Springs are often annealed by passing a current through them. Care must be taken to ensure that the temperature along the spring does not exceed the desired annealing range. Consider a thin wire of thermal conductivity, \(k\), diameter, \(d\), and length, \(2 L\). The current passed through the wire results in a uniform volumetric rate of heat generation, \(\dot{q}\left(\mathrm{~W} / \mathrm{m}^{3}\right)\). The wire is exposed to the atmosphere at a temperature of \(T_{\infty}\) and convection about the wire is sufficient to provide for a heat transfer coefficient, \(h\). The wire ends are also maintained at \(T_{\infty}\). Determine the temperature profile, \(T(x)\), and the magnitude and location of the maximum temperature.