A long, thin copper wire of radius \(r\) and length \(L\) has an electrical resistance of \(ho\) per unit length. The wire is initially kept at a room temperature of \(T_{a}\) and subjected to an electric current flow of I. The heat generation due to the current flow is simultaneously lost to the ambient by convection. Set up an equation to determine the temperature of the wire as a function of time. Mention the assumptions made in the derivation of the equation.