hi, I want to know if the following circuit can work.
Hola, quiero saber si el siguiente circuito puede funcionar.
That looks like it should work. Note that the transistor is an inverter so PWM 255 is fully-off and PWM 0 is fully-on, etc.
No, its not a good circuit for PWM, R3 is far too large for crisp switching. 680 ohms 1/2 watt would be a
better choice, but still not ideal (5µs switch on time or so). With R3=10k the device will take more like
100µs to switch on, causing severe switching losses.
A MOSFET driver chip is the standard, reliable, way to drive a MOSFET at PWM speeds. A power MOSFET
gate has a lot of capacitance and requires high current drive, the IRFZ44 has about 7nF gate capacitance.
R1 isn't doing much useful, lose it to further improve switching time. There should be a decoupling
capacitor on the 12V rail, a nice big one to match the load, so probably 100µF or more, 16V or more.
If the inductive load is very inductive you also need to worry about it pulling the 12V rail up above 12V.
It would be useful to know what the supply is, and what the load is.
MarkT:
If the inductive load is very inductive you also need to worry about it pulling the 12V rail up above 12V.
Curious concept - how would it do that?
Maybe with a length of 0000 AWG wire.
Yeah, I guess that might do it. 
Paul__B:
Curious concept - how would it do that?
Good point, I'm thinking of some other circuit topology there... Sorry.
commenting to follow