Dimensions - Disc Brake Surface Area

[jase03]

Dimensions -- Disc Brake Surface Area

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 130mm; inner radius 50mm; thickness 10mm. (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 heat transfer of the disk rotor is 120 W/m2/K, how much heat energy is radiatred from each of the disk rotors when the ambient air temperature is 30 C

Help with solutions and working out would be greatly appreciated.

 

[brewnog]

Have a go yourself here first.

 

[Ranger Mike]

welcome and you are close ...heat on rotoes is in excess of 650 C..over 1200 degrees F
the rotor is NOT a flat disc and has cooling grooves amchined into the sufaces ( on each side) to dispate build of of gases under braking conditions. The disc is not soldu but in fact, is machined to provide more cooling area...have you seen a disc rotor used in this application?
The brake fluid itself may be cylced through a cooler to reduce tmeperatures.

forced air to cool..some classes permit the use of electric fans to cool the caliper rotor which means the frontal area of the car would have less open area for air inlet thus reducing aero drag ..i.e faster car

simple calcualtions not taking int o account the above will not be correct

 

[Mech_Engineer]

Ranger Mike- He's posted a homework problem regarding forced convection and brewnog is having him post his work before we help. He isn't asking about real world applications.

 

[Nickie]

i) To calculate the surface area of the disk rotor, we can use the formula for the surface area of a donut shape:

Surface Area = 2πh(r1 + r2)

Where h is the thickness of the disk (10mm in this case), r1 is the outer radius (130mm) and r2 is the inner radius (50mm).

Plugging in the values, we get:

Surface Area = 2π(10mm)(130mm + 50mm)
= 2π(10mm)(180mm)
= 3600π mm2

Converting to m2, we get:

Surface Area = 3600π mm2 * (1m/1000mm)^2
= 0.011 m2

Therefore, the surface area of the disk rotor is 0.011 m2.

ii) To calculate the heat energy radiated from each disk rotor, we can use the formula:

Heat Energy = Surface Area * Heat Transfer Coefficient * (Temperature Difference)

In this case, the temperature difference is the difference between the disk rotor temperature (500C) and the ambient air temperature (30C).

Plugging in the values, we get:

Heat Energy = (0.011 m2) * (120 W/m2/K) * (500C - 30C)
= 0.011 m2 * 120 W/m2/K * 470C
= 61.32 J

Therefore, each disk rotor radiates 61.32 J of heat energy when the ambient air temperature is 30C.