Engine valves (Cp=440 J / kg · °C and ρ =7840 kg / m^3) are to be heated from 40°C to 800°C in 5 minutes in the heat treatment section of a valve manufacturing facility. The valves have a cylindrical stem with a diameter of 8 mm and a length of 10 cm. The valve head and the stem may be assumed to be

Question

Engine valves [latex] \left(C_{p}=440 J / kg \cdot{ }^{\circ} C ext { and } ho=7840 kg / m ^{3} ight) [/latex] are to be heated from 40°C to 800°C in 5 minutes in the heat treatment section of a valve manufacturing facility. The valves have a cylindrical stem with a diameter of 8 mm and a length of 10 cm. The valve head and the stem may be assumed to be of equal surface area, with a total mass of 0.0788 kg. For a single valve, determine (a) the amount of heat transfer, (b) the average rate of heat transfer, and (c) the average heat flux, (d) the number of valves that can be heat treated per day if the heating section can hold 25 valves, and it is used 10 hours per day.

Accepted Answer

Engine valves are to be heated in a heat treatment section. The amount of heat transfer, the average rate of heat transfer, the average heat flux, and the number of valves that can be heat treated daily are to be determined.

Assumptions Constant properties given in the problem can be used.

Properties The average specific heat and density of valves are given to be [latex] C_{p}=440 J / kg \cdot{ }^{\circ} C ext { and } ho=7840 kg / m ^{3}[/latex].

Analysis (a) The amount of heat transferred to the valve is simply the change in its internal energy, and is determined from

[latex] Q=\Delta U=m C_{p}\left(T_{2}-T_{1} ight)[/latex]

[latex] = (0.0788 kg )\left(0.440 kJ / kg \cdot{ }^{\circ} C ight)(800-40){ }^{\circ} C = 2 6 . 3 5 \mathrm { kJ } [/latex]

(b) The average rate of heat transfer can be determined from

[latex] \dot{Q}_{ ext {ave }}=\frac{Q}{\Delta t}=\frac{26.35 kJ }{5 imes 60 s }= 0.0878 kW = 87.8 W [/latex]

(c) The average heat flux is determined from

[latex] \dot{q}_{ ext {ave }}=\frac{\dot{Q}_{ ext {ave }}}{A_{s}}=\frac{\dot{Q}_{ ext {ave }}}{2 \pi D L}=\frac{87.8 W }{2 \pi(0.008 m )(0.1 m )}=1.75 imes 10^{4} W / m ^{2}[/latex]

(d) The number of valves that can be heat treated daily is

[latex] ext { Number of valves }=\frac{(10 imes 60 min )(25 ext { valves })}{(5 min )}=3000 ext { valves } [/latex]

Question 1.135: Engine valves (Cp=440 J / kg · °C and ρ =7840 kg / m^3) are ...

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