heat dissipated in mosfet and required copper

[mshh]

I want to design h bridge using mosfet gate driver ir2112 and transistor IRF3205. I want to calculate the dissipated heat in the Mosfet in order not to use heat sink. according to the datasheet of both devices I calculated the dissipated power. the power supply is 24 volt, current 10A,frequency 20khz.
Rds(on) at temperature 25 C is .008 ohm. at 125 C (hot ) RDs(hot)= RDson (at 25)[1+.005x(T125-T25)=0.008[1+.005(125-25)]=0.012 ohm or 12 mohm.
so to calculate PD RESISTIVE = [ILOAD² × RDS(ON)HOT] × (VOUT/VIN) = 100*.012*0.94=1.128 watt.
from the ir3205 datasheet CRSS=211pf, ir2112 datasheet the gate driver current is almost 350 mA so
PD SWITCHING = (CRSS × VIN² × fSW × ILOAD)/IGATE = 211*^-12*24*24*20*1000*10/.350 = 0.069 watt
so the total power dissipated = 1.128+0.069= 1.19 watt.
is this right. if so will it need heat sink?

[srizbf]

In Pd resistive ,
why the term Vout/Vin ?

[mshh]

Vout/Vin represent the duty cycle which affect the current value in the mosfet

[FvM]

Crrs @ 24V doesn't give the effectiv capacitance, due to non-linear characteristic. You better use plateau charge from Qg graph. Expectable rise/fall time is about 100 ns according to my calculation, switching loss about 0.5 W, still moderate.

Junction-to-ambient thermal resistance of 62 K/W demands for heat sink, e.g. a small PCB mounted type with 10 - 20 K/W.

[mshh]

what is the aproximate area of pcb copper required to dissipate the heat?