MEP460 Heat Exchanger Design

King Abdulaiz University Faculty of Engineering

Mechanical Engineering Department

MEP460 Heat Exchanger Design

2022

Review of heat transfer and fluid mechanics

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

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

10-Thermophsical properties and changes with temperature

Review of heat transfer and fluid mechanics

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

Heat exchange for human comfort

Home water boiler

Phase change heat transfer

Car radiator

Water heater

Air conditioning

Car AC

plit unit

Air conditioning

Window type

Electric power plant, Desalination plants, Industrial plants

Plate gasketed heat exchanger

Shell and tube heat exchangers

Most commonly used in industrial and power plants

Double pipe heat Exchanger

Counter flow and parallel flow arrangements

Cooling towers

1- Modes of heat transfer

Conduction Convection Radiation

1- Modes of heat transfer

𝑞 = −𝑘𝐴 𝑑𝑇

𝑑𝑥 𝑞 = ℎ𝐴(𝑇_𝑠 − 𝑇_∞) 𝑞_{𝑔𝑟𝑎𝑦} = 𝜖𝜎𝑇⁴

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}

Conduction Thermal resistance

2-Thermal resistance

Plane wall

2-Thermal resistance

Cylindrical coordinate system

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.

2

Cylindrical coordinate system

2-Thermal resistance

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

4-Fins

One way to increase heat transfer form a surface is 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

4-Fins

Pin fins on plain surface

Circular or annular fins on circular pipe

Fin types

𝑚 = ℎ𝑃 𝑘𝐴_𝑐

Fin efficiency

𝜂 _𝑓 = 𝑞 _𝑓

𝑞 _𝑚𝑎𝑥 = 𝑞 _𝑓 ℎ𝐴 _𝑓 𝜃 _𝑏

𝑞

= 𝜂

𝑞

= 𝜂

ℎ𝐴

𝜃

𝜃

= (𝑇

− 𝑇

)

Straight fins

𝜃

= (𝑇

− 𝑇

)

Efficiency for Straight fins

Efficiency for circular or annular fin

Other types of fins (used in compact heat exchangers)

Square array Staggered array

Continues fins on pipes

Continuous fins on non circular pipes

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

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_∞)

𝜂

= [1 − 𝐴

Τ 𝐴 (1 − 𝜂

)]

6-Fouling

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

𝑅

= 𝑚

𝐾

𝑊

1

𝑈_𝑜𝐴_𝑜 = 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

𝑈_𝑜𝐴_𝑜 = 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

𝑈_𝑜𝐴_𝑜 = 1

ℎ_𝑖𝐴_𝑖 + 𝑅_𝑓𝑖^′′

𝐴_𝑖 + 𝑅_𝑤 + 𝑅_𝑓𝑜^′′

𝐴_𝑜 + 1 ℎ_𝑜𝐴_𝑜

_I and _o are the inside and outside overall surface efficiency

7-Pressure drop ( major and minor losses)

Modified Bernoulli's equation

𝑃

+ 1

2 𝜌𝑉

+ 𝜌𝑔𝑧

= 𝑃

+ 1

2 𝜌𝑉

+ 𝜌𝑔𝑧

+ Δ𝑃

Δ𝑃_{𝐿𝑜𝑠𝑠} = 𝑓 𝐿 𝐷

𝜌𝑉²

2 + ෍ 𝐾 𝜌𝑉² 2

Major losses Minor losses

Friction factor, f

Friction coefficient, C_f

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

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)

Moody Diagram

Pipe roughness,  or e

Minor losses due to pipe fittings

Losses due to:

Valves Elbows

Sudden expansion

Sudden contraction

Entry

Loss coefficient for valves, elbows and tees

Loss coefficient due to sudden

Expansion and Contraction

Loss coefficient for pipe entrance

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

8-Hydrodynamic Entry length

8-Hydrodynamic Entry length

For laminar flow Re_D =2300

For turbulent flow Re_D> 2300

𝑥

𝐷 ≈ 0.05𝑅𝑒

10 ≤ 𝑥

𝐷 ≤ 60

Generally it is assumed the flow is fully developed turbulent when

𝑥

𝐷 > 10

8-Hydrodynamic Entry length

9-Dimensionless parameters related to heat transfer

Number Expression

1 Reynolds 𝑅𝑒 = 𝜌𝑉𝐿 𝜇 = 𝑉𝐿 𝜈Τ Τ

2 Nussult 𝑁𝑢 = ℎ𝐿 𝑘Τ

3 Prandtl 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)

𝐽_𝐻 = 𝑆𝑡 𝑃𝑟^{2 3Τ}

9-Dimensionless parameters

9-Dimensionless parameters

9-Dimensionless parameters

10-Thermophsical properties and changes

with temperature

11- Selected Nu relations for

external and internal flows

Selected Nu heat transfer relation for

external flows

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

Flow over ^{tube banks}

Flow over Tube banks

V_max at A₂ if

or V_max occurs at A₁ then 𝑅𝑒_{𝐷,𝑚𝑎𝑥} = 𝜌𝑉_𝑚𝑎𝑥𝐷

𝜇 Aligned

Fluid outlet temperature from a tube bank

Assuming the surface temperature is kept at constant temperature T_s. The fluid entering temperature is T_i, and the outlet temperature is T_o.  and Cp are fluid properties. N_T number of tube rows, N total number of tubes

𝑇 − 𝑇 𝜋𝐷𝑁ℎ

Pressure drop for tube banks

Aligned arrangement

Pressure drop for tube banks

Staggered arrangement

Selected Nu heat transfer relation for

internal

Laminar Flow

Selected Nu heat transfer relation for

internal

Turbulent Flow

Free convection

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

Where  is the angle the plate makes with the vertical

Free convection