PS5 - Problem Set 5 February 2012 MECH 375 Problem Set 5...

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Problem Set # 5- February 2012 MECH 375 1 Problem Set # 5 Given: Friday, Feb. 3 Recommended Completion Date: Friday, Feb. 10 Do not submit for grading Problem 1: During a special heat treatment process, a solid sphere of diameter D = 0.04 m is heated in a furnace to a uniform temperature of T i = 1000 C. It is then suddenly removed from the furnace and suspended from a very fine wire in a large room filled with an inert gas at a uniform temperature of T = 200 C. The surface of the sphere is highly polished, thus radiation heat transfer may be ignored. The sphere cools under the influence of natural convection. The thermal conductivity of the sphere is very high, as a result, lumped parameter analysis may be assumed to apply throughout. The convection heat transfer coefficient varies here as follows: h = ( T - T ) 0.25 , where is constant, and T is the sphere temperature. The sphere has the following properties: = 5000 kg/m 3 ; c = 1000 J/kg- C. The temperature of the sphere 30 min after initiation of the cooling process was measured as 523.4 C.
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