Problem 4.15: Consider steady heat conduction in a wire of circular cross-section with an...

Problem 4.15: Consider steady heat conduction in a wire of circular cross-section with an electrical heat source. Suppose that the radius of the wire is its electrical conductivity is and it is carrying an electric current density of During the transmission of an electric current, some of the electrical energy is converted into thermal energy. The rate of heat production per unit volume is given by Assume that the temperature rise in the wire is sufficiently small that the dependence of the thermal or electric conductivity on temperature can be neglected. The governing equations of the problem are

Determine the distribution of temperature in the wire using (a) two linear elements and (b) one quadratic element, and compare the finite element solution at eight equal intervals with the exact solution

Also, determine the heat flow at the surface using (i) the temperature field and (ii) the balance equations.