solutiontoin-classexam1

solutiontoin-classexam1 - ME 364 Exam #1, in-class portion...

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ME 364 Exam #1, in-class portion Name ____________________ Lecture time (circle one): 11:00 or 2:25 Note – there are 4 multiple choice questions worth 40 pts followed by a problem that is worth 60 pts. There is an extra credit question at the end that is worth 10 pts. You only have 50 minutes – make sure you budget your time appropriately. Multiple choice questions (40 pts) 1. (10 pts) Two solid rods are made of the same material with the same thermal conductivity. They are insulated on their outer radius and have the same temperatures on either end, as shown. The diameter of rod A is twice that of rod B and the length of rod A is half that of rod B. C L C L L A D A T 1 T 2 L B = 2 L A D B = D A /2 Rod A Rod B direction of heat flow Circle the letter of the correct statement about the thermal resistance to conduction associated with the flow of heat through these rods (along their centerline). a. The thermal resistances of the two rods are equal (R B = R A ). b. The thermal resistance of rod B is 2 times that of rod A (R B = 2 R A ). c. The thermal resistance of rod B is 4 times that of rod A (R B = 4 R A ). d. The thermal resistance of rod B is 8 times that of rod A (R B = 8 R A ). e. The thermal resistance of rod B is equal to the thermal resistance of rod A squared (R B = R A 2 ). The thermal resistance to conduction is 2 cond LL R kA k D π == Therefore, the ratio of the thermal resistance of rod B to rod A is: () 2 22 2 2 2 8 A BB A A AB AA A L RL k D D Rk DL L D ⎛⎞ = ⎜⎟ ⎝⎠ and the correct answer is (d)
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2. (10 pts) The steady-state temperature distribution within a plane wall with a constant thermal conductivity is shown below. x x = L x = 0 T T(x) Circle the letter of the correct statement (there is only one). a. The left hand side of the wall is adiabatic. b. There is no internal generation of energy within the wall. c. At x=0 (the left side of the wall) heat is being transferred out of the wall d. At x=L (the right side of the wall) heat is being transferred into the wall. (a) the temperature gradient at the left hand side of the wall is not zero – it cannot be adiabatic and (a) is not correct (b) there must be internal generation to account for the nonlinear temperature distribution and so (b) is not correct (c) at x=0 the temperature gradient is positive, therefore the heat transfer rate must be in the negative x-direction or out of the wall. Therefore (c) is the correct answer. (d) at x=L, the temperature gradient is negative, therefore the heat transfer rate must be in the positive x-direction or out of the wall and (d) is not correct 3. (10 pts) The composite wall is composed of two layers. Layer A has a thermal conductivity that is higher than layer B. The thermal conductivity in both layers is constant. For steady state conduction of heat through the wall from left to right, with no internal generation of energy, circle the letter of the temperature distribution that is possible.
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solutiontoin-classexam1 - ME 364 Exam #1, in-class portion...

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