Department of Engineering
2019-20
Pin Fin Design Review
Design Assessment of Pin Fin Heat Exchanger and
Improvements
Abstract
This study will include the design review of pin fin and any changes or
improvements to it. A numerical study was done to provide information about the
distribution of temperature of cylindrical fin in sturdy state and homogeneous material
characteristics. The previous works review shows that a lot of work has been carried out
logically and numerically in one dimensional and two dimensional conditions on fin. The
study is concerned about the distribution of temperature on pin fin, optimum dimensions
and reduction of heat or temperature of fin is decreased and the also the effectiveness and
efficiency of fin, when the base of fin at constant temperature. The partial differential
equation of given fin model is solved by Euler’s method. The whole investigation was done
using cartridge brass and dimension of fins to find out the suitable effectiveness and
efficiency for the given design.
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Design Assessment of Pin Fin Heat Exchanger
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Introduction
The fins have extended surfaces with given dimensions to allow the heat transfer when
they are exposed to convection method that will cause heat transfer. From Newton’s cooling
method which is defined as the transfer heat rate is direct related to h
and area A and it tells us that the heat loss or heat transfer rate can be increased by increasing
the surface area of material that is the fin area in this case or by increasing coefficient value.
The coefficient (ℎ) value is improved using two methods either by using a fan or by using a
bigger one if we are already using one. But we can’t use them just like that because it can
decrease the efficiency and overall effectiveness because the dimensions will be out of
constraints.
Finned surfaces can be manufactured by the process like welding or using a very thin
wrapping material on the Fin’s body that increase the process rate by conduction (touching)
of a huge surface area to the radiation and convection by the material used in pin fin. Usage
of pin fin can be sometimes the most efficient solutions to heat transfer problems.
Among standing technology of heat sinks, fin sink that loses the heat provide us the
effective way of cooling because they have very high area surface with in relation that will
have any surface volume for heat sink. Moreover, fins with the fin spacing will cause air to be
blown through them create an important amount of disorder between the fins. In this way
boundary around the fin in form of layering around the pin fins broke down and creating
thermal coefficients. Heat sinks of a fin are totally made of a base and a lot of pins that are
inserted. We will keep in mind the important considerations like dimensions of base plate and
density, length and material which we are using. In this way we can improve fins to be fitted
in different solicitations that depends on space that is being left and the flow of air.
The flow of air is also an important factor in this design method. We use the method of forced-
convection heat that is consistent with the rule of thumb and according to the factor of 10 to
1. This method is very effective but not in every case so it can’t be used. The level of air flow
can be controlled by controlling the density of the fin. We see that the high density of a fin
means that it will be effective and better and if the density is kept low than it is more better
if we use nature convection method.
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Design Assessment of Pin Fin Heat Exchanger
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In impingement cooling the heat sinks of a fin will be observed as more effective, in this a fan
on the upper level of fin will blow air on the body of fin. That will remove the gradient of
temperature and life expectancy of the fin will increase as well as the way of cooling is
improved.
Literature/Design Review
A pin fin is used for the removal of heat from electronic device to the air for the reduction of
the temperature of the device. In this case, design of a pin fin is very efficient for the heat
removal. There are various shapes of fin used for this removal regarding the device we are
using for. A circular pin fin shape is very efficient in this regard. The pin use the method of
conduction to take heat from pin fin and use the process of convention and reduction to
remove it to the surroundings air. This process is being used to decrease temperature as we
will see below.
In this design air is our surrounding fluid in which heat is lost. Since the circular
shape is considered a uniform shape and allow equality in all direction since the air connection
with each and every pointy on the surface is same , so the heat lost to the surroundings will
be same and maximize and in this case fin’s temperature will be maintained easily preventing
it from over-heating. And also conduction in the shape will occur easily and heat transfer rate
from device to the end surface of pin-fin will be high and allow eat lost widely.
Method
In our design review we have to apply the Euler’s Methods for solving a partial
differential equation of our design of fin that is given as equation no 1 to find out the all
necessary values for the fin effectiveness and efficiency and find out the required
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Design Assessment of Pin Fin Heat Exchanger
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improvements for our design. We used MATLAB for this and that code gave us all the results
provided and the equations also show the improvement.
Improvements
We made improvements in the design by changing the total length and diameter of
the fin. We found that the optimum dimension we assumed for the best working and heat
reduction from the fin is having .05m of length and 2×10^-3m of radius. We also found out
that this design of fin gave the maximum effectiveness and efficiency for the reduction of
temperature from the device. But the result can be change as we assume the other
dimensions but we found that with these given values of length and diameter, they become
very suitable for this design for the heat removal and it is a suitable method because it is
faster and it has more endurance as well. We can also change the material for the more
temperature removal through the fin to air and temperature will balance easily to our desire
level easily and more effectively. The mathematical work is shown as below:
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Design Assessment of Pin Fin Heat Exchanger
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Design Assessment of Pin Fin Heat Exchanger
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Design Assessment of Pin Fin Heat Exchanger
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Design Assessment of Pin Fin Heat Exchanger
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Result/Discussion
We can see that the differential equation of the fin that is cylindrical that was provided to us
as equation no 1 was converted to a linear algebraic equation using the Euler’s method. Then
we wrote the code in MATLAB using program for this specific design. This code is used to find
the temperature at each node in the given sphere of design. We are having material cartridge
brass 120 w/m-k for the analysis of cylindrical fin. The heat transfer coefficient of the nearby
space is 20 w/sqm-k .The fin base was maintained at a constant temperature with respect to
device at temperature (60°C) 333.15K and the ambient fluid temperature considered it at
(20°C) 293.15K. All these values were provided to us and we had to make a graph that will
show us the behavior in which temperature will act and that can be used as a model to
increase it and for improvements purposes. This result gives us information that it will
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Design Assessment of Pin Fin Heat Exchanger
and Improvements
continuously decreases with respect of time. Moreover if we want to find the values of each
iteration that can also be done by simply using the code written in appendix. It can be used
to provide data that is filled in excel sheet and be used to see the difference in each iteration.
Graph
Conclusion
From the above discussion, literature reviews and calculations we can say that the optimum
exact dimensions for this fin design is having .05m of length and 2*10^-3m of radius with a
minimal tolerance values that can be neglected because of the fin design. This fin design will
give the maximum effectiveness and efficiency in the temperature reduction of device under
the assumed condition. The best thing about this design is that we can see the design will be
long lasting as the weight of the model is equally divided and the fatigue conditions of design
are properly handled for it to work over a long period of time. The design can be further
improved by the improvements that have been suggested above. But these improvements
will be costly and OEE of the fin can also decrease because of it.
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Design Assessment of Pin Fin Heat Exchanger
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Bibliography
(Budimir, 2000)
(mamuni, n.d.)
(Bailin, n.d.) (sheikh,
n.d.)
References
Bailin, F. (n.d.). researche gate. Retrieved from
https://www.researchgate.net/publication/271123422_Research_on_the_Pin_Fin_Efficienc
y_and_Structure.com
Budimir, M. (2000, oct 10). Machine design. Retrieved from mechine design:
https://www.machinedesign.com/archive/article/21814903/cooling-the-pinfin-way
mamun, A. a. (n.d.). global journals. Retrieved from global journals:
https://globaljournals.org/GJRE_Volume16/6-Optimization-of-Effectiveness.pdf
sheikh, N. N. (n.d.). researche gate. Retrieved from
https://www.researchgate.net/publication/333815784_A_Review_Paper_on_Pin_Fin_Efficie
ncy_Enhancement.com
Appendices
Script code:
clear all ;
F = @FunctionC ;
h = 10^-3 ;
a0 = 0. ;
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Design Assessment of Pin Fin Heat Exchanger
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a1 = 1. ;
b0 = rand ;
b1 = rand ;
[a, b] = RK4(F,h,a0,a1,b0,b1) ;
Real Function:
Function c
function [derriv_value] = FunctionC(a,b)
h = 20 ; % heat transfer
p = 2.513 * 10^(-4) ; % perimeter of the pin
k = 120. ; % conductive heat transfer constant
Ac = 3.14159 * 10^(-6) ; % Cross sectional area ;
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Design Assessment of Pin Fin Heat Exchanger
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K = h*p/(k*Ac) ;
Ta = 20 ;
derriv_value = [b(2); K*(b(1)-Ta)]; % b(1) = b , b(2) = v end
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Pin Fin Design Review
Flow Chart
First the code will ask the initial values x=a, y=b, z, N, a, b. than find the values of h. than the
do condition implement the code and start the iteration with respect to l and N and the
condition apply if the given value of function exist than the code say yes and print the x,y,z
values and stop and fin.If no than the code goes for euler method where it finds values of y
and x and continuously finds next iteration in the do and carry on until the values for the x0=x
and y0=y are achieved and that will stop.
We can write stepwise as:
I. Begin
II. Introduce the given function
III. Give the values of 𝑥0 , 𝑦0 , 𝑥𝑛 and h
𝑥0 and 𝑦0 are starting values and h is the interval
𝑥𝑛 is the value to be found
𝑥𝑛 −𝑥0
IV. n=(𝑛 = ℎ
+ 1)
V. now a loop is started with i=1 to n
VI. 𝑦 = 𝑦0 + ℎ × 𝑓(𝑥0 , 𝑦0 )
VII. 𝑥 = 𝑥 + ℎ
VIII. Take a print and take values’ output of 𝑦0 𝑎𝑛𝑑 𝑥0
IX. See if value of x is less than xn
now if no, end the loop otherwise give x0 = x and y0 = y
X. End loop i
XI. Stop
Department of Engineering 12
Design Assessment of Pin Fin Heat Exchanger
and Improvements
Pin Fin Design Review
Department of Engineering 13
