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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