# Heat Sink Thermal Resistance and Size Calculation : Heat Sink Selection

Increase in heat dissipation rate and reduction in overall form factor has made thermal management of electronics products a challenging task. Heat sinks are used to cool electronics devices by increasing heat dissipating surface area. In this article, we will discuss how to select heat sink by calculating heat sink thermal Resistance?

## How does a Heat Sink work?

Heat sink works by increasing the heat dissipating area of heat dissipating component. It enables the heat sink to transfer more heat to a colder environment. Rate of heat transfer from a heat sink depends on the following factors:

• Heat Sink material thermal conductivity
• Available surface area
• Natural or forced convection (air speed)
• Ambient conditions such as air temperature.

## Heat Sink Thermal Resistance Calculations

Thermal resistance is a property of a material or body by which a material resists the flow of heat. It measures the temperature difference between two ends of a body. Similarly thermal resistance of a heat sink measures the heat transfer efficiency of a heat sink in a thermal circuit. To select a heat sink, firstly thermal resistance of the heat circuit is calculated.

Mathematically thermal resistance of a body is equal to the ratio of temperature difference and heat generated. R = Thermal resistance (°C/W), Q = Generated heat (watt), (T2-T1) = Difference in temperature.

###### Calculation of Thermal resistance in series

Rules of electrical resistance in series also apply to thermal resistance. To understand this, let’s consider an example of the cooling of heat dissipating chip on the PCB.

From the above Heat Sink Thermal Circuit: Q : Total power or heat dissipation in watt.

Tj : Device / chip junction temperature (°C).

Tc : Device / chip case temperature (°C).

Th : Heat sink temperature (°C).

Ta : Ambient air temperature (°C).

Rja : Junction to air thermal resistance.

Rjc : Junction to chip thermal resistance.

Rch : Chip to heat sink (Interface material) thermal resistance.

Rha : Heat sink to air thermal resistance.

Typical Values of Commonly used Electronic Package Thermal Resistance
Electronics Package (Rjc) Junction to Case (°C/W) (Rca) Case to Air (°C/W)
TO-3 5 60
TO-39 12 140
TO-223 30.6 53
TO-263 23.5 50

**Please note these values are for indicative purpose only please refer package datasheet.

## Heat Sink Selection

Selection of heat sink is done by comparing the values of the thermal resistance from junction to air (Rja) and sum of the thermal-resistance of junction to case (Rjc) & case to air(Rca)

If

Rjc + Rca < Rja ; Heat sink is not required.

If

Rjc + Rca > Rja ; Heat sink is required.

Selected heat sink thermal resistance (Rha) should always be greater than the total calculated required thermal resistance.

## How to Improve Heat sink Thermal Performance

Heat Sink thermal performance can be increased by improving conductive, convective or radiative heat transfer.  Following points should be considered to improve the performance of the heat sink without increasing its size.

###### 1) Heat Sink Design : Arrangement, Shape and Size of Fins Heat sink performance can be improved by improving the air flow in the heat sink. Size, design orientation, and the arrangement of fins on the heat sink has a direct impact of the airflow inside the heatsink. Therefore heat sink performance can be improved just by improving heat sink fins design.

###### 2) Air Flow Direction Direction of airflow also has an impact on the performance of the heat sink. Air flow in the direction parallel to fins is recommended. Because in this, air moves along the longer distance through fins. Whereas when air flows in the direction perpendicular to fins. Air does not reach the inside area of the heat sink.

###### 3) Airflow Speed and Type

Type of airflow (natural or forced convection) affect the heat sink thermal performance. Thermal resistance of a heat sink can be reduced by increasing the air speed.

###### 4) Heat sink Material

Highly conductive material reduces heat sink thermal resistance. For similar geometry, copper heat sink thermal resistance is less than aluminum heat sink. Therefore heat sink performance can be increased by using highly conductive material.

###### 5) Thermal interface Materials

Thermal paste or thermal pads are used to fill air gaps between heat sink and heat dissipating chip. Heat sink thermal performance can be increased by selecting a highly conductive thermal paste/pad.

###### 6) Heat Sink attachment Methods

Heat sink thermal performance can be increased by selecting an appropriate method of attaching a heat sink to heat dissipating components. Common heat sink attachment methods include :