basic heat transfer theory
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Fundamentals of Heat Transfer TheoryThree basic natural laws of physics:
1. Heat will always be transferred from a hot medium to a cold medium, until equilibrium is reached.
2. There must be a temperature difference between the two media for heat transfer to take place.
3. The heat lost by the hot medium is equal to the amount of heat gained by the cold medium, except for losses to the surroundings.
Q1 = Q2
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Modes of Heat Transfer
Conduction = Molecular or atomic vibrations
Convection = Transport of small mass elements
Three modes:
Radiation = Electromagnetic waves
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Modes of Heat Transfer
RadiationConvection
Conduction
A sunny but windy day on the beach!
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Which heat transfer mode is important in heat exchangers?
• Radiation?
• Conduction?
• Convection?
- Insignificant
- Interesting!
- The most effective way of heat transfer!
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Two heat exchanger types
• Direct
Principle: Product and service medium are in direct contact
Example: Water and air in a cooling tower
• Indirect
Principle: Product and service medium are separated by a wall
Example: Hot water and product in a plate heat exchanger
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Flow Principles: Laminar
• Parabolic velocity profile: friction close to wall -> lower velocitycentre of tube -> higher velocity
• Low velocity and low Reynolds number -> low pressure drop
• Distinct parallel fluid layers -> no mixing between layers
• Only conduction -> poor heat transfer efficiency
Flow profile Velocity profile
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Flow principles
• Two types of flow
• No orderly flow
• Random eddy motion mixes the fluid
• Always a laminar film closest to the wall
• Ex., water at higher velocity
– Turbulent
Velocity profileFlow profile
Convection
Conduction
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Heat Transfer Equations
Q = m * Cp * (Tin - Tout)
Qhot = Qcold
Q = rate of heat transfer or heat load, Wm = mass flow rate, kg / sCp = specific heat (amount of heat required to heat 1 kg of the media 1°C), J / kg / °C Tin = inlet temperature, °CTout = outlet temperature, °C
m2, T2in, Cp2
m1, T1in, Cp1
T2out
T1out
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Calculation Example
m2= 120 kg/s
T2in= 20 °C
Cp2= 4.2 kJ/(kg °C)
m1 = 100 kg/s
T1in= 80 °C
Cp1= 4.0 kJ/(kg °C)
T1out= 40 °C
What is the cold fluid outlet temperature?
T2 out= XX°C ?
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Heat Transfer Equations
Q = A * k * LMTD
k = overall heat transfer coefficient, W / m2,°CA = heat transfer surface area, m2
LMTD = Log Mean Temperature Difference, °C
Temperature difference is driving force for heat transfer!
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Q = k * A * LMTD
Heat Transfer Area
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LMTD = Logarithmic mean temperature difference
– Depend on counter-current or co-current flow
Area
T1 in
T2 in
T1 out
T2 out
Counter-Current Flow
1
2
Area
T2 outT2 in
T1 out
T1 in
Co-Current Flow
12
21
21LMTD
ln
Q = k * A * LMTD
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What is the LMTD for the two cases below?
Area
90°C
20 °C
45°C40 °C
Counter-Current Flow
1
2
Area
40 °C20 °C
45°C
90 °CCo-Current Flow
12
LMTD = (50-25) / ln(50/25)
= 25 / ln 2 = 36.1°C
LMTD = (70-5) / ln(70/5)
= 65 / ln 14 = 24.6°C
Counter-current flow gives a higher LMTD
21
21LMTD
ln
Q = k * A * LMTD - calculation
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The k-value consists of 3 different heat transfer resistancesWall
Flow direction
T1, Bulk temperature on hot side
T2, Bulk temperature on cold side
Hot side
Flow directionCold side
Heat transfer (Q) driven by temperature difference
T4
T3
Q = k * A * LMTD
Resistance from the wall
Wall thickness,
Wall conductivity, Film heat transfercoefficient on hot side
Called1-value
Film heat transfercoefficient on cold side
Called2-value
21
111
k
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Thermal lengthDescribes how “difficult” a duty is thermally
• Two names for the same thing:
– Number of Transfer Units (NTU)
– Theta, (mainly used in Alfa Laval)
• We use the “Theta” concept in several ways:
– Thermal duty (high / low theta duties)
– Unit (high / low theta PHE models)
– Plates (high / low theta plates)
– Channels (high / medium / low theta channels)
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Thermal length – Theta θ Theta is calculated for the hot and cold side
21
21LMTD
“How many times the LMTD that the fluid is cooled/heated”
Lower
Higher
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Thermal length – Theta θ
What factors decide Theta of a plate?
1. Channel Length
2. Pressing Depth
3. Chevron Angle
Theta Low theta Medium High
Length Short Medium Long
Pressing depth 4.0 mm 2.5 & 4.0 mm 2.5 mm
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Cold in
Hot outHot in
Cold out
Thermal length – Theta θ • Also possible to make multi-pass design
– For very high theta duties
– If there is no plate that fits in single pass
– Choose best available unit and make it multi-pass
• Example, 2 pass hot side / 2 pass cold side
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Thermal length - plates & channels
L: Low theta H: High theta
• We have two plate corrugations (L and H)
• These form three different channels (L, M and H)
L + L = L channels L + H = M channels H + H = H channels
• We choose between L, M and H channels
• Tailor-make it for the specific duty
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High turbulence & pressure drop
Medium turbulence& pressure drop
Low turbulence& pressure drop
Advantages
• Efficient heat transfer
• High wall shear stress
• Variable thermal length
• Strong construction
Benefits
• Increased heat recovery
• Low fouling
• Optimal design
• Insensitive to vibration
L + L = L channels L + H = M channels H + H = H channels
Thermal length - plates & channels
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