## Basics of Heat Transfer

**Fundamentals of Critical Temperature Calculation**

Determining critical temperatures is contingent upon a critical understanding of:

- The electrothermal analogue
- Thermal conductivity (k)
- Heat transfer coefficient (h)
- Thermal resistance R
_{th}

## Thermal Conduction, Convection, and Resistance

To understand the heat transfer properties of thermal interface materials (TIMs) we need to understand the meaning of thermal conduction, convection and resistance.**Conduction**

The notion of thermal conduction is not very old. Biot (1804) and Fourier (1822) were the first to quantitatively study the heat flow through a piece of solid material. Fourier observed that the heat flow q was proportional to the temperature difference ?T over the test piece, proportional to the cross sectional area A of the bar, and inversely proportional to the length or thickness, known as Fourier’s law:

The proportionality constant k is called the thermal conductivity in W/mK. It is a material property and a measure for the ability of a material to conduct heat. The range for engineering materials is from air (0.03W/mK), via plastics (0.2 W/mK), glass (1 W/mK), aluminum PCB board (200 W/mK) to copper board (400 W/mK). Typical TIM values cover the range 0.4-4 W/mK.

**Convection**

The heat generated in an electronic device is usually transported by conduction to a heat sink or an area where the heat is transferred to a fluid which is called convection. The fluid can be a gas such as air, or a ‘real’ fluid such as water. As a result, the convection heat is proportional to the area A and the temperature difference between the wall and the main stream flow:

This equation is commonly known as “Newton’s Cooling Law”; however, it should be realized that it is neither a law nor was it derived by Newton. In this equation, the proportionality coefficient h is called the heat transfer coefficient in W/m2 K. As a rule-of-thumb, take for natural convection h=10 W/m

^{2}K and for fan-driven forced convection h=50 W/m

^{2}K.

**Resistance**

The last term to discuss shortly is the thermal resistance. In a DC electrical circuit, Ohm’s law describes the relations between the voltages and the currents. It states that a voltage difference over a resistor causes an electrical current, which is proportional to the voltage difference: ?V = I * R.

In steady state heat transfer, a temperature difference causes a heat flow which is proportional to the temperature difference as is seen in equations (1,2). Both equations can be written in the form ΔT = q * Rth, with Rth the thermal resistance (also commonly noted as R when there is no chance for misreading it as an electrical resistance). This is analogous to Ohm’s law. In both the electrical and the thermal case we observe that a driving force exists (either voltage difference or temperature difference), which causes a flow (of current, or of heat) over a resistor.

The thermal resistance per unit area is equal to the ratio between thickness t and thermal conductivity k and is often used to allow for a direct comparison of the heat transfer performance of commercially available TIMs.

## The Heat Transfer Coefficient *h*

The heat transfer from a solid wall into a fluid (air, water) is called convection, and to first order this heat transfer is proportional to the area and the temperature difference between the wall and the fluid:

**q = h * A * ?T**The proportionality constant

*h*is called the ‘heat transfer coefficient’.

**Typical values:**

Natural convection: 10 W/m

^{2}K

Forced convection: 50 W/m

^{2}K

## LED Thermal Management

As the LED heat escalates, several key characteristics may become apparent, which deminstrate the importance of LED thermal mangament. The forward voltage will begin to decrease. The decreasing voltage can impose an increased load on related LED driver components causing their temperature to increase as well. In resistor driven circuits, the forward current will increase.As the LED lights temperature continues to rise, the optical wavelength can shift. The increasing wavelength can cause orange LED lights to appear red or even white LED lights to appear bluish. This color shift typically intensifies with the AlInGaP technologies (red, orange, amber, and yellow).

In addition, a thermally stressed LED lights will loose efficiency and light output will diminish. If the LED thermal management continues to race out of control, the LED junction may break down causing a state of complete thermal runaway. The result is typically catastrophic failure. Other affects of overstressed LEDs may include broken wire bonds, delaminating, internal solder joint detachment, damage to die-bond epoxy, and lens yellowing.

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## Heat Transfer Path

**Electro-Thermal Analogue**

A heat transfer path can be described by an electrical network.