Heat Sink Design

Contents Introduction.

Heat sinks definition.

Types of heat section cross section.

What we need from design heat sink?

How to start design heat sink.

Optimization.

Example.

Multiple Fins array

Introduction

Heat transfer is a thermal energy in transit due to a

spatial temperature difference .

Q=∆T/R Where R is a thermal resistance .

Heat transfer has three modes or mechanisms:

Conduction.

Convection.

Radiation.

Heat sinks

Heat sink is a device to effectively absorb or dissipate

heat from the surrounding (air) using extended

surface such as fins .

There are two ways to increase the rate of heat transfer.

To increase the convection coefficient (h).

To increase the surface area (As).

Noted that increasing (h) require external machine like fan or pumps

(forced convection ).

The alternative is to increase the surface area by attaching extended

surface called fins

Types of fins cross section area

What we need from design heat sinks?

We need from design heat sink is get maximum heat transfer rate by

get the optimum dimension like ( profile length , fine thickness and

space between tow fins )

How to start design of heat sink?

We start design by assuming single fin with uniform cross section area

like in the figure shown.

Energy balance : is the amount of heat entered into fin equal to heat

exist from the fin

Conduction

Convection

where

at the boundary condition

1

2 3

From eq. 1,2 and 3 in eq. below

The temperature

distribution at any

distance (x)

Now we will calculate the heat

transfer from the fin

From eq. 1,2

1

2

Because of the thinness of the fin the amount of heat transfer from the tip of

the fin is negligible compared to the surface area , so (ho) is equal zero

that mean no convection

heat transfer is that can convective according

to the geometry is :

Fin effectiveness

Fin efficiency

Optimization

We want to maximize heat transfer rate of a fin with respect to a fin

thickness and profile length.

Heat transfer rate is increase with increasing the thickness of the fin .

So we must get the optimum design for (t , b) the suitable heat transfer

rate

Optimization

Constant profile

area

Constant heat

transfer

Constant volume or

mass

Constant profile area

1-Heat transfer can calculated by:

2-the optimum fin thickness:

3-the optimum fin thickness:

Where β(t ,b) = = 1.4192

Constant heat transfer

1-Heat transfer can calculated by:

2-the optimum fin thickness:

3-the optimum fin thickness:

Constant volume or mass

1-Heat transfer can calculated by:

2-the optimum fin thickness:

3-the optimum fin thickness:

Example

Multiple fin array In the previous slides we discuss the design of single fin optimum thickness ,

profile length

In next slides we will discuss the another important parameters which complete

the geometry of heat sink .

number of fins required to dissipate the max heat transfer (n).

the optimum distance between to fins (z)

From this tow cases we will get the optimum distance between fins in the

free convection

Fins space (z)

Number of fins

For the first case

The heat transfer is get by :

From previous equations .

The heat transfer rate is:

Mass flow rate

Average velocity

Cross section flow area

For the second case

The heat transfer is get by :

Cross section flow area

Convection coefficient

The heat transfer rate is:

To get the optimum space between fins we equal to heat transfer

equation of to cases

References

Thermal design book by Husong lee .

Design of heat sink presentation by Dr/ Prabal Talukdar.

Wikipedia