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# Heat

Electrical heating occurs in any component or wire that carries an electrical current. How hot the component or wire gets depends on the rate that heat is generated and on how quickly heat can get out of the item into the surroundings. How quickly the item reaches a steady temperature also depends on how much heat the item can absorb or how ‘large’ it is thermally, i.e. on its ‘thermal mass’. The situation is more complicated in most motor control application because electrical heating can be very intermittent.

#### Heat generation.

Electrical heat is generated by electrical current (amps) flowing through a wire or component which has electrical ‘resistance’ (ohms). All electrical components and wires have resistance but the larger the wire, the lower its resistance. The heat generated is the square of the current multiplied by the resistance. Electricians refer to current as ‘I’ and resistance as ‘R’ so the heat generated is I²R. Note that the voltage does not come into this: heat generation has nothing directly to do with the voltage. However the power the device is handling is directly concerned with the voltage since power is volts times amps. This is why a 24v system is better than a 12v one: it can give double the power at the same heat or, if you halve the current, the same power for ¾ the heat.

#### Land / water

Most land based vehicle applications are very ´peaky´: a machine on land generally only takes a lot of current to accelerate or to climb a hill, both are usually only a few seconds.

Boats need a continuous rating since the faster you go, the higher the current as it takes power simply to move through water, not just to get up to speed. We recommend using a bigger controller than for the same motor on land – or take steps to remove the heat quicker.

#### Heat dissipation

A hot object dissipates heat, i.e. it looses heat into the surroundings. The rate of heat loss depends on the area over which the heat is dissipated, how good the ‘contact’ with the surroundings, hot much hotter than the surroundings the object is, the speed of airflow over the object and even the colour of the object. In practise the dissipation is eventually to the air (unless you are on a boat and can use water) so the ‘contact’ is down to the surface roughness (whether the object is finned) and the airflow. We have made some significant improvements to the thermal performance of our controllers by a] fitting cooling fans, and b] fitting either finned or water cooled heatsinks.

#### Heat conduction

Usually the object which is generating the heat is not the same object that is losing the heat to the air. The heat has to flow from one object to another, usually through other objects on the way.

The heat conduction path does not let the heat flow unless there is a temperature drop all the way along it. All the objects through which the heat must flow ‘resist’ the flow of heat. An object which has a high resistance (be it to heat flow or to electricity) has a poor ‘conductivity’. A good conductor does not resist the flow of heat so much as a poor conductor.

If there are several objects through which the heat has to flow the contact between each item and the next must be good: a very small gap, even in the form of surface roughness, can dramatically reduce the heat flow (i.e. it can add resistance to the thermal path) by trapping a thin film or air, which is an exceedingly good insulator. Obviously this is bad so it is common practise to use ‘heatsink compound’ to fill the gaps caused by roughness when joining two metal parts through which heat must flow.

#### Thermal mass

If an object has a lot of ‘thermal mass’ it takes a lot of heat to increase its temperature. If we do not want an object to heat quickly, then we must have a large thermal mass. Thermal mass will even out the heating, so a few short, high bursts of heat don’t cause overheating. However thermal mass alone won’t cool an object. The mass only stores the heat – which must still get dissipated safely. A high thermal mass increase the time the object takes to get hot, but its final temperature is still determined by the balance between heating and cooling rates.

#### Materials

How do various heatsink materials perform? The table below shows relative values for several metals.

Conductivity
Material Thermal Electrical Specific heat
Aluminium 50 339 20
Copper 92 562 9
Gold 70 413 3