Engine valves ( c p = 440 J/kg .K and p = 7840 kg/m 3 ) are to be heated from 40 o C to 800 o C in 5 min 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, (c) the average heat flux, and (cl) the number of valves that can be heat treated per day if the heating section can hold 25 valves and it is used 10 h per day.
Engine valves ( c p = 440 J/kg .K and p = 7840 kg/m 3 ) are to be heated from 40 o C to 800 o C in 5 min 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, (c) the average heat flux, and (cl) the number of valves that can be heat treated per day if the heating section can hold 25 valves and it is used 10 h per day.
Engine valves
(
c
p
=
440
J/kg
.K and
p
=
7840
kg/m
3
)
are to be heated from
40
o
C
to
800
o
C
in 5 min 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, (c) the average heat flux, and (cl) the number of valves that can be heat treated per day if the heating section can hold 25 valves and it is used 10 h per day.
2. Find a basis of solutions by the Frobenius method. Try to identify the series as expansions of
known functions.
(x + 2)²y" + (x + 2)y' - y = 0 ; Hint: Let: z = x+2
1. Find a power series solution in powers of x.
y" - y' + x²y = 0
3. Find a basis of solutions by the Frobenius method. Try to identify the series as expansions of
known functions.
8x2y" +10xy' + (x 1)y = 0
-
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