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LECTURE 4 External Forced Convection

Flow Across Tube Banks/Bundles

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Lesson Outcomes

Understand the basic principle of flow across tube banks/tube

bundles

Understand the characteristics of aligned and staggered

arrangement in tube banks

Solve a problem in flow across tube banks/tube bundles

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At the end of this lecture, students should be able to :

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Flow Across Tube Banks/Bundles

Heat transfer in flow across a bank of tubes is of

particular importance in the design of heat exchangers.

Heat exchangers are found in numerous industrial

applications, such as steam generation in a boiler or air

cooling in the coil of an air conditioner.

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Flow Across Tube Banks/Bundles

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Flow Across Tube Banks/Bundles

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Flow Across Tube Banks/Bundles

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Flow Across Tube Banks/Bundles

V

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All properties, are evaluated at the mean temperature :

Ti Te Ts

2

)( eim

TTT

Flow Across Tube Banks/Bundles

Ts

9

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The tubes in a tube bank are usually arranged either

in-line/aligned or staggered in the direction of fluid flow.

The characteristic length of tube bundle is the outer tube

diameter, D

The number of row and column in a tube bank are

defined as longitudinal direction, NL (row) and transverse

direction, NT (column), respectively

The total number of tubes in bank = N

Flow Across Tube Banks/Bundles

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Flow Across Tube Banks/Bundles

In-line/Aligned Staggered

V V

Transverse, NT = 6 Transverse, NT = 5

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Flow Across Tube Banks/Bundles

NT = ? NL = ? N = ?

NT = ? NL = ? N = ?

NT = ? NL = ? N = ?

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Flow Across Tube Banks/Bundles

NT = 6 NL = 4 N = 24

NT = 3 NL = 5 N = 15

NT = 5 NL = - N = 22

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Total surface area in tube bundles :

Ti Te

Ts

Flow Across Tube Banks/Bundles

Ts

)( NDLAs

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Flow Across Tube Banks/Bundles

In aligned tubes :

- transverse pitch (ST)

- longitudinal pitch (SL)

- transverse plane (A1)

In staggered tubes :

- transverse pitch (ST)

- longitudinal pitch (SL)

- diagonal pitch (SD)

- transverse plane (A1)

- diagonal plane (A2)

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In-line/Aligned Tubes

D = tube diameter ST = transverse pitch SL = longitudinal pitch A1 = transverse plane

A1 = ST - D

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D = tube diameter ST = transverse pitch SL = longitudinal pitch SD = diagonal pitch A1 = transverse plane A2 = diagonal plane

Staggered Tubes

A1 = ST - D

A2 = SD - D

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Flow Across Tube Banks/Bundles

Heating Process – boiler

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Ti = 100°C

Ts = 20°C

Te = 80°C

Heating Process

Flow Across Tube Banks/Bundles

Tm = 90°C

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Flow Across Tube Banks/Bundles

Heating Process – boiler

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Ti = 20°C Ts = 100°C Te = 40°C

Cooling Process

Flow Across Tube Banks/Bundles

Tm = 30°C

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Flow Across Tube Banks/Bundles

Cooling Process – heat exchanger

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Flow Across Tube Banks/Bundles

Ti

Ti

Te

Te

Ts

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Flow Across Tube Banks/Bundles

isiese TTTTTT and

)/ln(ln

ie

ie

TT

TTT

Logarithmic mean

temperature difference

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Flow Across Tube Banks/Bundles

)/ln(ln

ie

ie

TT

TTT

Logarithmic mean

temperature difference

Heat transfer rate in tube banks :

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Flow Across Tube Banks/Bundles

Mass flow rate of fluid:

V V

LSNm TTVρ air

* Properties of fluid is evaluated at an inlet temperature

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Flow Across Tube Banks/Bundles

Reynolds Number :

V V

Re = VmaxD /υ