An annealing furnace has a belt that moves material in at a specific velocity, (U) (Figure P10.34).
Question:
An annealing furnace has a belt that moves material in at a specific velocity, \(U\) (Figure P10.34). Only the region inside the oven is heated and the material sees a radiant heat flux of \(q_{o}^{\prime \prime}\). We would like to develop a steady-state model to describe the temperature profile in the material.
a. Pare down the energy equation to derive a differential equation to predict the temperature. List any assumptions you make in deriving the equation.
b. If we have a thin material moving through the furnace, like a system for continuously making pizza, the temperature will be uniform in the \(y\)-direction. How does this affect your differential equation?
c. What would be the boundary conditions for the equation in
(b) if the pizza is supposed to exit the oven at \(T_{\text {bake }}\) ?
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