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(MECH3310)[2013](s)midterm~=3_k^_87769.pdf
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MECH3310 Spring 2013 S.Yao
MECH3310 Heat Transfer Mid-Term Exam 27/03/2013 15:00-16:20
1.
A solid sphere with 10 mm in diameter has an internal heat generation of 2 MW/m3 and a thermal conductivity of 20 W/mK. The sphere is exposed to a convection environment, h = 100 W/m2K and T = 300 K. Radiation is negligible. Calculate surface temperature and the maximum temperature in the solid.

2.
A 2 mm diameter and 10 m long copper wire is tightly wrapped with a 1 mm thick plastic cover whose thermal conductivity is k = 0.15 W/(mK). A current of 12 A passes through the wire and the voltage drop across the wire is 10 V. If the insulated wire is exposed to a medium at T = 303 K with a heat transfer coefficient of h = 25 W/m2K, determine the temperature at the interface of the wire and the plastic cover in steady condition. If we double the thickness of the plastic cover, will this interface temperature be increased or decreased?

3.
A 10 mm in diameter nickel sphere with initial temperature Ti = 25C falls into a liquid at 150C with the heat transfer coefficient h = 100 W/m2K. For nickel alloy: .cp = 3.8 MJ/m3K and k = 15 W/(mK). Sketch the time dependence of the coin temperature. How long does it take for the coin to reach 125C?

4.
A long circular fin (assume infinitely long) with diameter D = 1 cm has one end kept at Ts = 400 K. the fin has thermal conductivity k = 25 W/(mK) and emissivity .. = 0.85. The fin is cooled by radiation and convection to the environment at T = 300 K.

(a)
Derive the fin equation which relates the temperature to the coordinate x and other
parameters. Use energy conservation to balance the heat transfer due to conduction,
convection, and radiation.
Convection: q = hconv (T- T), hconv = 8 W/m2K


Radiation: q = ..(T4- T4) hrad (T- T), where hrad 4..T3, ....5.67e-8 W/m2K4

(b)
Solve the differential equation obtained from (a) for the temperature variation in the fin in x direction (symbols only).

(c)
Solve for the position x at which the temperature is 340 K.