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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 1, MARCH 2009
Optimization of Cylindrical Pin-Fin Heat
Sinks Using Genetic Algorithms
Sajjad Mohsin, Ayesha Maqbool, and Waqar A. Khan
Abstract—In this paper, genetic algorithms (GAs) are applied for
the optimization of pin-fin heat sinks. GAs are usually considered
as a computational method to obtain optimal solution in a very
large solution space. Entropy generation rate due to heat transfer
and pressure drop across pin-fins is minimized by using GAs. Analytical/empirical correlations for heat transfer coefficients and friction factors are used in the optimization model, where the characteristic length is used as the diameter of the pin and reference velocity used in Reynolds number and pressure drop is based on the
minimum free area available for the fluid flow. Both inline and staggered arrangements are studied and their relative performance is
compared on the basis of equal overall volume of heat sinks. It is
demonstrated that geometric parameters, material properties, and
flow conditions can be simultaneously optimized using GA.
Index Terms—Genetic algorithm (GA), heat sinks, inline, optimization, pin-fins, pressure drop, staggered, thermal resistance.
NOMENCLATURE
Total base area
.
Exposed area of base plate
.
Cross-section or contact area of a single pin
Surface area of a single pin
.
Surface area of heat sink
.
Pin diameter
.
Friction factor.
Equality and inequality constraints.
Pin height
.
Resistance
.
Reynolds number
.
Entropy generation rate
.
Dimensionless diagonal pitch
.
Dimensionless streamwise pitch
.
Dimensionless spanwise pitch
.
Diagonal pitch
.
Pin spacing in streamwise direction
.
Pin spacing in spanwise direction
.
Absolute temperature
.
Thickness
.
Approach velocity
.
Maximum velocity in minimum flow area
Design variables.
Subscripts
.
Approach.
Ambient.
Base plate.
Contact.
Wall.
Heat transfer coefficient
.
Number of imposed constraints.
Constant defined in (18) and (19).
Thermal conductivity
Lagrangian function.
Number of rows in streamwise direction.
Dimensionless entropy generation rate
.
Number of rows in spanwise direction.
Nusselt number based on pin diameter.
Nusselt number based on heat sink length in flow
direction.
Total base heat flow rate
.
.
Length of heat sink in flow direction
Total number of pins in heat sink
Number of design variables.
.
.
Manuscript received November 13, 2007; revised May 21, 2008 and August
04, 2008. First published February 06, 2009; current version published February
27, 2009. This work was recommended for publication by Associate Editor R.
Prasher upon evaluation of the reviewers comments.
S. Mohsin is with the Department of Computer Science, COMSATS Institute
of Information Technology, Islamabad 44000, Pakistan.
A. Maqbool is with the Automatic Control and System Engineering Department, Sheffield University S1 3JD, U.K.
W. A. Khan is with the Department of Engineering Sciences, PN Engineering
College, National University of Sciences and Technology, PNS Jauhar, Karachi
75350, Pakistan.
Digital Object Identifier 10.1109/TCAPT.2008.2004412
Fluid.
Single fin.
All fins with exposed base plate area.
Heat sink.
Bulk material.
Greek Symbols
Pressure drop across heat sink
Slenderness ratio
.
Absolute viscosity of fluid
.
Kinematic viscosity of fluid
Fluid density
.
.
1521-3331/$25.00 © 2009 IEEE
.
.
MOHSIN et al.: OPTIMIZATION OF CYLINDRICAL PIN-FIN HEAT SINKS USING GENETIC ALGORITHMS
45
I. INTRODUCTION
HE ENETIC algorithm (GA) right from its inception is
being utilized as a global optimization technique. It was
started by Friedburg [1], [2] with the mutation to induce learning
in a small Fortran program. Holland [3] gave a boost to this
field by utilizing bit strings representation for GA operators of
selection/reproduction, crossover, and mutation. The boom in
the evolutionary computing in general and GA in particular is
due to the work of Koza [4]. Although GA has been used as
an optimization technique for many problems, yet it was not
considered for this particular problem.
Khan et al. [5] presented a detailed survey of conventional
optimization studies related to pin-fin heat sinks. Foli et al. [6]
determined the optimal geometric parameters of the microchannels in micro heat exchangers. They used multi-objective genetic algorithms in combination with computational fluid dynamics (CFD) and concluded that the performance of micro heat
exchangers depends on the operating conditions and aspect ratio
of the microchannels. Jeevan et al. [7] determined the optimal
dimensions for a stacked microchannel using the GAs under different flow constraints.
In this paper, GA is employed to optimize all relevant design
parameters for pin-fin heat sinks, including geometric parameters, material properties, and flow conditions simultaneously by
subject to manufacminimizing entropy generation rate
turing and design constraints. The potential and feasibility of
applying GA as an optimization tool in electronic cooling will
be demonstrated in this paper.
T
A. Genetic Algorithm
The idea of applying the biological principle of natural evolution to artificial systems, introduced more than three decades
ago, has seen impressive growth in the past few years. Usually
grouped under the term evolutionary algorithms or evolutionary
computation, we find the domains of genetic algorithms,
evolution strategies, evolutionary programming, and genetic
programming. Evolutionary algorithms are successfully applied to numerous problems from different domains, including
optimization, automatic programming, machine learning, economics, operations research, ecology, population genetics,
studies of evolution and learning, and social systems. Sajjad
and Mohsin [8] have used GA in optimization of codebook
generation through vector quantization in image compression
and have shown that GA has given good results.
Looking at the world around us, we see a staggering diversity
of life. Millions of species, each with its own unique behavior
patterns and characteristics, abound. Yet, all of these plants and
creatures have evolved, and continue evolving, over millions of
years. They have adapted themselves to a constantly shifting and
changing environment in order to survive. Those weaker members of a species tend to die away, leaving the stronger and fitter
to mate, create offspring, and ensure the continuing survival of
the species. The laws of natural selection and Darwinian evolution dictate their lives, and it is upon these ideas that genetic
algorithms are based. Goldberg [9] defines it as: Genetic algorithms are search algorithms based on the mechanics of natural
selection and natural genetics. Bauer [10] gives a similar definition in his book: Genetic algorithms are software, procedures
modeled after genetics and evolution.
Fig. 1. Flowchart of Genetic Algorithm.
B. Simple GA Algorithm
Fig. 1 shows the flow diagram of simple GAs. Genetic algorithms are used to find optimum solutions to any problem. The
problem is described by the string
(1)
we have to determine the way of evaluating the efficacy or fitness
.
A prototypical GA consists of the following steps:
1) generate initial population;
2) measure fitness;
3) select a mating;
4) pair members of the mating pool and perform crossover;
5) mutate each member of the crossover pool to obtain a new
generation;
6) return to (2) until some stopping condition is satisfied.
C. Encoding of a Chromosome
As for any search and learning method, the way in which candidate solutions are encoded is a central, if not the central, factor in
the success of a genetic algorithm. In recent years, there have been
many experiments with different kinds of encoding. A chromosome should in some way contain information about solution that
it represents. The most used way of encoding is a binary string.
A chromosome then could look like this, as follows.
Each chromosome is represented by a binary string. Each
bit in the string can represent some characteristics of the solution. Another possibility is that the whole string can represent a
number. Of course, there are many other ways of encoding. The
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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 1, MARCH 2009
TABLE I
BINARY STRING ENCODING
a very high probability. Crossover can be one-point or multipoint (Fig. 3). The one-point crossover involves cutting the chromosomes of the parents at a randomly chosen common point and
exchanging the right-hand-side sub-chromosomes.
4) Mutation: After a crossover is performed, mutation takes
place. Mutation is a random change in the genetic material of
a single individual (Fig. 4), and it is applied to prevent the solution to get into local minima. Mutation is applied to genes
by changing them with a low probability. In case of binary encoding, we can switch a few randomly chosen bits from 1 to 0
or vice versa. Mutation can be then illustrated as in Fig. 4.
E. Difference Between GA and Traditional Methods
Fig. 2. Roulette-wheel selection operator.
encoding depends mainly on the problem. For example, one can
encode directly integer or real numbers (Table I).
D. Operators of GA
Typical operators for all types of genetic algorithms are: selection, crossover, and mutation. These operators are used consecutively at each step.
1) Selection: The selection operator selects chromosomes
according to their fitness function values. In this procedure, the
well-fitted individuals have more chances to be selected. The
most common two selection operators are roulette-wheel selection and tournament selection. Elite approach is sometimes used
in tournament and roulette wheel selections results. When creating a new population by crossover and mutation, we have a big
chance, that we will loose the best chromosome. Elitism is the
name of the method that first copies the best chromosome (or
few best chromosomes) to the new population. The rest of the
population is constructed in ways described above. Elitism can
rapidly increase the performance of GAs, because it prevents a
loss of the best-found solution.
2) Roulette-Wheel Selection: The idea behind the
roulette-wheel selection technique is that each individual
is given a chance to become a parent in proportion to its fitness.
The chances of selecting a parent can be seen as spinning a
roulette wheel with the size of the slot for each parent being
proportional to its fitness. Obviously, those with the largest
fitness (slot sizes) have more chance of being chosen. Thus, it
is possible for one member to dominate all the others and get
selected a high proportion of the time. Roulette-wheel selection
can be implemented as follows.
1) Sum the fitness of all the population members. Call this
(total fitness).
2) Generate a random number , between 0 and
.
3) Return the first population member whose fitness added to
the preceding population members is greater than or equal
to .
A roulette-wheel proportional to the fitness function can be
demonstrated in Fig. 2.
3) Crossover: Crossover is a random exchange of genetic
material between two parents to produce a unique offspring with
The following list is a very quick look at the essential differences between GAs and other forms of optimization. (Goldberg,
[9]).
1) Genetic algorithms a coded form of the function values (parameter set), rather than with the actual values themselves.
So, for example, if we want to find the minimum of the
, the GA would not deal
function
directly with or values, but with strings that encode
these values. For this case, strings representing the binary
values should be used.
2) Genetic algorithms use a set, or population, of points to
conduct a search, not just a single point on the problem
space. This gives GAs the power to search noisy spaces
littered with local optimum points. Instead of relying on a
single point to search through the space, the GAs looks at
many different areas of the problem space at once, and uses
all of this information to guide it.
3) Genetic algorithms use only payoff information to guide
themselves through the problem space. Many search techniques need a variety of information to guide themselves.
The only information a GA needs is some measure of fitness about a point in the space. Once the GA knows the
current measure of “goodness” about a point, it can use
this to continue searching for the optimum.
4) GAs are probabilistic in nature, not deterministic. This is
a direct result of the randomization techniques used by
GAs. However, recently some deterministic methods are
also searched and worked on to get better results.
5) GAs are inherently parallel. Here lies one of the most powerful features of genetic algorithms. GAs, by their nature,
are very parallel, dealing with a large number of points
(strings) simultaneously.
II. ANALYSIS
The entropy generation rate associated with heat transfer
and frictional effects serve as a direct measure of the ability
to transfer heat to the surrounding cooling medium. A model
that establishes a relationship between entropy generation rate
and heat sink design parameters can be optimized using GAs
in such a manner that all relevant design conditions combine
to produce the best possible heat sink for the given constraints.
Following Khan et al. [5], the entropy generation rate for a fluid
flowing across a heat sink (Fig. 5) can be written as
(2)
MOHSIN et al.: OPTIMIZATION OF CYLINDRICAL PIN-FIN HEAT SINKS USING GENETIC ALGORITHMS
47
Fig. 3. Single point crossover.
where
(6)
(7)
(8)
with
(9)
(10)
Khan [5] has developed the following analytical correlation for
the dimensionless heat transfer coefficient for a cylindrical fin
in a fin array:
Fig. 4. Mutation at a given point.
(11)
This expression shows that the entropy generation rate depends
and the pressure drop
across
on the thermal resistance
the heat sink, provided that the heat load , mass flow rate ,
and ambient conditions are specified. Assuming the same area
of heat source and base plate, the thermal resistance of the heat
sink can be written as
where
is a constant which depends upon the longitudinal
and transverse pitch ratios, arrangement of the fins, and thermal
boundary conditions. For an isothermal boundary condition, it
is given by
(12)
(3)
for inline arrangement, and
where
is the bulk material resistance, given by
(4)
(13)
and
is the overall resistance of the fins and the exposed
base plate, which can be written as
for staggered arrangement. The heat transfer coefficient for the
base plate
can be determined by considering a finite plate.
Khan [5] has developed the following analytical correlation for
the dimensionless heat transfer coefficient for a finite plate
(5)
(14)
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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 1, MARCH 2009
TABLE II
DIMENSIONS USED FOR OPTIMIZATION OF PIN-FIN HEAT SINKS
Fig. 5. Geometry of an inline pin-fin heat sink.
where is the length of the base plate in the streamwise direction. The mass flow rate through the fins is given by
(15)
The pressure drop associated with flow across the pin fins is
given by
(16)
where the friction factor depends on the Reynolds number and
the array geometry, and can be written as
(17)
for inline arrangement, and
(18)
for staggered arrangement, and
is a correction factor depending upon the flow geometry and arrangement of the pins. It
is given by
(19)
for inline arrangement, and
(20)
for staggered arrangement. All the correlations for friction and
correction factors are derived from graphs given by ukauskas
[11]. The velocity
, in (15), represents the maximum average velocity seen by the array as flow accelerates between
pins, and is given by
(21)
where
is the dimensionless diagonal
pitch. The simplified expression for the dimensionless entropy
generation rate can be written as
(22)
where
is a fixed dimensionless duty parameter
that accounts for the importance of fluid friction irreversibility
relative to heat transfer irreversibility. The duty parameter is
fixed as soon as the fluid, fin material, and the base heat transfer
rate are specified. The greater the base heat transfer rate, the
smaller will be the fluid friction irreversibility. The constants
and
in (22) are given by
(23)
(24)
(25)
MOHSIN et al.: OPTIMIZATION OF CYLINDRICAL PIN-FIN HEAT SINKS USING GENETIC ALGORITHMS
III. OPTIMIZATION PROCEDURE
The problem considered in this study is to minimize the entropy generation rate using GA, given by (2) or (22), for the
optimal performance of cylindrical pin-fin heat sinks. If
represent the entropy generation rate that is to be minimized
subject to equality constraints
and inequality constraints
, then the complete
mathematical formulation of the optimization problem may be
written in the following form:
minimize
(26)
subject to the equality constraints
(27)
and inequality constraints
(28)
where
and are the imposed equality and inequality constraints and are given by
In (26),
denotes the vector of the design variables
. In this paper, we focus to find optimized
values through GA with binary coding having roulette-wheel
selection with elitism, single point crossover, and bitwise mutation. For optimization purpose, we chose three design variables,
the approach
i.e., , the pin height , diameter of pin, and
velocity. The other related dimensions and physical properties
are given in Table II. The variable is of 10 bit where its range
5.00 mm. Variable of 8 bits are dedicated
is 0.7 mm
for ranging from 0.8 mm
10.00 mm; here, we have to
keep in mind that, in order to select the most optimized value,
we have to consider not only the least entropy generation but
also the practically feasible solution. Thus, the range for the
is kept under than three times of , but care is taken that it must
not increase the maximum limit of 10 mm. And the last variable
is of 11 bits having range from 1 m/s to maximum 8 m/s
is
due to acoustic problems. These three variables
are then concatenated to form a gene of 29 bits Size of Gene .
In this paper, the initial parent population of size 21 is randomly
generated. For the selection the roulette-wheel method with
elitism is used. Fitness is the dimensionless entropy generation
rate
. In roulette-wheel selection, each individual is given
a chance to become a parent in proportion to its fitness, those
with larger fitness have more chance of being selected. In this
paper, we have selected only those parents that results in real
entropy generation. The discarded parent is replaced by new
randomly generated gene that does not yield a complex value.
This selection procedure is repeated until 21 offsprings had
49
been generated. Then, the individual showing minimum
(i.e., the fitness function matrix), in the population of parents
, in the
is exchanged with the individual showing maximum
population of offsprings. This is elitist preserving strategy.
For single-point crossover, two individuals were chosen from
the population of the offsprings. It is a random exchange of genetic material between two parents to produce a offspring with
a random probability of 0.6. It involves cutting of the chromosome at randomly chosen point and exchanging the sub-chromosomes among two randomly selected genes. This crossover
process is carried out until the new population of gene is generated. For mutation, each bit of chromosome is altered with the
probability of 0.5. After mutation the fitness, i.e., the entropy
generation is computed for all offsprings. This process of selection crosses over, and mutation is repeated for 2000 generations.
The values of probability of crossover, mutation, and population
size are all obtained empirically.
IV. RESULTS AND DISCUSSION
This paper shows the implementation of GAs to optimize
the performance of a pin-fin heat sink under different operating conditions. GAs are global search techniques based on
the mechanism of natural selection and genetics. Unlike the
Newton Raphson method, used by Khan et al. [5], GAs do not
require detailed mathematical derivations for unknown parameters; instead, the same model of entropy generation minimization can be used for optimization irrespective of the number of
unknown parameters. Moreover, GAs do not require an accurate initial guess of the variable. The computational cost does
increase whenever GAs are applied instead of any traditional
method. This cost is dependent on the population size and the
total number of iterations. In brief, GAs are best suited for the
optimization of pin-fin heat sinks involving several variables,
and they produce a high-quality solution. For optimization, the
25.4
objective is set to select the best heat sink to fit the 25.4
mm footprint but not to exceed a maximum overall height of
12 mm (Table II). The maximum height restriction is selected
to represent a typical board pitch found in communications systems. It is also assumed that a total heat dissipation of 10 W is
uniformly applied over the entire base plate which has a uniform thickness of 2 mm. The ambient temperature is fixed at
27 C, and the problem is solved for the low and high thermal
conductivities 25 and 237 (enhanced plastics composites and
aluminum). Parametric variations include the pin diameter
approach velocity,
, and the pin height . With reference
to this, each arrangement for different thermal conductivities is
examined for optimal heat sink geometry that leads to overall
optimized performance where both heat transfer and viscous effects are considered.
Minimum entropy generation rate for different number of
generations corresponding to different number of pins for an inline arrangement is shown in Fig. 6. It is clear from figure that
as the number of generations increases from 20 to 600, the entropy generation rate decreases with the increasing number of
generations and number of pins as well. With the increase in the
number of pins, the pressure drop increases, but at the same time
thermal resistance decreases. As a result, the entropy generation
rate decreases. The number of generations were increased up to
2000 as shown in Fig. 7 for an inline arrangement using low
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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 1, MARCH 2009
Fig. 6. Entropy generation rate versus number of generations.
Fig. 7. Entropy generation rate versus number of generations for inline arrangement.
and high thermal conductivities. It is clear from Fig. 7 that the
entropy generation rate decreases with the increase in thermal
conductivity. It is observed that, in each case, it starts from a
random minimum
and reaches an optimum minimum solution using its basic parameters, selection, crossover, and mutation. It is also observed that the GA has evolved itself and
have reached a stable condition as the generation progress. This
shows that the 2000 generations is sufficient for this experiment.
The results of optimization for low and high thermal conductivities are summarized in Tables III and IV. The same experiment was repeated for different number of generations corresponding to different pin diameters, pin heights, and approach
velocities for an inline arrangement, and the results are plotted
in Figs. 8–11.
MOHSIN et al.: OPTIMIZATION OF CYLINDRICAL PIN-FIN HEAT SINKS USING GENETIC ALGORITHMS
51
TABLE III
RESULTS FOR OPTIMIZATION OF THREE PARAMETERS
FOR INLINE ARRANGEMENT
Fig. 8. Dimensionless entropy generation rate versus pin diameter for different
approach velocities.
Fig. 9. Dimensionless entropy generation rate versus pin diameter for different
number of pin-fins.
For each approach velocity, optimum diameter exists that decreases with the increase in approach velocity. The minimum dimensionless entropy generation rate increases with the increase
in approach velocity.
The effect of number of pins on dimensionless entropy generation rate and optimum diameter for fixed pin height and approach velocity are shown in Fig. 9. It is obvious that optimum
pin diameter and minimum dimensionless entropy generation
rate decrease with the increase in number of pins. This is due
to the fact that for fixed pin height and approach velocity, the
thermal resistance decreases with the increase in surface area.
The variation of dimensionless entropy generation rate with
number of pins for different approach velocities is shown in
Fig. 10. The pin diameter and pin height are kept constant in
this case. The optimum number of pins exist for each approach
velocity and decreases with the increase in approach velocity.
The minimum dimensionless entropy generation rate increases
with the increase in approach velocity due to higher pressure
drop in the heat sink.
V. SUMMARY AND CONCLUSION
Fig. 10. Dimensionless entropy generation rate versus number of pins for different approach velocities.
Fig. 8 shows the variation in dimensionless entropy generation rate versus pin diameter for different approach velocities.
The number of pins and pin height are kept constant in this case.
GAs are successfully employed for the optimization of
pin-fin heat sinks. GAs are usually considered as a computational method to obtain optimal solution in a very large solution
space. Entropy generation rate due to heat transfer and pressure
drop across pin-fins is minimized by using GAs. The effects
of pin diameter, approach velocity, and pin density for low and
high thermal conductivities are examined with respect to their
role in influencing optimum design conditions and the overall
performance of the heat sink. The following is observed.
1) GA has evolved itself and has reached a stable condition as
the generation progresses.
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IEEE TRANSACTIONS ON COMPONENTS AND PACKAGING TECHNOLOGIES, VOL. 32, NO. 1, MARCH 2009
TABLE IV
RESULTS FOR OPTIMIZATION OF THREE PARAMETERS
FOR STAGGERED ARRANGEMENT
[6] K. Foli, T. Okabe, M. Olhofer, Y. Jin, and B. Sendhoff, “Optimization
of micro heat exchanger: CFD, analytical approach and multi-objective
evolutionary algorithms,” Int. J. Heat and Mass Transfer, vol. 49, no.
5–6, pp. 1090–1099, 2006.
[7] K. Jeevan, G. A. Quadir, K. N. Seetharamu, I. A. Azid, and Z. A. Zainal,
“Optimization of thermal resistance of stacked micro-channel using genetic algorithms,” Int. J. Numer. Methods Heat Fluid Flow, vol. 15, no.
1, pp. 27–42, 2005.
[8] S. Sajjad and S. Mohsin, “Comparative study on VQ with simple GA
and ordain GA,” in Proc. 9th WSEAS Int. Conf. Autom. Control, Modeling, Simulation (AMCOS 07), Istanbul, Turkey, May 27–29, 2007, pp.
203–207.
[9] D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning. New York: Addison-Wesley, 1989.
[10] R. J. Bauer, Genetic Algorithms and Investment Strategies. New
York: Wiley, 1994.
[11] A. Zukauskas, “Heat transfer from tubes in crossflow,” Adv. Heat
Transfer, vol. 8, pp. 93–160, 1972.
Ayesha M. Sheikh received the M.S. degree in computer science from COMSATS Institute of Information Technology, Abbottabad, Pakistan, in 2005. She
is currently pursuing the Ph.D. degree in the Automatic Control and System Engineering Department,
Sheffield University, Sheffield, U.K.
Her research interests include intelligent agents,
unmanned autonomous vehicles (UAVs), cooperative
planning, and stochastic modeling.
2) Optimum dimensionless entropy generation rate increases
with the increase in approach velocity and decreases with
the increase in number of pins and pin diameter.
3) Staggered arrangement gives the highest thermal performance for the same material and the pin density.
4) Both inline and staggered arrangements show the same behavior for thermal resistance, pressure drop, and dimensionless entropy generation rate.
REFERENCES
[1] R. M. Friedberg, “A Learning Machine,” IBM J., pt. Part I, pp. 2–3,
1958.
[2] R. M. Friedberg, “A learning machine,” IBM J., pt. Part II, pp. 282–287,
1959.
[3] J. Holland, Adaptation in Natural and Artificial Systems. Ann Arbor,
MI: Univ. of Michigan Press, 1975.
[4] J. Koza, Genetic Programming: On the Programming of Computers by
Means of Natural Selection. Cambridge, MA: MIT Press, 1992.
[5] W. A. Khan, “Modeling of Fluid Flow and Heat Transfer for Optimization of Pin-Fin Heat Sinks,” Ph.D. dissertation, Univ. of Waterloo, Waterloo, ON, Canada, 2004.
Waqar Ahmed Khan is an Associate Professor of
mechanical engineering at the National University
of Sciences and Technology, Karachi, Pakistan.
He has developed several unique analytical models
for the fluid flow and heat transfer across single
cylinders (circular/elliptical), tube banks, and pin-fin
heat sinks to Newtonian and non-Newtonian fluids.
His research interests include modeling of forced
convection heat transfer from complex geometries,
microchannel heat sinks, thermal system optimization using entropy generation minimization, forced
and mixed convection, and conjugate heat transfer in air and liquid cooled
applications. He has more than 28 publications in refereed journals and
international conferences.
Dr. Khan is a member of ASME, AIAA and the Pakistan engineering council.
Sajjad Mohsin received the M.Sc. computer science
degree from Quaid-i-Azam University, Islamabad,
Pakistan, in 1987, the M.E. degree in computer
science and systems engineering from Muroran
Institute of Technology, Japan, in 2002, and Ph.D.
degree from the Muroran Institute of Technology,
Muroran, Japan, in 2005.
He is an Associate Professor in Department
of Computer Science, COMSATS Institute of Information Technology, Islamabad, Pakistan. His
research interests include neural networks, genetic
algorithms, fuzzy logic, soft computing, evolutionary computing, pattern
recognition, vector quantization. He has more than 15 refereed journal and
conference publications to his credit. He is a member the editorial board of
three international journals.