A very long rod of 5-mm diameter and uniform thermal

Chapter , Problem 3.124

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A very long rod of 5-mm diameter and uniform thermal conductivity k 25 W/mK is subjected to a heat treatment process. The center, 30-mm-long portion of the rod within the induction heating coil experiences uniform volumetric heat generation of 7.5 106 W/m3 . The unheated portions of the rod, which protrude from the heating coil on either side, experience convection with the ambient air at T 20 C and h 10 W/m2 K. Assume that there is no convection from the surface of the rod within the coil (a) Calculate the steady-state temperature To of the rod at the midpoint of the heated portion in the coil. (b) Calculate the temperature of the rod Tb at the edge of the heated portion.

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