University of New Mexico Mechanical Engineering Spring 2012 PhD qualifying examination Heat Transfer
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1 University of New Mexico Mechanical Engineering Spring 2012 PhD qualifying examination Heat Transfer Closed book. Formula sheet and calculator are allowed, but not cell phones, computers or any other wireless device. Time allowed: 150 minutes.
2 Part 1: General knowledge questions (25 points)
3 1. The physical significance of the Biot number is (a) the ratio of elapsed time to time required to reach steady-state. (b) the ratio of conductive resistance on one side of the interface to convective resistance on the other. (c) the ratio of convective resistance on one side of the interface to conductive resistance on the other. 2. For large Biot numbers in steady-state problems, the temperature distribution is (a) uniform, but time dependant. (b) uniform and not time dependant. (c) time dependant, not necessarily uniform. 3. In radiant heat transfer, the emissivity is a number which represents (a) the capacity of a real surface to emit thermal radiation relative to an ideal surface. (b) the capacity of a surface to reflect photons from a nearby emitter. (c) the capacity of a surface to emit visible radiation. 4. In radiant heat transfer, a blackbody surface is (a) a surface which absorbs all photons in the visible spectrum. (b) a surface which reflects all photons in the visible spectrum. (c) a surface which absorbs all photons in the thermal spectrum. 5. Sometimes, increasing the thickness of insulation on a pipe actually increases the heat loss. This is because: (a) sometimes the insulation materials is a bad insulator. (b) there is more heat loss because the insulation heats up when in contact with the pipe. (c) while the conductive resistance increases, the convective resistance is reduced.
4 6. When an incandescent light is turned off, the filament loses heat primarily by (a) conduction. (b) convection. (c) radiation. 7. A long cylinder is heat-treated by immersing it in an oil bath. For the purposes of calculating transient behavior, the relevant characteristic dimension is the (a) radius. (b) diameter. (c) length. 8. Dimensional analysis in heat transfer is useful because? (a) it allows us to perform experiments with the smallest parameter space. (b) it makes certain correlations look much more elegant. (c) it eliminates the confusion of converting between units. 9. The Fourier number represents (a) the number of terms necessary in a transient heat conduction solution by Fourier series. (b) the dimensionless time scale resulting from the shape and properties of the solid object being cooled. (c) the dimensionless time scale resulting from the convection process around the solid object being cooled. 10. Electronic components in a space vehicle must be cooled by some cooling device. In turn, the device rejects heat to the outside by (a) radiation. (b) convection. (c) both convection and radiation.
5 Part 2: Problems (25 points per question) Attempt all problems in this section, clearly stating any assumptions and simplifications used in your solution.
6 Problem 1 In the vulcanization of tires, the carcass is placed into a jig and steam at 150 C is admitted suddenly to both sides. The tire thickness is 2.5 cm, initial temperature is 21 C, the convection coefficient h is 150 W/m 2 K, the density ρ is 240 kg/m 3, the specific heat capacity c is 1650 J/kg K, and the conductivity k is 0.16 W/m K. What is the time required for the center of the rubber to reach 132 C?
7 Problem 2 A beer can 160 mm long and 75 mm in diameter is initially at 30 C, and is to be cooled in a refrigerator to 2 C. In the interest of maximizing the cooling rate, should the can be laid horizontally or vertically in the compartment? As a first approximation, neglect heat transfer from the ends.
8 Problem 3 Solar irradiation of 1100 W/m 2 is incident on a large flat horizontal metal roof on a day when air flowing over the roof causes a heat transfer coefficient of 25 W/m 2 K. The outside air temperature is 27 C, the metal surface absorptivity for solar radiation is 0.6, the metal surface emissivity is 0.2. The sky temperature is 70 K. If the roof is well insulated from below, calculate the steady-state temperature of the roof.
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University of New Mexico Mechanical Engineering Fall 2012 PhD qualifying examination Heat Transfer
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PERFORMANCE EVALUATION OF REFLECTIVE COATINGS ON ROOFTOP UNITS Report on DRAFT Prepared for: California Energy Commission 1516 9th Street Sacramento, CA 95814 Prepared by: Design & Engineering Services
Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)
Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,