Consider a gas metal arc welding electrode as shown in Figure P10.29 where we are consuming the

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Consider a gas metal arc welding electrode as shown in Figure P10.29 where we are consuming the electrode as we weld ( rod velocity \(\left.=v_{o}\right)\). We are interested in the steady-state temperature distribution in the welding rod. Initially we assume that resistance heating of the rod is negligible and that heat loss via convection from the surface of the rod is also negligible. Since the rod is thin, radial temperature gradients can also be neglected. The rod melts at its tip at a temperature, \(T_{m}\), and is held at a constant temperature, \(T_{b}\), at the base of the electrical contact.

a. What does the energy equation look like for this problem?

b. Solve the equation using the specified temperature boundary conditions to obtain the axial temperature profile within the rod.

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