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electric current flows through an infinitely long hollow cylindrical copper bar having internal and external diameters...

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Mechanical Engineering

electric current flows through an infinitely long hollowcylindrical copper bar having internal and external diameters of 15mm and 25 mm respectively. The temperature on the bar internal andexternal surfaces are maintained constant. The bar carries acurrent density of 5.5 x 107 A/m2 and the internal surfacetemperature is maintained at 45oC with no heat loss from theexternal surface due to insulation. The copper bar has thermalconductivity of 380 W/m.K and electrical resistivity of 2.5 x10-8Ωm.Assume that the temperature changes in the radial directiononly and neglect the end effects in the bar.(a)Derive thetemperature distribution equation in the radial direction.(b)Findthe temperature on the insulated external surface of the copperbar. (c)Calculate the amount of heat flux through the internalsurface per metre length of the bar.

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