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final exam open book solutions

# final exam open book solutions - Ts,i Ts,o h X 1 qdot...

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.18 ε λ .1 λ ( μ m) 10 h 1 , T ,1 q dot = 2 X 10 4 T s,o T s,i CHEN- 3210 , Fall, 2010 Final Exam – Open Book Please put your name on each page and separate the three problems. Name _______________________________ Signature_____________________________

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( 29 + 1. A horizontal cylinder with a diameter of 2 cm is located in a large black enclosure maintained at 5 C. Surrounding the cylinder is 40 C stagnant air. If the surface temperature of the cylinder is 350 C and thermal energy is generated uniformly within the cylinder at a rate of 800 W, what is the length of the cylinder? The spectrum for ε λ is shown below. (20 pts) α = 38.3 X 10 -6 m 2 /s = ν 26.4 X 10 -6 m 2 /s k = 0.0338 W/m-K Pr = .69 First find ε : ε = ε 1 (F 0 10 ) + ε 2 (F 0 →∞ - F 0 10 ) λ T = 10*350 = 3500; F 0 10 = .38 ε = .1(.38) + .18(1-.38) = .15 (5 pts) Next find h for the stagnant air: 6 pts for ε , 2 pts for beta, 2 pts for Ra, 3 pts for Nu (could use other correlations), 2 pts for h, 5 pts for L L = 2.27 m q conv = 624 W q rad = 176 W
2. Heat is uniformly generated at the rate of 2 X 10 5 W/m 3 in a wall of thermal conductivity 25 W/m-K and thickness 60 mm. The square wall (0.25m on a side) is exposed to convection on both sides, with the

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