Fins are popularly used to keep the temperature of electric devices low. This project is aimed to find out the best configuration of the fins as shown in Figure 1. Figure 2 is the design of the fins....

Summary:
The problem of finding the optimum configuration for cooling of fins was studied. Three
different configuration for the inlet and outlet ducts and two for fins were considered. The results
were obtained from numerical simulation using ANSYS Fluent software. It was found that the
configuration where the ducts are at a height 70mm above the bottom of the box or the fin and
where the fin is placed parallel to the x-direction the one with minimum temperature inside the
fin. Different problems with the simulation are also discussed in detail and detailed explanation
was given for overcoming these problems.
Problem statement:
Fins are very popularly used in different devices where there is a need to increase the heat
transfer from the device to control its temperature. For example, in engine cylinder of an air-
cooled engine, the fins help in controlling the temperature variations and thermal stresses and in
other application such as the electric cooling. In the problem at hand, the surfaces of the fin
(assumed to made out of Aluminum) was releasing 100 W. This fin was subjected to forced
convection by using a fan placed in a box of size 100 X 100 X 150 (all dimension in mm). The
aim was to study the effect of positioning of the inlet and outlet ducts in the box relative to the
fin on the temperature distribution of the fin ad then suggesting best height for the duct height in
the box using the temperature in the fin. For this purpose, three different configurations of the
inlet and outlet ducts were analyzed using the ANSYS Fluent Solver.
Introduction:
Fins are extended surfaces that are used to increase the heat transfer by using the principal of
convection. Fins helps in increasing the overall surface area of an object that increases the
amount of heat transfer to or from the object. Fins are one of the most economical solution of
increasing heat transfer and thus is extensively studied in the subject of heat transfer.
For a uniform cross-sectional area fin with no heat generation and heat transfer to be uniform and
one-directional, the steady state equation can be written as:
̇( ) ̇( ) ̇ ( )
Using the Fourier law of conduction:
̇( )


Where,
Also:
( )
Where,
Therefore, substituting in equation (1), we can write the general form of the fin equation as:



(

) ( ) ( )
Where:
̇ ( )
But usually in real world the problem is not one-dimensional and also the fin cross-section is not
constant, therefore the equation (2) in not that useful. In three dimensions, Navier-Stokes
equation is used. The steady state, three-dimensional, time-averaged Navier stokes equation can
e written as:


( )
( )


̅


( ̅̅ ̅̅ ̅̅ ̅) ( )
Where,
̅
̅̅ ̅̅ ̅̅ ̅

And the energy equation can be written as:
( )


( ̅̅ ̅̅ ̅) ( )
Where,
̅̅ ̅̅ ̅
There various mathematical models available for approximating the unknown Reynold’s stresses
and heat fluxes in equation (4) and (5). The most popular one is the eddy-viscosity tu
ulence
models and of all the eddy-viscosity models available, the k-ε is the most common which can be
derived from the Reynolds transport equation and for high Re models the approximate equations
can be written as:
( )

(


)
( )
( )

(


)






( )
Where,
( )



(





)
In the series of numerical...