A long homogeneous resistance wire of radius r_o = 0.6 cm and thermal conductivity k = 15.2 W/m·K is being used to boil water at atmospheric pressure by the passage of electric current. Heat is generated in the wire uniformly as a result of resistance heating at a rate of 16.4 W/cm³. The heat generated is transferred to water at 100°C by convection with an average heat transfer coefficient of h = 3200 W/m²·K. Assuming steady one-dimensional heat transfer,

(a) Express the differential equation and the boundary conditions for heat conduction through the wire,

(b) Obtain a relation for the variation of temperature in the wire by solving the differential equation,

(c) Determine the temperature at the centerline of the wire.

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E Water TA Resistance heater To h