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Computational Fluid Mechanics and Heat Transfer Third Edition_8

Tham khảo tài liệu 'computational fluid mechanics and heat transfer third edition_8', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 262 Chapter 5 Transient and multidimensional heat conduction molten rock at 4144 K 7000 F and that it had been cooled by outer space at 0 K ever since. To do this he assumed that Bi for the earth is very large and that cooling had thus far penetrated through only a relatively thin one-dimensional layer. Using rock 1-18 X 10 6 m s2 and the measured surface temperature gradient of the earth 27 C m Find Kelvin s value of Earth s age. Kelvin s result turns out to be much less than the accepted value of 4 billion years. His calculation fails because internal heat generation by radioactive decay of the material in the surface layer causes the surface temperature gradient to be higher than it would otherwise be. 5.46 A pure aluminum cylinder 4 cm diam. by 8 cm long is initially at 300 C. It is plunged into a liquid bath at 40 C with h 500 W m2K. Calculate the hottest and coldest temperatures in the cylinder after one minute. Compare these results with the lumped capacity calculation and discuss the comparison. 5.47 When Ivan cleaned his freezer he accidentally put a large can of frozen juice into the refrigerator. The juice can is 17.8 cm tall and has an 8.9 cm I.D. The can was at -15 C in the freezer but the refrigerator is at 4 C. The can now lies on a shelf of widely-spaced plastic rods and air circulates freely over it. Thermal interactions with the rods can be ignored. The effective heat transfer coefficient to the can for simultaneous convection and thermal radiation is 8 W m2K. The can has a 1.0 mm thick cardboard skin with k 0-2 W m-K. The frozen juice has approximately the same physical properties as ice. a. How important is the cardboard skin to the thermal response of the juice Justify your answer quantitatively. b. If Ivan finds the can in the refrigerator 30 minutes after putting it in will the juice have begun to melt 5.48 A cleaning crew accidentally switches off the heating system in a warehouse one Friday night during the winter just ahead of the .