During frequent braking under race conditions the disk brake rotors on the car d

Question

During frequent braking under race conditions the disk brake rotors on the car described above reach a temperature of 500C. These disk brakes rely on forced convection to cool them. The dimensions of each disk rotor are: outer radius 135mm; inner radius 70mm; thickness 12mm. (Assume the disk is a simple donut shape ).

i) What is the surface area of the disk rotor (in m2)? (Include both sides and the edges)


ii) Given the emmisivity of the disk rotor is 0.4, how much heat energy is radiated from each of the disk rotors at 400C (The stephan boltzman constant is 5.67 x 10^-8 W/M^2/K^4
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I can understand how to get i) but dont know how to work out ii)


Thank yo

Explanation / Answer

i) Area A = 2*(Rout^2 - Rin^2) + 2t(Rout+Rin) = 2*(0.135^2 - 0.07^2) + 2*0.012*(0.135+0.07) = 0.099 m^2

ii) Energy emitted = AT^4 = 0.4*(5.67*10^-8)*0.099*(400+273)^4 = 460.6 W

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