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Heat sinks were invented to absorb heat from an electronic circuit conduct, and then to dissipate or radiate this heat to the surrounding supposedly, ventilated space, at a rate equal to or faster than that of its buildup. Ventilation was not initially recognized as an essential factor to thermal dispersion. However, as electronic circuit-boards continued to heat up, circuit failure became a problem, forcing the inclusion of miniaturized high speed fans. Later, heat sinks with fins and quiet fans were incorporated in most manufactured circuits. Now heat sinks come in the form of a fan with fans made to function as fins to disperse heat. Heat sinks absorb and radiate excess heat from circuit-boards in order to prolong the circuit’s life span. The higher the thermal conductivity of the material used the more efficient and effective the heat sink is. This paper is an attempt to theoretically design a heat sink with a temperature gradient lower than that of the circuit board’s excess heat.

The way that the heat sink is attached to the circuit-board is a major contributor to the efficiency of its heat conductive-absorptivity. The heat-sink’s ability to dissipate and radiate heat at a rate faster than or equal to its absorbency pace is critical to protect, maintain and extend the lifespan of the circuit. The type of material used for the sink and the juncture is crucial in terms of thermal conductivity, heat capacity, emissivity, resistivity and absorptivity. Heat is absorbed or transferred from a material at a higher temperature to a material at a lower temperature. The greater the temperature disparity among the materials, in the direction from the board to the heat sink on to the surrounding, the faster the pace at which heat is either absorbed or transferred. Heat moves among metals through the diffusion of electrons among atoms until a heat balance between the two contacting materials is established [

Equation (1) displays the heat and ampere equations’ parallelism they are to a certain extent equivalent in form and behavior.

The heat sink design must emphasize a large surface area in order to utilize the forced convection heat transfer induced by the fan-made airflow.

The heat sink, the base and the juncture are made up of copper. The base and the heat sink are heat-based welded so the heat resistivity between the two parts can be considered equal to the thermal resistivity of copper. The base is attached to the juncture by rolling the plates around the side of the base and using high pressure guns to attach them. The bottom of the base is attached to the plates using high pressure, and beryllium oxide is used to fill the gaps for lower heat resistance and higher thermal conductivity. The thermal conductivity of beryllium oxide (>200) is greater than that of aluminum. This will make it possible for us to neglect under certain circumstances the existence of a ceramic-grease-based gap-filler.

The fans will provide the heat sink with continuous air flow that will lower the temperature of the heat sink and facilitate the transfer and dissipation of heat through the ducted stream. The two fans provide us with many advantages, faster air streaming through the heat sink fins’ spacing due to the vacuuming effect created by the second fan and continuous air flow in case one of the two fans went out; assuming, of course, a fan functional sensor is available and working.

Assuming the fans are timed to alternate that will create the wind tunnel effects of gusting which increases the affected fins’ surface area. The two fans, due to the difference in size will have a different rotational speed and timely alternating flow as follows [

The air volume flux can be calculated using the area of the fan’s opening, and the fans air speed.

(2)

where w is the width of the duct, and L is the length)

To calculate the gusting of the air movement we have

The area of the smaller fan is used to measure and gauge its rotational speed in order to attain adequate energy to produce the necessary speed.

The alternation can be timed using a switching control system [

1) The increase of air velocity increases the “forced” convective heat transfer;

2) The air speed increases the areas reached by the air flow inside the spacing of the sink’s fins, which in turn increases the functionality of the heat sink, and decreases thermal resistance;

3) This technique supports an increase in the duct’s air pressure over the surface of the sink’s fins; although the design where the duct’s outlet narrows gradually towards the duct’s opening creating a bottleneck effect and increasing the pressure on the sink’s leading edge and inner surface, especially the deep ends of the fins’ spacing on both sides of the sink;

4) A noticeable pressure drop will be noticed at the outlet;

5) The alternating fans create an air flow’s gusting effect that acts as an additional coolant to the sink’s heated surface;

6) This method extends both the life of the computer, its major components including the fans;

7) The system will increase the surface area by allowing for more fins and thinner spacing between the fins.

The thermal resistance can be obtained using Equation (1)

Since both the radiation and forced convection heat transfer are active for the sink in our ducted heat sink scheme then starting with forced convective heat transfer we have the following:

Heat transferred out of the sink is measured on the basis of the temperature difference between the heat sink- fins’ surfaces and the surrounding:

But the convective heat transferred to the surrounding seeps through the sink’s bases and fins where their positioning and attributes, length, height, angles, thickness and spacing, have a lot to do with the heat exchange.

where

But since

We know that

However, we know that the quantity of heat absorbed by the air is:

But since the thermal resistivity is dependent on the fins’ surface area and type of material we have

We know that heat capacitance

and air mass flux rate

with density

and for fins in series

Respectively we have

where

Then

where

The second channel of emitting heat through the heat sink is the radiation of heat through the fins which is influenced by the material used, emissivity and the energy radiated by a surface in relationship to a black body.

where

The heat transfer coefficient of radiation

Where

The Boltzmann

The thermal resistance in the radiation case is inversely proportional to both the surface area

Now it is a good idea to go back to the thermal resistance of the heat between the circuit and the heat-sink’s surrounding where total thermal resistance between the sink-circuit board-juncture and the air surrounding the heat sink

but

Equation (18) shows the need for a high dissipative outlet to prevent over heating however the unknown in this case is the added element that is not made obvious by Equation (15), the forced-convective heat transfer dispersing heat through cooling of the fins surface by the high, double-fanned air flow velocity.

The total rate of convective and radiative heat transfer for the entire heat sink fins is

Assuming we have ^{3}, as in ^{2} as its inlet, and is 60 mm long, the rest of the duct 60 mm long, narrowing down at a (2/5) gradient in the direction of the flow; so for each 5 mm length the duct is narrower by 2 mm, with a (36 * 36) cross section outlet. The convective heat transfer through the duct is

where

Now consider Equation (20) again where

In Equation (23) however, radiation is ignored and

This means that only a small percentage of the heat transferred from the surface of the sink is done through radiation, and considering the radiation heat Equation (16) we can tell that

Radiation heat transfer is almost negligible in comparison to the convective heat transfer for the following reasons |
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1) Radiation within the fins spacing goes into other fins. |

2) Only radiation from the tips of the fins’ surfaces reaches surrounding bodies. |

3) Radiation is subject to exposed surface material and its emissivity. |

4) Forced convective heat-transfer amplifies convection of the sink’s heat and diminishes the importance of the radiation heat transfer in scope and magnitude. |

Now the ambient temperature

If we set Equation (25) equal to zero, and differentiating over the distance before and after the sink, and assuming constant air speed (velocity), which means that the mass flow rate ṁ, is also constant, also assuming constant heat transfer coefficient

by dividing both sides by the total heat transfer we get

where

and by integrating over the duct’s length over the perimeter of the sink we have

where, in this case _{ }

Equation (26) becomes

Using the integration process

We have

Using log rules

Now we can get the average ambient temperature, which we already assumed to be equivalent to the average temperature across the duct in air flow direction:

At

To get the average ambient temperature

We use Equation (39) in Equation (25) to get

Now we can get the total heat transfer by using Equation (41) in Equation (24) to get

Now it is obvious that the difference in temperature between the sink temperature and the inlet can be used to derive the total juncture to ambient thermal resistance. And it can also be assumed that the difference between the sink’s temperature and the outlet temperature can be used to derive the radiative heat transfer. The difference between the two thermal resistances is the forced convective thermal resistance.

The ratio of radiative to total heat transfer is

And so

Based, of course, on the material’s high thermal conductivity, however, its dissipative-dispersive and radiative attributes are due not only to its above mentioned heat transfer qualities, but also due to the forced-convective heat transfer feature [

The heat sinks are neither expensive nor difficult to design or manufacture. The major aspect in heat sinks’ design is sampling of the parts in central areas within the circuit board for better easier access to the heat source for better absorption. Central areas within circuit boards are not easily accessible for heat sinks’ fusing and sampling. The central circuit-board locations’ inaccessibility is a bit challenging to electronic designers when attempting to link the separate parts together for better and faster bussing and data communication. The right heat sink in the right spot within a circuit board facilitates heat conductivity-absorption and dissipation, and extends the life span of the board and its major components. The dual fan design keeps a constant air flow, infiltrates the heat sink’s narrow fins’ spacing, increases surface area, leads to higher convective heat transfer, and reduces pressure at the outlet. The design is made to force the air into the inner regions of the fins’ spacing, and the outlet fan alleviates the pressure build up-forward to the sink. I recommend this system for high heat circuit-boards.