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NATIONAL UNIVERSITY OF SINGAPORE

Department Mechanical Engineering

ME 3122 Heat Transfer

TUTORIAL 1- CONDUCTION

1. Figure 1 shows a typical nuclear reactor used for commercial power production.

Heat is generated at the rate of 74.52 MW/m3 in the long 50 mm OD uranium fuel

rods (k = 0.03 kW/mK) which are jacketed by an annulus to permit cooling water

to flow. For an average temperature, 130C of cooling water and a convective

heat transfer coefficient of 56.79 kW/m2K, determine the maximum temperature

of the fuel. [Ans: 534.3C]

Thermal

Shield

Fuel rods

ReinforcedShieldVertical safety rods

Cooling waterpassage

Cooling tubes

Figure 1. Graphite-moderated reactor(Source: General Electric Review)

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2. A power transistor is capable of operating at up to 4.5 W. The manufactures

specification for the case to ambient thermal resistance of the transistor is 28C/W

and the case temperature is not to exceed 75C. To reduce the operatingtemperature, the transistor is mounted on a black anodized aluminum frame which

serves as a heat sink. The frame provides an additional 1500 mm 2 surface area for

cooling. In order to minimize the thermal contact resistance between the transistorand the heat sink, and at the same time maintain proper electrical insulation, the

surface is first cleaned and coated with thermal grease. A special electrical

insulation gasket is then inserted and the transistor is bolted lightly to the frame.In general, for proper thermal contact, resistance is of the order of 0.75C/W.

Determine the maximum power at which the transistor can be safely operated if

the surrounding walls and air are at 26C and h = 11 W/ m2K.

[Ans: 3.09W]

3. One surface of a thin metallic plate (thermal conductivity, k= 245W/mK) has a

surface temperature Ts equal to 120C. The other surface is exposed to air attemperature, Ta = 25C. The convective heat transfer coefficient between the

surface and the air is 80 W/m2K. A circular pin fin (diameter, d = 2 mm andlength, L = 10 mm) is attached to the surface. Determine,

(a) the rate of heat transfer from the surface,(b) the efficiency of the fin,

(c) the effectiveness of the fin, and

(d) the number of fins required per square meter of primary surface to

increase the rate of heat transfer by 100%.[Ans: (a) 0.4645 W, (b) 97.3%, (c) 19.45, (d) 17,245]

4. A thermocouple is introduced into a pipe to measure the temperature of steam

flowing through it. The thermocouple junction may be approximated as a sphere.

The convection coefficient between the junction surface and the steam is knownto be 380 W/m2K and the thermophysical properties of the junction are given as

follows:

Thermal conductivity, k: 25 W/mK

Specific heat, cp: 380 J/kgK

Density, : 8000 kg/m3

Determine the diameter of the junction needed for the thermocouple to have atime constant of 1 second. If the junction is at 30C and it is placed inside a tube

carrying steam at 250C, how long will it take for the junction to reach 240C?

[Ans: 0.75mm, 3.09 sec]