MEP460 Heat Exchanger Design

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King Abdulaiz University Faculty of Engineering

Mechanical Engineering Department

MEP460 Heat Exchanger Design

Sep. 2018

Review of heat transfer and fluid mechanics

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0-Heat exchangers idea and applications 1-Modes of heat transfer

2-Thermal resistance (Wall resistance for plain wall and hollow cylinders)

3-Overall heat transfer coefficient 4-Fins

5-Overall surface efficiency 6-Fouling

7-Pressure drop ( major and minor losses) 8-Enty length

10-Dimensionless parameters (Re, Pr, Pe, Nu, …)

11-Thermophsical properties and changes with temperature

Review of heat transfer and fluid mechanics

2

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0-Heat exchangers idea and applications

Typical applications:

1-Human thermal comfort (heat exchange of human body with the surroundings)

2-Kettle water boiler 3-Water heater

4-Car radiator

5-Air conditioning system (evaporator and condenser) 6-Power, Desalination and Chemical plants (Shell & tube HX, plate HX, double pipe HX, other types HX)

7-Cooling towers

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Heat exchange for human comfort

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Home water boiler

Phase change heat transfer

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Car radiator

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Water heater

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Air conditioning

Car and split types

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Air conditioning

Window type

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Electric power plant Desalination plants, Industrial plants

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Plate gasketed heat exchanger

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Shell and tube heat exchangers

Most commonly used in industrial and power plants

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Double pipe heat Exchanger

Counter flow and parallel flow arrangements

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Cooling towers

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1- Modes of heat transfer

Conduction Convection Radiation

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1- Modes of heat transfer

𝑞 = −𝑘𝐴 𝑑𝑇

𝑑𝑥 𝑞 = ℎ𝐴(𝑇_𝑠 − 𝑇_∞) 𝑞_{𝑔𝑟𝑎𝑦} = 𝜖𝜎𝑇⁴

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2-Thermal resistance

𝑞 = −𝑘𝐴 𝑑𝑇

𝑑𝑥 ≈ 𝑘𝐴 Δ𝑇

Δ𝑥 = Δ𝑇

Δ𝑥 𝑘𝐴Τ = Δ𝑇 𝑅_𝑤

𝑅_𝑤 = Δ𝑥

𝑘𝐴 = 𝐾 𝑊 a) Conduction in Plane wall

b) Convection resistance

𝑞 = ℎ𝐴 𝑇_𝑠 − 𝑇_∞ = 𝑇_𝑠 − 𝑇_∞ 1 ℎ𝐴

= 𝑇_𝑠 − 𝑇_∞ 𝑅_{𝑐𝑜𝑛𝑣}

𝑅_{𝑐𝑜𝑛𝑣} = 1 ℎ𝐴

𝐾 𝑊

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Conduction Thermal resistance

Convection Thermal resistance

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2-Thermal resistance

Plane wall

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2-Thermal resistance

Cylindrical coordinate system

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3-Overall heat transfer coefficient

𝑞 = 𝑇_∞,1 − 𝑇_∞,2

σ 𝑅 = 𝑇_∞,1 − 𝑇_∞,2 1

ℎ₁𝐴 + 𝐿

𝑘𝐴 + 1 ℎ₂𝐴

= 𝑈𝐴(𝑇_∞,1−𝑇_∞,2)

1

𝑈𝐴 = ෍ 𝑅 = 1

ℎ₁𝐴 + 𝐿

𝑘𝐴 + 1

ℎ₂𝐴 U units is the same as h units i.e.

[W/(m².K] ²¹

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Cylindrical coordinate system

2-Thermal resistance

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3-Overall heat transfer coefficient

Cylindrical coordinate system

𝑞 = ₁ ^𝑇^∞,1^−𝑇^∞,2

ℎ𝑖𝐴𝑖+^ln^{(𝑟2 𝑟1)}^Τ

2𝜋𝐿𝑘 + ¹

ℎ𝑜𝐴𝑜

= ^𝑇^∞,1^−𝑇^∞,2

σ 𝑅 = 𝑈_𝑖𝐴_𝑖 𝑇_∞,1 − 𝑇_∞,2 = U_oA_o(𝑇_∞,1−𝑇_∞,2)

1

𝑈_𝑖𝐴_𝑖 = 1

𝑈_𝑜𝐴_𝑜 = 1

ℎ_𝑖𝐴_𝑖 + ln(𝑟₂Τ𝑟₁)

2𝜋𝐿𝑘 = 1 ℎ_𝑜𝐴_𝑜

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4-Fins

One way to increase heat transfer form a surface is to by increasing the heat transfer area

𝑞_𝑐 = ℎ𝐴(𝑇_𝑠 − 𝑇_∞)

There are many types and shapes

Most common are straight fin on plain surface and circular fins on circular tubes

Extended surfaces

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4-Fins

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Pin fins on plain surface

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Circular or annular fins on circular pipe

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Fin types

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𝑚 = ℎ𝑃 𝑘𝐴_𝑐

𝜃

_𝑏

= (𝑇

_𝑏

− 𝑇

_∞

)

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Fin efficiency

𝜂 𝑓 = 𝑞 𝑓

𝑞 𝑚𝑎𝑥 = 𝑞 𝑓 ℎ𝐴 𝑓 𝜃 𝑏

𝑞

_𝑓

= 𝜂

_𝑓

𝑞

_𝑚𝑎𝑥

= 𝜂

_𝑓

ℎ𝐴

_𝑓

𝜃

_𝑏

𝜃

_𝑏

= (𝑇

_𝑏

− 𝑇

_∞

)

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𝜂_𝑓 = tanh(𝑚𝐿) 32

𝑚𝐿 ^{𝑚 =}

ℎ𝑃 𝑘𝐴_𝑐

Straight fins

𝜃

_𝑏

= (𝑇

_𝑏

− 𝑇

_∞

)

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Efficiency for Straight fins

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Efficiency for circular or annular fin

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Other types of fins (used in compact heat exchangers)

Square array Staggered array

Continues fins on pipes

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Continuous fins on non circular pipes

Application example: Car radiator

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Other types of fins used in compact heat exchangers Plat fin heat exchangers

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Heat transfer from finned surface Overall surface efficiency

𝑞 = 𝑞_𝑢𝑛 + 𝑞_𝑓 = 𝐴_𝑢𝑓ℎ𝜃_𝑏 + 𝐴_𝑓ℎ𝜂_𝑓𝜃_𝑏

𝐴 = 𝐴_𝑓 + 𝐴_𝑢𝑓

𝑞 = 𝐴 − 𝐴_𝑓 + 𝜂_𝑓𝐴_𝑓 ℎ𝜃_𝑏 = 𝐴ℎ (1 − 𝐴_𝑓

𝐴 1 − 𝜂_𝑓 𝜃_𝑏 𝑞 = 𝐴𝜂_𝑜ℎ𝜃_𝑏 = 𝜃_𝑏

1 𝐴𝜂_𝑜ℎ

𝜃

_𝑏

= (𝑇

_𝑏

−𝑇

_∞

)

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6-Fouling

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Fouling is generally defined as the deposition and accumulation of unwanted materials such as scale, algae, suspended solids and insoluble salts on the internal or external surfaces of

processing equipment including boilers and heat exchangers

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𝑅

_𝑓^′′

= 𝑚

²

𝐾

𝑊

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1

ℎ_𝑖𝐴_𝑖 + 𝑅_𝑤 + 1 ℎ_𝑜𝐴_𝑜

𝑅_𝑓𝑖^′′= Fouling resistance for the interior surface [m².K/W]

𝑅_𝑓𝑜^′′ Fouling resistance for the exterior surface [m².K/W]

Fouling factor & Overall heat transfer coefficient

R_w Wall thermal resistance [K/W]

1

ℎ_𝑖𝜂_𝑖𝐴_𝑖 + 𝑅_𝑓𝑖^′′

𝜂_𝑖𝐴_𝑖 + 𝑅_𝑤 + 𝑅_𝑓𝑜^′′

𝜂_𝑜𝐴_𝑜 + 1 ℎ_𝑜𝜂_𝑜𝐴_𝑜 No fins, no fouling

With fouling

With fouling and fins

1

ℎ_𝑖𝐴_𝑖 + 𝑅_𝑓𝑖^′′

𝐴_𝑖 + 𝑅_𝑤 + 𝑅_𝑓𝑜^′′

𝐴_𝑜 + 1 ℎ_𝑜𝐴_𝑜

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7-Pressure drop ( major and minor losses)

Modified Bernoulli's equation

𝑃

₁

+ 1

2 𝜌𝑉

₁²

+ 𝜌𝑔𝑧

₁

= 𝑃

₂

+ 1

2 𝜌𝑉

₂²

+ 𝜌𝑔𝑧

₂

+ Δ𝑃

_𝐿

Δ𝑃_𝐿 = 𝑓 𝐿

𝐷 𝜌𝑉₂² + ෍ 𝐾 𝜌𝑉² 2

Major losses Due to

Wall friction

Minor losses Due to

Fittings

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Friction factor, f

Friction coefficient, C_f

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7-Pressure drop ( major and minor losses)

From balance of forces for a section of pipe, one can get the relation

between the friction factor f and the friction coefficient C_f

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𝑓 = 64 𝑅𝑒_𝐷

1

√𝑓 = −2.0 𝑙𝑜𝑔 𝑒 𝐷Τ

3.7 + 2.51 𝑅𝑒_𝐷 𝑓

𝑓 = 0.79 − 𝑙𝑛𝑅𝑒_𝐷 − 1.64 ⁻² Friction factor

Laminar flow (Re_D<=2300) General Turbulent flow inside a pipe

Turbulent flow inside

smooth pipes 3000 < Re_D < 5*10⁶

7-Pressure drop ( major and minor losses)

e or  is the pipe roughness in meters

Use MOODY Diagram to find the friction factor

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From Incropera 7^th edition 48

Moody Diagram

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Pipe roughness,  or e

Source: F. White, 5^th edition

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Minor losses due to pipe fittings

Losses due to:

Valves Elbows

Sudden expansion

Sudden contraction

Entry

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Loss coefficient for valves, elbows and tees

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Loss coefficient due to sudden

Expansion and Contraction

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Loss coefficient for pipe entrance

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Hydrodynamic Entry length is the distance form the pipe entrance until the flow is converted to fully developed flow

8-Hydrodynamic Entry length

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8-Hydrodynamic Entry length

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For laminar flor Re_D =2300

For turbulent flow Re_D> 2300

𝑥

_𝑓𝑑,ℎ

𝐷 ≈ 0.05𝑅𝑒

_𝐷

10 ≤ 𝑥

_𝑓𝑑,ℎ

𝐷 ≤ 60

Generally it is assumed the flow is fully developed turbulent when

𝑥

_𝑓𝑑,ℎ

𝐷 > 10

8-Hydrodynamic Entry length

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9-Dimensionless parameters related to heat transfer

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Number Expression

1 Reynolds 𝑅𝑒 = 𝑉𝐿 𝜈Τ

2 Nussult 𝑁𝑢 = ℎ𝐿 𝑘Τ

3 Prandl 𝑃𝑟 = Τ𝜈 𝛼

4 Peclet 𝑃𝑒 = 𝑅𝑒 ∗ 𝑃𝑟 = 𝑉𝐿 𝛼Τ

5 Grashof 𝐺𝑟 = 𝑔𝛽 𝑇_𝑠 − 𝑇_∞ 𝐿³Τ𝜈²

6 Railegh 𝑅𝑎 = 𝐺𝑟𝑃𝑟 = 𝑔𝛽 𝑇_𝑠 − 𝑇_∞ 𝐿³Τ𝛼𝜈

7 Lewis 𝐿𝑒 = Τ𝛼 𝐷_𝐴𝐵

8 Jacob 𝐶_𝑝(𝑇_𝑠 − 𝑇_∞) ℎΤ _𝑓𝑔

9 Stanton 𝑆𝑡 = 𝑁𝑢 𝑅𝑒𝑃𝑟 = ΤΤ ℎ 𝜌𝑉𝐶_𝑝

10 Weber Number 𝑊𝑒 = 𝜌𝑉²𝐿 𝜎Τ

11 Colburn J_H factor

12 Friction factor 𝑓 = Δ𝑃 (( ΤΤ 𝐿 𝐷) 𝜌𝑉²Τ2) 13 Friction coefficient 𝐶_𝑓 = 𝜏_𝑤Τ(𝜌𝑉²Τ2)

𝛼 = Τ𝑘 𝜌𝐶_𝑝 𝜈 = 𝜇/𝜌 Thermal

diffusivity Momentum

diffusivity

Mass

diffusivity

𝐷_𝐴𝐵

[m²/s] [m²/s] [m²/s]

𝐽_𝐻 = 𝑆𝑡 𝑃𝑟^{2 3}^Τ

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9-Dimensionless parameters

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9-Dimensionless parameters

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9-Dimensionless parameters

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10-Thermophsical properties and changes

with temperature

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Selected Nu relations for

external and internal flows

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Selected Nu heat transfer relation for

external flows

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Decide on min. area of the flow and find V_max, and Re_D,max

Flow over ^{tube banks}

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Flow over Tube banks

V_max at A₂ if

or V_max occurs at A₁ then use

𝑅𝑒_{𝐷,𝑚𝑎𝑥} = 𝜌𝑉_𝑚𝑎𝑥𝐷 𝜇 Aligned

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Pressure drop for tube banks

In lined arrangement

Aligned arrangement

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Staggered arrangement 78

Pressure drop for tube banks

Staggered arrangement

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internal

^flows

Laminar Flow

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80

internal

^flows

Turbulent Flow

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Free convection

Use the equation above and replace g by gcos() 0<<60 .

Where  is the angle the plate makes with the vertical

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Free convection