 (BTU/h.ft2.F)	U=100 (BTU/h.ft2.F)	U=150 (BTU/h.ft2.F)
175	90	95	100
150	75	80	85
125	70	75	80
100	60	65	70
90	55	60	65
80	50	55	60
70	48	50	55
60	45	48	50
50	40	41	42

(This table is based on an ambient temperature in between 32 and 37c)

7. STEP 7 : Calculate the size of the air cooled heat exchanger

The heat exchanger width can be calculated with the following formula :

Y = width = FA / L

With :

FA = Q / [FV*(T₂-T₁)*1.95]

Q = w*c*(t₂-t₁)

Y = width of the heat exchanger (ft)
FA = face area of the heat exchanger (ft²)
L = length of the tubes (ft)

Note that the length of the heat exchanger L has a typical maximum of 48 ft , although it may be required to shorten it due to plant layout reasons.

Q = required heat duty of the heat exchanger (BTU/h)
FV = face velocity (ft/min)
T₁ = air inlet temperature (c)
T₂ = air outlet temperature (c)
w = flowrate of the fluid to cool (lb/h)
c = specific heat of the fluid to cool
t₁ = inlet temperature of the fluid to cool (c)
t₂ = outlet temperature of the fluid to cool (c)

8. STEP 8 : Verify if the calculated heat exchanger is sufficient

Air cooled heat exchangers have standard sizes. An actual design must then be chosen. The table below is providing some references for those standard sizes :

	Number of tube rows
	4	5	6
Bundle width (ft)	12	10	9.5

The actual width of the heat exchanger must then be calculated to have a width close to the calculated width via :

Y/standard_width = number of elements

One must then verify if the number of elements calculated is able to deliver the right heat exchange duty. To verify if the proposed heat exchanger is fulfilling the design requirement, the following must be calculated :

• Calculate the exhaust temperature T₂

(T₂-T₁) = Q / [FA*FV*1.95] = Q / [Y*L*FV*1.95]

T₂ = Q / [Y*L*FV*1.95] + T₁

• Calculate the mean temperature difference :

ΔT_m = [(t₁-T₂)-(t₂-T₁)]/ln[(t₁-T₂)/(t₂-T₁]

• Calculate the area required for reaching the exchange duty under this mean temperature difference :

A_calculated = Q/(U*ΔT_m)

• The last step is to verify if the calculated area is less than the available area in the heat exchanger, in case it can be used, or is the calculated area is more than the available area, which means the design of the heat exchanger must be reviewed.

A_available = Nr*Nt*π*D₀*L

With :

N_t = Y/pitch = number of tubes per row
N_r = number of rows
D_o = outside diameter of the tubes
L = length of the tubes

• If the area available is > area calculated (required) then the design is acceptable
• If the area available is < area calculated (required) then the design must be changed, typically the width of a bundle must be increased (it increases by steps of 0.5 ft)

9. STEP 9 : calculate the air side pressure drop and fan power requirement

The following correlations can be used to calculate the air pressure drop :

For 10 fins / in 2.3175 in spacing	ΔPa = 0.0047*Nr*(FV/100)1.8
For 8 fins / in 2.3175 in spacing	ΔPa = 0.0044*Nr*(FV/100)1.8
For 10 fins / in 2.5 in spacing	ΔPa = 0.0037*Nr*(FV/100)1.8

With :

ΔPa = air pressure drop (in water)
N_r = number of rows
FV = face velocity (ft/min)

The fan power requirement can be calculated thanks to the following correlation :

bhp = FV*FA*(T₂+273.15)*(ΔPa+0.1)/(1.15*10⁶)

With :

bhp = brake horse power require for the fan drive
FV = face velocity (ft/min)
FA = face area, in ft2 (Nb.Y.L)
T₂ = air outlet temperature (c)
ΔPa = air pressure drop (in water)

10. STEP by STEP Example : air cooler calculation

An air cooled heat exchanger must be calculated with the following characteristics :

• The heat exchanger is to be built in Stainless Steel
• The outside diameter of the tubes in 1 inch
• The tubes have fins, with 10 fins / inch
• The cooling air is assumed to be 35c
• The process fluid (water) to cool down is assumed to be 150c
• The target process fluid temperature is 50c
• The process fluid flow rate is 500 000 lb/h

What is the size of the air cooled heat exchanger that fulfills this duty ?

Please refer to the Excel calculation tool

11. Free air cooled heat exchanger design calculator Excel

Air cooled heat exchanger design can be estimated thanks to this free Excel calculator : Calculation Tool - air cooled heat exchanger design calculator Excel (click here)

Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.

Sources

[Chopey] Handbook of Chemical Engineering calculations, Chopey et al, McGraw Hill, 2004