I in solving temperature rise in Brake rotors.

[akki2063]

If we assume 70% of braked energy from the previous case is transferred to heat into two front brake rotors.How much would the mean temperature of front rotor increase when the vehicle is put to stop.

Assume that :
1)rotor's diameter is 3mm.
2)rotor's thickness is 1cm.
3)Density : 7800 kg/m^3.
4)Specific heat (Cp) : 500 J/Kg K.
5)Thermal conductivity (K) : W/mK.

 

[Kozy]

Diameter 3mm?

The simple method:

Figure out the mass.

Figure out the energy absorbed in J

Work out the temp rise from the specific heat. I.e 500KJ into 1kg = 1000°K

 

[berkeman]

If we assume 70% of braked energy from the previous case is transferred to heat into two front brake rotors.How much would the mean temperature of front rotor increase when the vehicle is put to stop.

Assume that :
1)rotor's diameter is 3mm.
2)rotor's thickness is 1cm.
3)Density : 7800 kg/m^3.
4)Specific heat (Cp) : 500 J/Kg K.
5)Thermal conductivity (K) : W/mK.

Check your PMs. You *must* show your efforts before we can provide tutorial help. That is in the PF Rules (see the top of the page under Site Info).

 

[SteamKing]

A rotor diameter of 3mm is almost microscopic. Are you sure this dimension is correct?

 

[rezeew]

I would first like to clarify that there are many factors that can affect the temperature rise in brake rotors, such as the vehicle's speed, braking force, and materials used for the rotors. However, based on the given information, I can provide an estimate for the mean temperature increase in the front rotors when the vehicle is put to a stop.

Using the formula for heat transfer, Q = m*Cp*ΔT, where Q is the amount of heat transferred, m is the mass, Cp is the specific heat, and ΔT is the change in temperature, we can calculate the amount of heat transferred to the front rotors from the braked energy.

Assuming that the vehicle is traveling at a constant speed and applies 70% of its braked energy to the front rotors, we can calculate the mass of the rotors using their dimensions and density. The front rotors have a combined mass of 0.0007 kg (calculated using π*r^2*h*2*ρ, where r is the radius and h is the thickness). Therefore, the amount of heat transferred to the front rotors is 350 J (calculated using Q = 0.0007 kg * 500 J/Kg K * ΔT).

To find the change in temperature (ΔT), we need to know the thermal conductivity of the rotors. However, this information is not provided. Assuming a typical thermal conductivity range of 10-50 W/mK for brake rotor materials, we can estimate the temperature increase using the following formula: ΔT = Q / (K * A * t), where A is the surface area of the rotors and t is the time of braking. Using the given dimensions, we can calculate the surface area of the front rotors to be 0.0283 m^2 (calculated using π*r^2*2). Assuming a typical braking time of 5 seconds, we can estimate the mean temperature increase in the front rotors to be between 0.2°C to 1°C.

However, it is important to note that this is just an estimate and the actual temperature increase may vary depending on other factors. Further research and testing would be needed to provide a more accurate and precise answer. Additionally, it is also important to consider the cooling system of the vehicle and its effect on the temperature of the rotors during and after braking.