A solid wire of constant density ? moves downward with uniform speed v into a liquid metal bath at temperature T ₀ as shown in Fig. It is desired to find the temperature profile T(z). Assume that T = T _? at z = ?, and that resistance to radial heat conduction is negligible. Assume further that the wire temperature is T = T ₀ at z =0.

First solve the problem for constant physical properties C? _p and k. Obtain.

N Temperature of wire far from liquid metal surface is To Wire moves downward with constant speed v Liquid metal surface at temperature To e(z) = T(z) - To To-Too = exp pc,vz k