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Everyday Heat Transfer Problems: Sensitivities to Governing Variables

M. Kemal Atesmen
M. Kemal Atesmen
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ASME Press
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A hot drawn bar, assumed to be moving at a constant velocity out of a die at constant temperature, will be treated as a one-dimensional heat transfer problem. The Biot numberfor the bar, htD∕2k, will be assumed to be less than 0.1, to assure no radial variation of temperature in the bar. Here ht is the total heat transfer coefficient from the bar surface in W∕m2-K, the sum of the convection heat transfer coefficient and radiation heat transfer coefficient, D is the bar diameter, and k is the bar thermal conductivity in W∕m-K. Conduction, convection, and radiation heat transfer mechanisms affect the temperature of the drawn bar.

Energy balance can be applied to a small element of the bar with a width of dx:  
Conduction heat transfer into the elementConduction heat transfer out of the elementConvection heat transfer out of the element to the environmentRadiation heat transfer out of the element to the environment=Rate of change of internal energy of the element
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