Electronic – How to calculate the thermal rise of the MOSFET

(100*10%)^2 * 4.5mohm P = 0.45W is wrong because the square of a mean value is not equal to the mean of the squares.

You are interested in the mean power that's why you first have to calculate the power for continuous current and then multiply by 0.1 for the duty-cycle, i.e. you have to calculate

\$(100A)^2 \cdot 4.5m\Omega \cdot 0.1 = 4.5W\$

in order to get the mean power dissipation in the MOSFET.

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EDIT:
For calculating the temperature rise you must not use the derating factor (units [\$W/°C\$]; it just gives you an estimate how much the max. power dissipation has to be derated per each °C above 25°C) like you have done, but the thermal resistance \$R_\theta\$ (units [\$°C/W\$]; it tells you how much the temperature rises per Watt).

If you don't use a eat sink the datasheet tells you that thermal resistance from junction to ambience is

\$R_{\theta JA} = 62°C/W\$

If you use a heat sink the datasheet tells you that thermal resistance from junction to heat sink is

\$R_{\theta JS} = R_{\theta JC} + R_{\theta CS} = 0.402°C/W + 0.5°C/W \approx 1 °C/W\$

So without heat sink junction temperature rise with respect to ambience would be

\$4.5W \cdot 62°C/W = 279°C\$ (which is much too high; i.e. you need a heat sink).

With heat sink junction temperature rise with respect to heat sink would be

\$4.5W \cdot 1°C/W=4.5°C\$.

Of course it depends on the thermal resistance of the heat sink what you will get as total temperature rise with respect to ambience.

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Still you have to take care that instantaneous power (=45W) is within limits during the on-time.

You will find detailed data on the LFPAK33 package in this document LFPAK MOSFET thermal design guide.

As a rule of thumb, in an automotive environment with 80°C max Ta, the maximum power dissipation on FR4 laminate is 1W. At 85°C it will obviously be less.

So you can forget about your 14W without a very, very substantial heat sink or equivalent structure to remove the heat.

The 79W is not only with a heatsink, it's with an extremely unrealistic heatsink that holds the mounting base temperature at 25°C despite 79W flowing into it. You might be able to accomplish that by fast-flowing chilled water through a copper heatsink. In short, it's not a realistically useful number except as kind of a theoretical extrapolation.

As an aside, I fear we are losing the intuition of power dissipation with the phasing out of incandescent bulbs. Anyone who has unscrewed a 60W or 100W incandescent bulb just after it has been illuminated for some time will know what I mean.