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HeatTransfer-I-Section-7

# Using an appropriate model for obtaining the heat

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Unformatted text preview: Use a fundamental heat transfer law to explain your results. •  Assume that the proper'es of air are: ρ = 1.2 kg/m3, ν = 18.6 x 10 ­6 m2/s, kf = 0.025 W/mK, Pr = 0.71. State all assump'ons and jus9fy the selec'on of your heat transfer coeﬃcient model. 10 Example 2 •  Examine the hot rolling process used in manufacturing steel sheets. The steel sheet is passed between two rollers, each having a diameter of 1 m, a length 5 m, and turning at a speed of 0.1 rad/s. The size of the contact region between the two rollers has been determined from an elas'c stress analysis to be 2 cm. The rollers are maintained at 400 C and a steady state heat transfer rate of 10 kW is removed from the coolant, which is passed over the two rollers. –  Using an appropriate model for obtaining the heat transfer coeﬃcient, determine the mean temperature of the contact region, Tc. Hint: since the roller radius is much larger than the contact length, R>>L, the velocity of the solid is essen'ally constant in the region where a thermal boundary layer forms, therefore you can treat this “solid” region as a low Prandtl number ﬂuid, i.e. Pr  ­> 0. –  If the thickness of the plate in the contact region is 10 mm and the bulk temperature entering the contact region Ti is ini'ally 1000 [C], what is the bulk temperature at the exit of the contact region To. •  The proper'es of the steel rollers are: r = 7854 kg/m3, Cp = 434 J/kgK, k=42 W/mK, a = 17.7 x 10 ­6 m2/s, while the proper'es of the steel plate are the same except for the thermal conduc'vity which at 1000 C is k = 29 W/mK. Note: solid steel has no viscosity, you do not need viscosity or Pr number if you consider the Peclet num...
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