A plate of thickness 2L25 mm at a temperature of600C is

Chapter 5, Problem 5.54

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A plate of thickness 2L?25 mm at a temperature of600C is removed from a hot pressing operation andmust be cooled rapidly to achieve the required physicalproperties. The process engineer plans to use air jets tocontrol the rate of cooling, but she is uncertain whetherit is necessary to cool both sides (case 1) or only oneside (case 2) of the plate. The concern is not just for thetime-to-cool, but also for the maximum temperaturedifference within the plate. If this temperature differ-ence is too large, the plate can experience significantwarping.The air supply is at 25C, and the convection coefficienton the surface is 400 W/m2?K. The thermophysical prop-erties of the plate are ??3000 kg/m3, c?750 J/kg?K,and k?15 W/m?K.(a) Using the IHTsoftware, calculate and plot on onegraph the temperature histories for cases 1 and 2for a 500-s cooling period. Compare the timesrequired for the maximum temperature in the plateto reach 100C. Assume no heat loss from theunexposed surface of case 2.(b) For both cases, calculate and plot on one graph thevariation with time of the maximum temperaturedifference in the plate. Comment on the relativemagnitudes of the temperature gradients within theplate as a function of time.