Arduino Uno running in a car

With a surge Zener designed for the purpose (they can pass 100 amps), you don't need a current limiting resistor. Instead, you need a fuse. I've attached a good all-around transient, overvoltage and reverse polarity protection circuit for automotive electronics. The in-line fuse is not shown -- it should preceded the Zener -- and should be chosen considering your ciruit's absolute maximum current draw (as you have done for the circuit you proposed).

Automotive_Filter.png