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Homework 5 solutions

Homework 5 solutions - Homework 5 1(15 pts In Class 9 we...

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Homework 5 1. (15 pts) In Class 9 we looked at an infinite cylinder with a convection coefficient h = 1000 W/m 2 -K. Let’s say the centerline temperature must be increased from T i = 300 K to T = 750 K. Plot the centerline temperature distribution vs. time for h = 100, 500 and 1000 W/m 2 -K. In each case, stop the calculation when T = 500 K. (10 pts) How long does it take to reach a centerline temperature of 500 K for each convection coefficient.(3 pts) Can any of these be treated as lumped capacitance? θ* o = T(0,t) - T /T i - T = C 1 exp(-ζ 1 2 *Fo) T = C 1 exp(-ζ 1 2 *Fo)( T i - T ) + T With h = 100, it can be treated as lumped capacitance.
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2. (20 pts) One way to determine thermal conductivity of a solid is to embed a thermocouple in a thick slab and measuring the response to a change in temperature. Consider a material with a density of 950 kg/ m3 and a c = 1100 J/kg-K. The material is heated to a uniform temperature of 100 o C and the cooled by passing air at 25 o C over one surface. If a thermocouple is embedded a distance of 10 mm below the surface, the h
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