Question: A liquid metal flowing with a uniform velocity V through a pipe of periphery P and cross section A is electrically heated at the rate of u"' over a length l of the pipe (Fig. 3P-2). The inlet temperature of the liquid is equal to the ambient temperature T∞. The outside heat transfer coefficient is h. Neglecting the effect of axial conduction:
(a) Find the steady axial temperature distribution of the liquid metal.
(b) The flow of the liquid metal is suddenly stopped because of a pump failure. Find the unsteady temperature of the liquid metal.