Funciones Específicas.-

The size of a heated surface has a big influence on the rate of heat transfer. Basically,

the heat transfer increases as the heated surface area increases. The best way to

increase the area of the heated surface is by installing fins. These fins may take

different shapes such as pin fins or plate fins. In general, parallel plate fin arrays are

often used to enhance heat transfer by free convection and the fluid flow between the

fins is usually assumed as two-dimensional which gives results close to the three-

dimension analysis as shown by Hung et al (1989). There are limited investigations

for using a heat sink inside an enclosure installed on the substrate. Also, the CPU

thermal analysis in a dimensional form and with realistic boundary condition is

scarce in the literature.

Elenbaas (1942) noticed that there is an interaction between the fin height and

spacing. He concluded that, if the plates are close enough to allow interaction of the

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decreased. He also presented a relationship to calculate the mean Nusselt number for

heat sink in natural convection mode. This relationship is used in this work.

Heindel et al. (1996) investigated numerically and experimentally steady state and

laminar natural convection of heat transfer from an array of highly finned discrete

heat sources mounted on one of the walls of a cavity. The isoflux condition was

applied on the back of the heaters while the opposite wall was assumed isothermal

and was maintained at approximately 15℃. The cavity is filled with a dielectric liquid FC-77. In their experimental study, the temperature difference between the fin

base and the cold plate was maintained below 70℃. Their results show that the discrete heat sources with parallel plate fin arrays experienced a heat transfer

enhancement by as much as 24 and 15 times for vertical and horizontal cavity

orientations, respectively, when compared to un-finned heaters. They concluded that

although the simplifying assumptions in the 2-D numerical model, it however

provides a good approximation to the results of a dense parallel plate fin array which

was determined experimentally. In addition, they stated that the relationship that was

proposed by Elenbaas (1942) gave good prediction for values of mean Nusselt

number.

Lakhal et al (1997) investigated numerically the natural convection heat transfer in

inclined tall rectangular enclosures. Different number of fins attached horizontally to

one heated vertical wall and the opposite wall was isothermal as a cold wall. The two

horizontal walls were adiabatic and the enclosure filled with air. They studied the

effect of Rayleigh number, fin length and enclosure inclination.

They indicate that the heat transfer through the enclosure is considerably affected by

the presence of the fins. At low Rayleigh numbers, the heat transfer regime is

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length increased. That is because the enclosure is divided into small cavities with

increase number and lengths of fins. They examined the enclosure inclination angle in the range of (0 − 60°) and they noticed that the heat transfer decreased with increasing inclination angle of the tall enclosure and the strength of the circulation in

the cavity was also decreased.

Nada (2007) investigated experimentally the natural convection heat transfer in

vertical and horizontal rectangular narrow enclosures filled with air. The enclosure

was heated from one wall and the opposite wall was isothermal while the other two

walls were adiabatic. Different number of plate fins attached to the base and then

were installed on the heated wall. The fin spacing and fin lengths were examined for

both orientations at a wide range of Rayleigh number.

It has been found that, the rate of heat transfer was increased by using fins with any

fin array geometries. Also, Nusselt number and fin effectiveness (defined as the ratio

of the total heat transfer rate in presence of fins to that in absence of fins) increased

with increasing the fin length. Again, the Nusselt number and finned surface

effectiveness increased with increasing fin length in the examined range. For both

orientations, the Nusselt number increased as the fin spacing decreased, then after

certain value of fin spacing, Nusselt number decreased with further decrease in fin

spacing.

Frederick and Moraga (2007) studied numerically 3-D natural convection of air in a

cubical enclosure with horizontal fin attached to the vertical hot wall. The opposite

wall is kept at a constant temperature and the horizontal walls were assumed

adiabatic. They investigated the effect of Rayleigh number, fin width and thermal

conductivity ratio (the ratio between thermal conductivity of fin to air) on the heat

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They found that the addition of fin with low thermal conductivity ratio reduces the

heat transfer compared to the un-finned case. With increasing the thermal

conductivity ratio, there was an enhancements of about 20% and that is because of more heat is dissipated from fin faces. They concluded that finding the optimum

width of the fins is important to enhance heat transfer. Fins shorter or wider than the

ones considered in their study would give lower heat transfer rates. The short fins

have small area, their contribution to overall heat transfer is limited, and the wide

fins block the air flow inside the cavity.

Bocu and Altac (2011) studied 3-D laminar natural convection heat transfer in

rectangular enclosures filled with air numerically. The enclosure was heated from

one of its vertical wall and was cooled from the opposite isothermal wall while the

other walls of the enclosure were insulated. Also, a number of isothermal pin fins

were installed to the interior of the hot wall in different arrangements, diameters and

lengths to enhance the heat transfer.

Different values of Rayleigh numbers were imposed for all cases to obtain the

temperature field and the mean Nusselt numbers over the cold wall. They pointed

that for a fixed case (pin fin configuration, pin length and/or diameter) the Nusselt

number increased as the Rayleigh number incremented. The ratio of Nusselt number

for the case which has fins to that without fins increased as the number of pins

increased, as illustrated in Figure (2.4).

From the different arrangements of the pin fins, the staggered arrangement seems to

be the best configuration. The heat transfer from horizontal arrangement is about 4- 7% more than that of the vertical arrangement.

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