## Finned-Tube Heat Exchanger Design

## Finned-Tube Heat Exchanger Design

(OP)

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.

Density of diesel fuel: ρD = 820 kg/m3

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

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

Outside Surface Area of bare pipe: Ao = 0,3475 m2/m

Surface Area of one fin, both sides: Apo = 0,0701 m2/m

Pipe exterior surface not covered by fins: Afo = 0,2774 m2/m

PipeOD = 26,7mm

PipeID = 21,4mm

Temperature Engine Data: TE_Data = 25°C

Engine Speed: neng = 2100 rev/min

Engine Power: Peng = 243 kW

Specific Fuel Consumption: MSC = 0,220 kg/kW*hr

Combustion Volume Flow: VCom_air=21,11679 m3/min

Exhaust Volume Flow: VExh = 51,8 m3/min

Exhaust Temperature: TExh = 430°C

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

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

Specific Heat Exhaust @ Mean Temperature Exhaust:

CpE_mean = ((2,74357*10^-13)*(TE_mean^4)-(1,06956*10^-9)*(TE_mean^3)+(1,44395*10^-6)*(TE_mean^2)-(5,86591*10^-4)*(TE_mean)+1,07896)*10^3

Dynamic Viscosity Exhaust @ Mean Temperature Exhaust:

μE_Mean = ((-1,052338*10^-7)*(TE_mean^2)+(4,832851*10^-4)*(TE_mean)+5,087291*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]

∆Temperature Exhaust: ∆TE = TE_in - TE_out

Heat Rejection From Exhaust: QE = CpE_mean * MExh * ∆TE

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-0,0128*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)

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

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

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)

Mass Flow unit Area: Gn = MExh/AFF

Renynold's Number: Ren = (Gn*PipeOD)/μE_Mean

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 = 0,986-0,0068*[(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 )))])

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.

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

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?

What could 47mm be? I would like to change it with a variable as well.

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 = 0,986-0,0068*[(hr*ft2*R°)/BTU]*ha, are 0,986 and 0,0068 constants or variables?

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)

Thank You so much for all the inputs!

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 = 0,3475 m2/m

Surface Area of one fin, both sides: Apo = 0,0701 m2/m

Pipe exterior surface not covered by fins: Afo = 0,2774 m2/m

**Pipe Dimensions**PipeOD = 26,7mm

PipeID = 21,4mm

**Engine Data**Temperature Engine Data: TE_Data = 25°C

Engine Speed: neng = 2100 rev/min

Engine Power: Peng = 243 kW

Specific Fuel Consumption: MSC = 0,220 kg/kW*hr

Combustion Volume Flow: VCom_air=21,11679 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 = ((2,74357*10^-13)*(TE_mean^4)-(1,06956*10^-9)*(TE_mean^3)+(1,44395*10^-6)*(TE_mean^2)-(5,86591*10^-4)*(TE_mean)+1,07896)*10^3

Dynamic Viscosity Exhaust @ Mean Temperature Exhaust:

μE_Mean = ((-1,052338*10^-7)*(TE_mean^2)+(4,832851*10^-4)*(TE_mean)+5,087291*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-0,0128*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 = 0,986-0,0068*[(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-0,0128*Mix)*10^3, which originally was (4,4-0,0128*Mix)*10^3, I changed 4,4 with variable MF_coolant. Is that correct? Where does 0,0128 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_tubeWhat 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 = 0,986-0,0068*[(hr*ft2*R°)/BTU]*ha, are 0,986 and 0,0068 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 13000+. 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!

## RE: Finned-Tube Heat Exchanger Design

## RE: Finned-Tube Heat Exchanger Design

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