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A thin wire of cross-sectional area A and Perimeter P is extruded at a fixed vetocity V through and extrusion nozzle as shown in fig. The tempertaure of the wire at the extusion nozzle is T0, high enough to make the metal extudable.
The wire aftter extrusion pass through air at temprature T for some distance L and then is rolled onto a large spool, where the termprature reduces to TL. Let the heat transfer coefficent be constant h.
(a) Starting from the basic principles, derive a differential equation that governs the variation of the temperature of the wire as at Function of the distance x from the extrusion nozzle. Also specify the boundary conditions.
(b) Solve the problem formulated in (a) and obtain an expression for the vanution of the wire temperature as a function of x.
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