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


Modes of Heat Transfer

Conduction = Molecular or atomic vibrations

Convection = Transport of small mass elements

Three modes:

Radiation = Electromagnetic waves


Modes of Heat Transfer

RadiationConvection

Conduction

A sunny but windy day on the beach!


Which heat transfer mode is important in heat exchangers?

• Radiation?

• Conduction?

• Convection?

- Insignificant

- Interesting!

- The most effective way of heat transfer!


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


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


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


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


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 ?


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!


Q = k * A * LMTD

Heat Transfer Area


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


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


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


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)


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


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


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


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


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

Basic Heat Transfer Theory

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