Feb 252013
 

Introduction

This article is essential for anyone who deals with or has to use a cooling radiator for a particular electronic unit (audio transistor circuits, transistors, cooling of semiconductor SSR relays, cooling of triacs, cooling of powerful diodes, cooling of powerful LEDs, cooling of thyristors, cooling of CPU, cooling of a laser diode, integrated circuits of all types and other electronic units). The article sets out the methodology and principles necessary for the selection of a cooling radiator. We hope to be particularly useful, given the scarcity of information on the Internet on this topic. We will not discuss the forced cooling by a fan or an operating fluid.

STM products

The transfer of thermal energy is carried out by a body with higher temperature to a body or environment with lower temperature (usually air, but could be water, a refrigerant or oil). Practically in electronics, in order to generate heat transfer from the cooling radiator towards the surrounding environment, the temperature of the radiator has to be higher than that of the medium. The law of the French scientist Joseph Fourier about the heat conduction, in the case of one-dimensional form of direction x, shows that:

When there is a temperature gradient in a body, the heat will be released by the body having higher temperature to the body with lower temperature (in this case the environment). The heat, which will be released through conduction is proportional to the temperature gradient and the cross-sectional area.

Cooling radiators

Cooling radiators become more and more necessary also due to the widely spread powerful LED diodes. Very often manufacturers make products with a good design, but with not so good coolants. Thus, the LEDs operate in a much hotter environment than their normal working environment, and thereby burn too quickly.

FF1 LED lamp

In the whole process of transferring heat, the heat passes through different elements with different heat capacity and different thermal conductivity. In order to make reliable calculations of the cooling radiator, we need to refer to the ambient temperature. Ambient temperature of 25 ˚C is considered a good starting point in our climate. It is imperative to preliminary set the highest possible ambient temperature as well as take into account factors such as the radiator’s location (for better heat transfer), well-polished surfaces, the use of thermally conductive silicone paste, altitude, etc. The main goal of designers of finished products is to achieve the lowest possible thermal resistance.

 

Thermal resistance

We can compare thermal resistance with electrical resistance and heat transfer – with the size of the electric current. The lower the total thermal resistance of the cooling system is, the more power can be dissipated. Of course, it is good to note that the heat transfer is not an instantaneous process. There is a definite time for distribution and other factors which we are not going to discuss in this article. The transfer of thermal energy between the semiconductor chip and the ambient air is modeled as a series of resistances for the heat flow, a semiconductor resistance, crystal – body, body – radiator and radiator – environment. The sum of these resistances gives the total thermal resistance. The temperature resistance is defined as the increase of temperature in ˚С for a unit of power in W, analogously to the electrical resistance and is expressed by the measuring unit ˚C/W. The overall calculation is comparatively relative, since the irregular distribution of heat with respect to the radiator is not taken into account. It refers to models that are in thermal balance and the temperature alteration over time is not taken into account.

 

Images of fluid motion by natural convection, calculation method: numerical methods (Computational fluid dynamics-CFD)

razpredelenie na traektoriq fluid pri krygyl radiator sys styr4ashti lameli

CFD analysis showing the distribution of the trajectory of a fluid in the case of a circular radiator with protruding axial lamellae.

razpredelenie na traektoriq fluid pri radiator s radialno razpolojeni lameli

CFD analysis showing the distribution of the trajectory of a fluid in the case of circular radiator with radial lamellae.

CFD_Forced_Convection_Heat_Sink_v4

CFD analysis showing temperature contours; surface and circular trajectories and air flow caused by a fan.

 eoa_watermann1_305 estesvena konvekcia

 

 

Cooling of a semiconductor device or other electronic device through a cooling radiator

We could say that the cooling of an item is realized through the transfer (release) of heat from one body to another through heat exchange. In order to implement the best heat transfer the most important parameter of the material is its thermal resistance. It is similar to the electrical resistance. Respectively, the lower the thermal resistance of a given material is, the more quickly it will be able to transfer heat. Thermal resistance is reciprocal of thermal conductivity. The measuring unit in the SI system is kelvin per watt [K /W], as you all know the change in temperature by 1K is equal to the change by 1˚C, Δ1 K = Δ1°C, therefore we use the equivalent measuring unit [C˚/W]. All semiconductor devices emitting heat must be supplied with proper cooling otherwise irreversible changes will occur in the crystal structure. The maximum temperature of the semiconductor Tj is specified by the manufacturer as well as the thermal resistance semiconductor crystal – casing Rthj-c and the absolute thermal resistance Rth. Based on this information, the designer of the finished product must calculate the surface area and the size of the required cooling radiator so that the device can operate properly. The calculation of a cooling radiator has to guarantee that the working temperature is less than the highest temperature specified by the manufacturer.

 

Tj – temperature of the semiconductor crystal
Tc – temperature of the semiconductor casing
Tf – temperature of the radiator
Ta – air temperature
Rthj-c – thermal resistance of semiconductor crystal-casing (transistor)
Rthc-r – thermal resistance of the dielectric substrate and the silicone paste
Rthr-a – thermal resistance of the radiator

Comparative table of the possibility of a semiconductor device to release thermal energy depending on the ambient temperature. As you can see, by increasing the ambient temperature (the temperature of the room), the system’s ability to dissipate heat is reduced.
There is a graph by the manufacturer describing a transistor or a semiconductor device and its ability to dissipate thermal energy equal to 75W at ambient temperature of 25 ˚C. It can be seen very well on the graph that by increasing the ambient temperature to100˚C, the semiconductor device can dissipate heat up to 30 W. By the same analogy we can conclude that the lower the ambient temperature, the more intense the cooling radiator would exchange heat, therefore the temperature of the semiconductor will be lower and it will increase its durability, respectively the same size radiator could dissipate more power . The durability of a semiconductor device is strongly dependent on its transition temperature and this applies to absolutely all semiconductors: transistors, diodes, thyristors, triacs, integrated circuits, SSR relays, LEDs, which are manufactured to be more and more powerful, as well as to any other type of electronic components who need extra cooling through a radiator. The sample transistor that we discuss in this article has thermal resistance transition – casing 1.67 ˚C /W, thus the temperature of a semiconductor crystal would be higher than the temperature of its casing.

Firstly we will calculate what the transition temperature will be if the temperature of the casing is 25˚C and the power dissipation is 75 W. The thermal resistance is equal to 1.67, the power is 75 W, therefore the transition temperature is 1.67×75 = 125 ˚C

The most efficient use of powerful transistors, light emitting diodes (LED), SSR relays, diodes, thyristors and other semiconductor elements that need additional cooling is only possible when the heat release in the environment is well-calculated. In order to simplify the further explanations, we will refer only to transistors, and the calculations may be used for other semiconductor devices. Thermal resistances in this heat transfer are:

– thermal resistance between the collector transition of the transistor and its casing Rthj-c which can be obtained from the datasheet catalog of semiconductor elements;
– thermal resistance between the casing and the radiator Rthc-r which depends primarily on the proper thermal contact between the two surfaces (smoothness of the surfaces, the applied clamping force, the presence of a diathermanous silicone paste, material and thickness of the dielectric substrate, etc.)
– thermal resistance between the radiator and the environment Rthr-a, depending on the surface of the radiator and its condition (color, coverage, smoothness) position of the radiator (horizontal, vertical, length and distance of the fins);
The total resulting resistance is: Rth = Rthj-c + Rthc-r + Rthr-a. All these thermal resistances are measured in C ˚/W.

As a result of the cooling the transition temperature tj transition (˚C) will be obtained as the sum of all individual thermal resistances of the transistor (or another semiconductor device) and the radiator, multiplied by the collector power Pc (W) which needs to be dissipated (or the power required for dissipating from a semiconductor device). All this is summed up with the ambient temperature ta. In these calculations we need to include the highest ambient temperature that may be reached, i.e:

formula (1)

Calculations by formula (1) are made when we have a radiator at our disposal and we need to check its efficacy. By the same formula we can calculate the highest allowable power of dissipation:

formula (2)

Where tj max is the highest allowable transition temperature of the transistor specified in the manufacturer’s datasheet catalog (C˚). In most cases, it can be roughly assumed that tj max is 70˚C for germanium transistors and 150˚C for silicic semiconductor items. For better protection and long term performance of semiconductor devices, these temperatures can be lowered by 10-15%.
The thermal resistance of the radiator to be installed so as not to exceed the maximum allowable power Pc max would be:

formula (3)

If the surface of the transistor’s casing and its channel in the radiator are not enough tight-fitting and the surface areas that come into contact are not smooth enough, the thermal resistance Rthc-r could increase by 2-3 (C˚/ W). The filling of these jogs with thermally conductive silicic paste decreases the Rthc-r to 0.5 (C˚/W). The use of a dielectric substrate between the casing of the semiconductor and the coolant is often required. This increases the thermal resistance depending on the thickness and the material of the substrate. The following table shows the dependence according to certain types of substrates having various thicknesses:

 

Material of the substrate Thickness of the substrate µm Thermal resistence Rthcr

(C˚/W)

Polyethylene or Teflon tape

10

1,1

Mica

60

0,6

Mica

140

2

Mica

400

2,7

Mica with silicone paste

40

0,5

Anodized surface

–––

1

 

Example: There is a transistor with thermal resistance Rthj-c = 1.5 (C˚/W), which has to dissipate thermal power of 15 W. It is mounted to a radiator with thermal resistance Rthr-a = 1.8 (C ˚ / W), and is insulated from it by a mica plate with Rthc-r = 0.5 (C˚/W), the ambient temperature is 25˚C.

The transition temperature of the semiconductor will reach: tj = 15 (1.5 +0.5 +1.8) +25 = 82 C ˚

By formulas (1), (2) and (3) we can calculate various characteristics in suitable versions.

 

Flat panel radiators


Flat panel radiators have the simplest design of all types of radiators – a flat aluminum plate with a square or rectangular shape. The necessary surface area S (cm2) can be calculated by the formula:

formula (4)

wherein Rthr-a is the aforementioned thermal resistance of the radiator and A is a factor depending on the condition of the surface area and on the heat transfer conditions:
A = 2200 with untreated aluminum plate and difficult air exchange (horizontal position);
A = 1600 with untreated aluminum plate and facilitated air exchange (vertical position) ;
A = 1200 with treated (by sandblasting) aluminum plate and vertical position.
Formula (4) can be used for П – shaped radiators, provided that there is streamline at both sides.
Example: the transistor…….. has to dissipate 6 W of power. There has to be such sizing for a flat panel radiator that the transition temperature tj max does not exceed 150˚C at ambient temperature TA = 35˚C. The location of the radiator will be vertical.

 The temperature of the radiator will be determined by:

In this case we will choose the option in which the transistor does not need a dielectric substrate, therefore Rthc-r=0 , Rthj-c  = 10 C˚/W,:


Hence we substitute in 

The vertical position of the cooling radiator causes streamline at both sides and the calculated value of S can be reduced twice.

A table showing the sizing of a flat panel aluminum radiator, untreated, vertically mounted (in case of horizontal mounting the surface area must be 20% larger)

Thermal resistence Rthr(C˚/W)

Required cooling surface area  in cm2, plate thickness 1mm Required cooling surface area  in cm2, plate thickness 2 mm Required cooling surface area  in cm2, plate thickness 3 mm

2

––––-

700

550

3

600

350

280

4

280

220

190

5

180

160

140

6

135

125

120

7

120

100

95

8

90

82

80

9

80

72

70

10

70

65

63

50

55

52

50

100

42

40

40

200

30

30

30

300

20

20

20

Finned tubed radiators

In cases of calculated radiators in which the surface area S has large and inconvenient dimensions– we need to use finned tubed radiators. There are various forms of finned tubed radiators. The installation principles listed above in this article can be applied to them.

Forced_convection_heat_sink_using_CFD_v1

Forced cooling by a fan

Below graphs give enough information for designers who can quickly and easily select the length of the radiator, depending on the required power, which has to be dissipated by a cooling radiator. We need to consider not only the power that we want to dissipate, but also what temperature difference we want to maintain. These graphs show some types of radiators:

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