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Unformatted text preview: ME 4102 Name: Homework #4 (due October 4, 2010) Homework Format l.
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3. @999? 1. Use this page as a cover sheet. One problem per page. Always state what is given, your assumptions, provide a sketch, and analysis. Circle your answer.
Include units. Write legibly. No late homework accepted. Work independently. Use paper with four straight edges. Staple together your work. A type K ChromelAlumel thermocouple is quickly placed into a hot air ﬂow to measure its temperature. In
particular, it is desired to know the response time of the thermocouple to attain 99% of the initial
temperature difference between the hot air and the initial temperature of the thermocouple junction. The
thermocouple junction can be modeled as an isolated sphere with a diameter of 0.6 mm and the properties:
ksond = 35 W/mK, p = 8500 kg/m3, and c = 320 J/kgK. The convection heat transfer coefficient, h, between the ﬂow and the sphere is 65 W/mzK. i) What is the Biot number associated with this problem? ii) Derive the appropriate differential equation for T(t).
iii) Solve this equation to attain the time for thermocouple junction to attain 99% of the initial temperature difference between the hot air and the initial temperature of the thermocouple junction. A long circular shaft of 0.2 m diameter and thermo physical properties k = 21 W/mK, p = 7900 kg/m3, and
c = 570 J/kgK is initially at a uniform temperature of 600°C and is cooled in a convective ﬂow maintained
at 200°C. What is the shaft centerline temperature after exposure to the convective ﬂow for 45 minutes? The
convection heat transfer coefficient, h, is 80 W/mzK. You must check the validity of your answer. A thick steel slab (k = 50 W/mK, p = 7800 kg/m3, and c = 480 J/kgK) is initially at 300°C and is cooled by
water jets impinging on one of its surfaces. The temperature of the water is 25°C, and the jets maintain an
extremely large, approximately uniform convection coefﬁcient at the surface. Assuming that the surface is
maintained at the temperature of the water throughout the cooling, how long will it take for the temperature to 50°C at a distance of 25 mm from the surface? l. Given A L Assume MS 3
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