A long homogeneous resistance wire of radius ro = 0.6cm and thermal conductivity k=15.2W/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 16.4W/cm3. The heat generated is transferred to water at 100∘C by convection with an average heat transfer coefficient of h=3200W/m^2K. 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, and (c) determine the temperature at the centerline of the wire.