1-D ANALYTICAL TOOL
FOR HEAT EXCHANGER
Sourav Kumar Patel
Objectives
What is 1-D (One dimensional Analytical) Tool ???
It is a tool used for calculation of heat exchanger performance and pressure drop by using correlations
derived from experimental /analytical methods.
The Primary Objectives of 1-D Analytical tool are to calculate:
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•
•
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Heat Exchanger Performance / Heat Transfer Rate.
Coolant Side Pressure Drop.
Air Side Pressure Drop.
Coolant Outlet Temperature.
Air Outlet Temperature.
Note:
Primary objectives are the requirements of OEMs.
The Secondary objectives of 1-D Analytical tool are:
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Heat transfer coefficient calculated from 1-D tool can be used as boundary condition for CFD simulation.
Can be used for correlation between 1-D tool and experimental / CFD data.
Inlet (Coolant)
Outlet (Air Side)
Inlet (Air Side)
Outlet (Coolant)
Flow Pattern in Automobile Radiator
Note:
Coolant: Water (50%) + Ethylene Glycol (50%)
1-D Analytical Tool
Input Parameters
Derived Geometrical Parameters
Colburn Factor (j) & Nusselt Number (Nu) Calculation
Heat Transfer Coefficient (h) Calculation
Heat Transfer Calculation
Friction Factor (f) Calculation
Pressure Drop Calculation
Core Size of HX (W x H x D)
Tank Size
Geometrical Parameters
Tube Parameters
Decided by Supplier
Fin Parameters
Mass Flow Rate
Input Parameters
Coolant
Inlet Pressure
Inlet Temperature
Velocity
Flow Parameters
Provided by OEMs
Pressure
Ambient Air
Temperature
Atmospheric Humidity
Geometrical Parameters
Core Size
Width
Height
Depth
Tank Parameters
Width
Tube Parameters
Fin Parameters
Width
Fin Pitch
Height
Fin Height
Depth
Fin Depth
Thickness
Fin Thickness
Height
Depth
I &O Pipe Dia.
I &O Pipe Lengths
Louver Height
Louver angle
Louver Length
Louver Pitch
No. of Louver Bank
Derived Geometrical Parameters
Tube (Coolant Side)
Fin (Air Side)
Free Flow Area
Free Flow Area
Frontal Area
Frontal Area
Contraction Ratio
Contraction Ratio
Hydraulic Diameter
Hydraulic Diameter
Internal Heat Transfer Area
External Heat Transfer Area
Total Free Flow Area
Total Free Flow Area
Nusselt Number (Nu) Calculation (Tube Side)
Laminar Flow:
Turbulent Flow:
Dittus-Boelter Correlation (Smooth Surface and fully Turbulent flow
•
Re > 10000
•
Gilenski Correlation (Rough Surface and Turbulent flow.
2300 < Re < 10000
0.5 < Pr < 2000
Where
(Most widely used correlation)
𝒇 = 𝑭𝒂𝒏𝒏𝒊𝒏𝒈 𝒇𝒓𝒊𝒄𝒕𝒊𝒐𝒏 𝒇𝒂𝒄𝒕𝒐𝒓
Colburn Factor (j) Calculation (Air Side)
𝑗 = 𝑓 𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝑛𝑢𝑚𝑏𝑒𝑟, 𝐺𝑒𝑜𝑚𝑒𝑡𝑟𝑖𝑐𝑎𝑙 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝑇𝑝 = 𝐹ℎ + 𝑇ℎ
𝐹𝑙 = 𝐹ℎ 2 + 𝐹𝑝 Τ2
2
Heat Transfer Coefficient (h) Calculation
Tube (Coolant Side)
ℎ𝑡 𝐷ℎ
𝑁𝑢 =
𝑘
Fin (Air Side)
Heat Transfer Rate (Q) Calculation
∈ −𝑵𝑻𝑼 𝑴𝒆𝒕𝒉𝒐𝒅
• 𝑄 = ∈ * 𝑄𝑚𝑎𝑥
• ∈ = 1 − 𝑒𝑥𝑝
𝑁𝑇𝑈0.22
𝐶𝑟
exp −𝐶𝑟 𝑁𝑇𝑈0.78 − 1
𝐶
• 𝐶𝑟 = 𝐶𝑚𝑖𝑛
∈∶ 𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠
𝑚𝑎𝑥
𝑄𝑚𝑎𝑥 = 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 ℎ𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑟𝑎𝑡𝑒
𝐶𝑟 = 𝐻𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑟𝑎𝑡𝑖𝑜
𝑈𝐴
• 𝑁𝑇𝑈 = 𝐶
𝐶𝑚𝑖𝑛 = 𝑀𝑖𝑛 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
𝑚𝑖𝑛
𝐶𝑚𝑎𝑥 = 𝑀𝑎𝑥 ℎ𝑒𝑎𝑡 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦
•
1
𝑈𝐴
=
1
ℎ𝑡 𝐴𝑡
𝑘 𝐴
1
𝑡
η𝑓 ℎ𝑓 𝐴𝑓
+ 𝑡 𝑡+
• 𝑄𝑚𝑎𝑥 = 𝐶𝑚𝑖𝑛 ∗ 𝑇ℎ,𝑖 − 𝑇𝑐,𝑖
𝑁𝑇𝑈: 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑢𝑛𝑖𝑡𝑠
𝑈: 𝑂𝑣𝑒𝑟𝑎𝑙𝑙 𝐻𝑒𝑎𝑡 𝑡𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡
Note:
h: Hot Side (Coolant)
c: Cold Side (Air)
Algorithm for Heat Transfer Calculation
1. Initially guess the outlet temperatures of coolant 𝑇ℎ𝑜 and air 𝑇𝑐𝑜 .
Note:
h: Hot Side (Coolant)
c: Cold Side (Air)
2. Calculate mean fluid temperatures 𝑇ℎ𝑚 &𝑇𝑐𝑚 .
𝑇ℎ𝑚 =
𝑇ℎ𝑖 + 𝑇ℎ𝑜
2
𝑇𝑐𝑚 =
𝑇𝑐𝑖 + 𝑇𝑐𝑜
2
3. Calculate fluid properties of hot and cold sides at mean fluid temperatures.
4. Calculate Heat Transfer Rate 𝑄 .
5. Calculate 𝑇ℎ𝑜 ′ & 𝑇𝑐𝑜 ′ .
𝑇ℎ𝑜 ′ = 𝑇ℎ𝑖 −
𝑄
𝐶𝑝ℎ
𝑇𝑐𝑜 ′ = 𝑇𝑐𝑖 +
𝑄
𝐶𝑝𝑐
6. Calculate absolute error for assumed and calculated outlet temperature for hot and cold
side.
∆𝑇ℎ = 𝑎𝑏𝑠 𝑇ℎ𝑜 ′ − 𝑇ℎ𝑜
∆𝑇ℎ = 𝑎𝑏𝑠 𝑇𝑐𝑜 ′ − 𝑇𝑐𝑜
7. 𝐼𝑓∆𝑇ℎ < 0.001 & ∆𝑇𝑐 < 0.001
Stop the iteration and assign
𝑇ℎ𝑜 = 𝑇ℎ𝑜 ′
𝑇𝑐𝑜 = 𝑇𝑐𝑜 ′
8. Otherwise continue the iteration (From step 2 to 7) till it converges to the specified
absolute error.
9. Calculate heat transfer rate after converging the iteration as:
𝑄ℎ = 𝑚ℎ 𝑐𝑝ℎ 𝑇ℎ𝑖 − 𝑇ℎ𝑜
𝑄𝑐 = 𝑚ℎ 𝑐𝑝ℎ 𝑇𝑐𝑜 − 𝑇𝑐𝑖
Friction Factor (f) Calculation : Tube Side
Laminar Flow
Darcy friction factor for laminar flow in a pipe is given as:
𝑓=
64
𝑅𝑒
𝑅𝑒 < 2300
Turbulent Flow
Swamee and Jain have developed the following equation to the Darcy friction factor for pipe
𝑅𝑒 > 2300
Friction Factor (f) Calculation : Air Side
Fanning friction factor (f) is calculated from Chang and Wang correlation:
Where
Pressure Drop Calculation (Tube Side)
Tube Side (Coolant)
∆𝑃𝑇𝑜𝑡𝑎𝑙
= ∆𝑃𝑓
𝑖𝑛𝑙𝑒𝑡 𝑝𝑖𝑝𝑒
+ ∆𝑃𝑒 𝑖𝑛𝑙𝑒𝑡 𝑝𝑖𝑝𝑒−𝑖𝑛𝑙𝑒𝑡 𝑡𝑎𝑛𝑘 + ∆𝑃𝑐 𝑖𝑛𝑙𝑒𝑡 𝑡𝑎𝑛𝑘−𝑐𝑜𝑟𝑒 𝑖𝑛𝑙𝑒𝑡 + ∆𝑃𝑓
+ ∆𝑃𝑐 𝑜𝑢𝑡𝑙𝑒𝑡 𝑡𝑎𝑛𝑘−𝑜𝑢𝑡𝑙𝑒𝑡 𝑝𝑖𝑝𝑒 + ∆𝑃𝑓
𝑐𝑜𝑟𝑒
+ ∆𝑃𝑒 𝑜𝑢𝑡𝑙𝑒𝑡 𝑡𝑎𝑛𝑘−𝑐𝑜𝑟𝑒 𝑜𝑢𝑡𝑙𝑒𝑡
𝑜𝑢𝑡𝑙𝑒𝑡 𝑝𝑖𝑝𝑒
Inlet Pipe
Inlet Tank
Core (Coolant side)
Outlet Tank
Outlet Pipe
𝑓𝜌𝐿𝑉 2
∆𝑃𝑓 =
2𝐷
∆𝑃𝑓 : Frictional Pressure Drop
𝑘𝑒 𝜌𝑉 2
∆𝑃𝑒 =
2
∆𝑃𝑐 : Contraction Pressure Drop
𝑘𝑐 𝜌𝑉 2
∆𝑃𝑐 =
2
𝑘𝑐 : Contraction Coefficient
∆𝑃𝑒 : Expansion Pressure Drop
𝑘𝑒 : Expansion Coefficient
Note: If there will be bend in inlet
and/or outlet pipes, pressure drop due
to bend will also be taken into
consideration.
Pressure Drop Calculation (Fin Side)
Fin Side (Air Side)
∆𝑃𝑇𝑜𝑡𝑎𝑙= ∆𝑃𝑐 𝑎𝑡𝑚−𝑓𝑖𝑛 𝑖𝑛𝑙𝑒𝑡 + ∆𝑃𝑓
In
𝑓𝑖𝑛
+ ∆𝑃𝑒 𝑓𝑖𝑛 𝑜𝑢𝑡𝑙𝑒𝑡−𝑎𝑡𝑚
out
𝑓𝜌𝐿𝑉 2
∆𝑃𝑓 =
2𝐷
Atmosphere
Atmosphere
∆𝑃𝑓 : Frictional Pressure Drop
∆𝑃𝑒 : Expansion Pressure Drop
𝑘𝑒 𝜌𝑉 2
∆𝑃𝑒 =
2
∆𝑃𝑐 : Contraction Pressure Drop
𝑘𝑐 𝜌𝑉 2
∆𝑃𝑐 =
2
𝑘𝑐 : Contraction Coefficient
𝑘𝑒 : Expansion Coefficient
Thank You