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Finned-Tube Heat Exchanger Design

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Finned-Tube Heat Exchanger Design

Finned-Tube Heat Exchanger Design

optymista93

(Student)

(OP)

11 Aug 21 11:51

Hi,

I'm a graduate Mechanical Engineer and currently working on design of finned-tube heat exchanger. (Liquid cooling exhaust gases from diesel engine.)

I found some pre-planning calculations that my previous co-worker did. After reading about heat exchange, I re-arranged and defined some more variables. Since I didn't really learn much about heat exchange at the curses I had on university, I want to ask for explanation of some of the equations. Additionally, it would be great if anyone can confirm that equations used are in fact correct.

Input values are marked with orange color.

Constants for calculation

Density of diesel fuel: ρD = 820 kg/m3

Atmospheric pressure: patm = 1atm = 101,3 kPa

Air Gas Constant: Rair=287,058 J/(kg*K)

Fin Tube Data (Constants from manufacturer, thus not an input)

Outside Surface Area of bare pipe: Ao = 0, m2/m
Surface Area of one fin, both sides: Apo = 0, m2/m
Pipe exterior surface not covered by fins: Afo = 0, m2/m


Pipe Dimensions

PipeOD = 26,7mm
PipeID = 21,4mm

Engine Data

Temperature Engine Data: TE_Data = 25°C
Engine Speed: neng = rev/min
Engine Power: Peng = 243 kW
Specific Fuel Consumption: MSC = 0,220 kg/kW*hr
Combustion Volume Flow: VCom_air=21, m3/min
Exhaust Volume Flow: VExh = 51,8 m3/min
Exhaust Temperature: TExh = 430°C

Mass Calculation

Mass Fuel Consumption: MDiesel = Peng*MSC
Volume Fuel Consumption: VDiesel = Mdiesel / ρD
Combustion air mass flow: MCom_air = (patm*VCom_air)/(Rair*TE_Data)
Total Mass Flow Engine in: Min = Mdiesel + MCom_air
Exhaust Mass Flow: MExh = (patm*VExh)/(Rair*TExh)
Ratio inlet mass/ outlet mass: Ratioin_out = Min/MExh


Design Limits

Ambient Design Temperature: Tamb = 40°C
Temperature Exhaust Gas Cooler Outlet: TE_out = 130°C

Temperature Exhaust Corrected for Ambient Design: TE_in = TExh+(Tamb-TE_Data)
Mean Temperature Differance Exhaust: TE_mean = (TE_in + TE_out)/2

Exhaust Constants

Specific Heat Exhaust @ Mean Temperature Exhaust:
CpE_mean = ((2,*10^-13)*(TE_mean^4)-(1,*10^-9)*(TE_mean^3)+(1,*10^-6)*(TE_mean^2)-(5,*10^-4)*(TE_mean)+1,)*10^3


Dynamic Viscosity Exhaust @ Mean Temperature Exhaust:
μE_Mean = ((-1,*10^-7)*(TE_mean^2)+(4,*10^-4)*(TE_mean)+5,*10^-2)*10^-4


Thermal Conducitity Exhaust:

k = (2,46*10^-14)*(TE_mean^4)-(5,04*10^-11)*(TE_mean^3)+(1,15*10^-8)*(TE_mean^2)+(7,96*10^-5)*(TE_mean)+2,49*10^-3


Faul Factor: FaulFactor = 0,01*[(hr*ft2*R°)/BTU]
C = 0,005*[(hr*ft2*R°)/BTU]


Heat Rejection from Exhaust

&#;Temperature Exhaust: &#;TE = TE_in - TE_out
Heat Rejection From Exhaust: QE = CpE_mean * MExh * &#;TE


Coolant Calculation

Coolant Flow Rate: Vcoolant = 250 L/min
Coolant Temperature Inlet: TC_in = 65°C
Water/Glycol Mixture (% Glycol): Mix = 40%

Density of Coolant Fluid: ρcoolant = (1,1*Mix+971,8)
Specific Heat of Coolant Fuild: Cpcoolant = (MF_coolant-0,*Mix)*10^3
Mass Flow Coolant: MF_coolant = Vcoolant * ρcoolant
&#;Temperature Coolant Fluid: &#;Tcoolant = QE/(Cpcoolant*MF_coolant)
Coolant Temperature Outlet: TC_out = TC_in + QE/(Cpcoolant*MF_coolant)

Fin Tube Calculation

Number of Tubes First Row: Firstrow = 8

Number of Tubes Second Row: Secondrow = Firstrow-1

Length of Fin Tube: Lfin_tube = 220mm
Number of fins per meter: nf = 118 fins
Fin Height: hf = 9,5mm
Fin Thickness: tf = 1,4 mm

Cross Section Area Calculation

Wfin = (nf*hf*2*tf)/m
Aduct = Firstrow*47mm*Lfin_tube
Tube footprint area: Atube_fp = Firstrow*(PipeOD+Wfin)*Lfin_tube
Free flow Area: AFF = Aduct - Atube_fp

Temperature Fin Surface Calculation

Average Temperature Inside: Ti = (TC_in+TC_out)/2
Mean Temperature Differance Exhaust: TE_mean = (TE_in + TE_out)/2
Average Temperature Fin: TS = Ti+0,3*(TE_mean-Ti)

Reynold's Number Calculation

Mass Flow unit Area: Gn = MExh/AFF
Renynold's Number: Ren = (Gn*PipeOD)/μE_Mean

Heat Transfer Calculation

Convection Coefficient, hc: 0,2*CpE_Mean*Gn*(Ren^-0,35)*((TE_mean/Ts)^0,25)*((k/(CpE_mean*G77))^μE_Mean)

Convection Coefficient, ha = 1/(hc^(-1)+FaulFactor)

Fin Efficiency, E = 0,986-0,*[(hr*ft2*R°)/BTU]*ha
Final outside convection heat transfer coefficient (metric), hf = (ha*(E*Afo+Apo))/AO
Total design heat transfer coefficient(metric), u = 1/(hf^(-1)+C)

Log Mean Temperature Difference, &#;TLMTD = ([(T_(E_in )-T_(c_out ) )-(T_(E_out )-T_(C_in ) )])/(ln&#;[((T_(E_in )-T_(C_out ) ))/(&#;(T&#;_(E_out )-T_(C_in )))])

Area Calculation

Total Area Required, Atot = QE/&#;TLMTD*u
Total Length of Fin Tube, LFT = Atot/AO
Length of 1 Array, Larray = (Firstrow+Secondrow)*Lfin_tube
Number of Arrays, narrays = LFT/Larray

Efficient fin tubes, according to design = E*(8*Secondrow+6*Firstrow)
Above equation depends on the design.

Pressure Drop Fin Tube Array

Number of rows, Nr = round(narrays)*2
Density at bulk temperature, ρb = patm/(Rair*TE_Mean)
Density of Inlet Exhuast, ρ1 = patm/(Rair*TE_in)
Density of Outlet Exhuast, ρ2 = patm/(Rair*TE_out)

Calculation factor, 1: f1 = 0,083+9,44*Ren^(-0,45)

Calculation factor, 2: f2 = [(1+(A_FF/Aduct )^2)/(4&#;Nr )]&#;ρb&#;[(1/ρ2 )-(1/ρ1 )]

Pressure drop over fin tube: &#;Pfin_tube = (2*(f1+f2)*Gn^2*Nr)/ρb

Questions

1. Calculating fault factor, FaulFactor = 0,01*[(hr*ft2*R°)/BTU], we also define C, which is half in value of FaulFactor. What is it?
2. In the equation for Density of Coolant Fluid, ρcoolant = (1,1*Mix+971,8). What is the value 1,1?.
I assume that 971,8 is the density of water at 80deg Celsius. Is the value constant or should be determined as variable of temperature?

3. In the equation for Specific heat of Coolant Fluid: Cpcoolant = (MF_coolant-0,*Mix)*10^3, which originally was (4,4-0,*Mix)*10^3, I changed 4,4 with variable MF_coolant. Is that correct? Where does 0, come from? I couldn't navigate this equation online. Could anyone guide me to properly understand it?

4. In the equation for cross sectional area calculation, Aduct = Firstrow*47mm*Lfin_tube
What could 47mm be? I would like to change it with a variable as well.

5. Heat transfer calculation.
I couldn't find any equation that is similar to the one used for convection coefficient, hc = 0,2 * CpE_Mean * Gn * Ren^(-0,35) * (TE_Mean/TS)^0,25 *(k/(CpE_Mean*μE_Mean)^0,67
Calculating fin efficiency, E = 0,986-0,*[(hr*ft2*R°)/BTU]*ha, are 0,986 and 0, constants or variables?
6. Pressure drop calculation.
Calculation factors 1 and 2. I assume these are friction factors?
Are values 0.083, 9.44 and -0.45 constants? f1 = 0,083+9,44*Ren^(-0,45)
7. The value of Reynold's number is +. Does this mean that flow is turbulent? If it is, shouldn't calculations check for turbulent flow and use different formulas depending on the state of flow?


Thank You so much for all the inputs!

Replies continue below

Recommended for you

RE: Finned-Tube Heat Exchanger Design

Jacob Henry

(Industrial)

11 Aug 21 12:53

I read you equation almost 5 times. and I cant find any mistakes. I think yes. this is right equation. if I am wrong. then any other person tell me is this right equation or wrong.?

RE: Finned-Tube Heat Exchanger Design

optymista93

(Student)

(OP)

11 Aug 21 13:31

Hi Jacob!

Thank You for the reply. Do You have the answer to any of 7 questions stated above?

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News

Given the detailed nature of this content, let's break down each quiz question and provide a brief explanation or guideline to help you answer them.

### Quiz 1: Typical Values of Fouling Coefficient and Resistances

- Explanation: Fouling coefficients and resistances are crucial for the thermal design of heat exchangers. Typical values can be found in engineering handbooks and depend on the type of fluid and operating conditions. For example, water might have a fouling factor of 0. to 0. (m²·K/W).

If you are looking for more details, kindly visit Industrial Finned Tube Heat Exchanger.

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### Quiz 2: Guidelines for Placing the Fluid in Order of Priority

- Explanation: When deciding which fluid should be on the shell side or tube side, factors such as fluid corrosiveness, fouling tendency, and pressure drop requirements are considered. Generally, the more corrosive fluid or the fluid with higher fouling tendency is placed on the tube side to simplify cleaning and maintenance.

### Quiz 3: Features of Shell and Tube Type Exchanger

- Explanation: Shell and tube heat exchangers are versatile, capable of handling high pressures, and are easily cleaned. Features include multiple pass configurations, varied baffle designs, and the ability to handle a wide range of temperatures and pressures.

### Quiz 4: Determination of Number of Tube Passes Based on Shell ID

- Explanation: The number of tube passes in a shell-and-tube heat exchanger affects the heat transfer coefficient and pressure drop. More passes can increase heat transfer efficiency but also increase pressure drop.

### Quiz 5: Supplements for Type Selection

- Explanation: Choosing the right type of heat exchanger involves considering factors such as operating pressure, temperature ranges, fluid properties, maintenance needs, and cost.

### Table 6: Common Tube Layout

- Explanation: Tube layout patterns include square, triangular, and rotated triangular patterns. The choice affects heat transfer efficiency and pressure drop.

### Quiz 7: Tube Pattern Relationship

- Explanation: Tube patterns influence heat transfer rates and pressure drop. Triangular patterns are typically more compact and provide higher heat transfer coefficients, while square patterns are easier to clean.

### Quiz 8: Typical Heat Exchanger Parts and Connections

- Explanation: Key components include the shell, tubes, baffles, tube sheets, headers, and nozzles. Each part plays a role in directing fluid flow and enhancing heat transfer.

### Quiz 9: Standards- Comparison of Classes R, C, & B

- Explanation: These classes define different standards and codes for heat exchanger design, construction, and testing. Class R is typically for refinery and petrochemical applications, Class C for commercial, and Class B for building services.

### Quiz 10: Selection Guide Heat Exchanger Types

- Explanation: A selection guide helps choose between different types such as shell and tube, plate, air-cooled, and spiral heat exchangers based on application specifics.

### Quiz 11: Shell and Tube Exchanger Selection Guide (Cost Increase from Left to Right)

- Explanation: This guide typically compares different shell and tube configurations, showing cost implications. More complex designs generally cost more but offer better performance.

### Quiz 12: Minimum Temperature Approach for Heat Exchangers

- Explanation: The minimum temperature approach is the smallest temperature difference between the hot and cold fluids at any point in the heat exchanger. It's critical for ensuring effective heat transfer.

### Quiz 13: Typical Metal Thermal Conductivities,

- Explanation: Thermal conductivity values for metals (e.g., copper, stainless steel, aluminum) are essential for designing heat exchangers. Copper has high thermal conductivity (~400 W/m·K), while stainless steel is lower (~16 W/m·K).

### Quiz 14: Typical Heat Transfer Coefficients, U and Fouling Resistance,

- Explanation: The overall heat transfer coefficient (U) and fouling resistance (rf) depend on the specific fluids and flow conditions. For water to water, U might range from 500 to W/m²·K, while fouling resistances vary by fluid type.

### Quiz 15: Tube Dimensions

- Explanation: Tube dimensions include diameter, wall thickness, and length. Standard dimensions depend on application requirements and industry standards.

### Quiz 16: The Common Tube Pitches Used

- Explanation: Tube pitch is the center-to-center distance between tubes. Common pitches are 1.25 to 1.5 times the tube diameter to balance heat transfer and cleaning capability.

### Quiz 17: Approximate Heat Transfer Coefficients for Shell-and-Tube Heat Exchangers (KJ. Bell, )

- Explanation: Provides a range of heat transfer coefficients for different shell and tube exchanger configurations based on empirical data.

### Quiz 18: Added Surface Area for Typical Fluid Combinations

- Explanation: Sometimes additional surface area is required to achieve desired heat transfer, influenced by fluid properties and flow regimes.

### Quiz 19: Fouling Resistance vs Heat Transfer Coefficient

- Explanation: There is an inverse relationship between fouling resistance and heat transfer coefficient. Higher fouling resistance decreases the effective heat transfer rate.

### Quiz 20: Features of Some Typical Exchanger Types

- Explanation: Different exchanger types (e.g., plate, spiral, finned tube) have specific features and advantages for various applications.

### Quiz 21: Troubleshooting Checklist

- Explanation: A troubleshooting checklist helps diagnose and solve common issues like fouling, leaks, and thermal performance degradation in heat exchangers.

### Quiz 22: Selected Heat-Transfer Fluids

- Explanation: Different fluids (e.g., water, glycol, oil) have unique thermal properties and suitability for various heat exchanger applications.

### Quiz 23: Summary of Heat-Exchanger Approach Temperature Differences and Pressure Drops

- Explanation: Summarizes expected temperature differences and pressure drops for various heat exchanger types and applications.

### Quiz 24: Typical Overall Coefficient

- Explanation: Provides typical values for the overall heat transfer coefficient for different heat exchanger designs and fluid combinations.

### Quiz 25: Constants for Use in Equation

- Explanation: Lists constants for use in heat transfer equations, such as those for calculating Nusselt number, Reynolds number, and other dimensionless groups.

By understanding these concepts, you'll be well-prepared to tackle questions on heat exchanger design, selection, and troubleshooting. If you have any specific question or need detailed explanations for any particular quiz, feel free to ask!

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