Fundamentos de la teoría de transferencia de calor

Fundamentos de la teoría de transferencia de calor

Three basic natural laws of physics:

1. El calor siempre se transfiere de un medio caliente a un medio frío, hasta que se alcanza el equilibrio.

2. Debe haber una diferencia de temperatura entre los dos medios para que se lleve a cabo la transferencia de calor.

3. El calor perdido por el medio caliente es igual a la cantidad de calor

ganado por el medio frío, con excepción de las pérdidas a los

alrededores.

Q1 = Q2

Modos de transferencia de calor

Conducción = vibraciones moleculares o atómicas

Conveccion = Transporte de elementos de pequeñas masas

Tres modos:

Radiación = Ondas electromagneticas

Modos de transferencia de calor

Radiation

Convection

Conduction

Un dia soleado con ligera nubosidad en la

playa!

¿Qué modo de transferencia de calor es importante en intercambiadores de calor?

• 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 velocity centre 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 profile Flow profile

Convection

Conduction

Heat Transfer Equations

Q = m * Cp * (Tin - Tout)

Qhot = Qcold

Q = rate of heat transfer or heat load, W m = mass flow rate, kg / s Cp = specific heat (amount of heat required to heat 1 kg of the media 1°C), J / kg / °C Tin = inlet temperature, °C Tout = 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,°C A = 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 out T2 in

T1 out

T1 in

Co-Current Flow

1 2

2

1

21LMTD

ln

Q = k * A * LMTD

What is the LMTD for the two cases below?

Area

90°C

20 °C

45°C 40 °C

Counter-Current Flow

1

2

Area

40 °C 20 °C

45°C

90 °C

Co-Current Flow

1 2

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

2

1

21LMTD

ln

Q = k * A * LMTD - calculation

The k-value consists of 3 different heat transfer resistances

Wall

Flow direction

T1, Bulk temperature on hot side

T2, Bulk temperature on cold side

Hot side

Flow direction Cold side

Heat transfer (Q) driven by temperature difference

T4

T3

Q = k * A * LMTD

Resistance

from the wall

Wall thickness,

Wall conductivity, Film heat transfer

coefficient on hot side

Called

1-value

Film heat transfer

coefficient on cold side

Called

2-value

21

111

k

Thermal length Describes 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

LMTD

T1T1=NTU

outin

1

1 NTU

T2 T2

LMTD2

in out2

Area

T1 in

T2 in

T1 out T2 out

1

2

2

1

21LMTD

ln

“How many times the LMTD that the fluid is cooled/heated”

Lower

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 out Hot 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