Consider an electrical wire of the circular cross section with radius (r) and electrical conductivity (kc; ohm 1cm1). There is an electrical current with a current density (I;ampcm2) through this wire. The transmission of an electrical current is an irreversible process and some electrical energy is converted into heat, thermal energy. The rate of heat production per unit volume is given by an expression: Se=I2/ke where Sc is the heat source produced by electrical dissipation. Assume that the wire is onedimensional. The surface of the wire is maintained at temperature T0. If at r=0, assume that the temperature is not changed by r. (a) Write all assumptions to derive this mathematical model. (1 point) (b) Derive an energy balance equation for the radial temperature change within the wire at steady state condition. (3 points) (c) State the necessary initial and/or boundary conditions to solve the equation. (2 points) (d) Using these initial and/or boundary conditions, obtain the radial temperature profile within the wire. ( 2 points) (e) Determine the maximum temperature at which position of r. (2 points)