“…where T is the temperature of the billet at position x along its length, k is the average thermal conductivity of the billet material, a_ is the radius of the billet, v is the speed of the billet, C is the heat capacity of the billet material, and h_ is the coefficient of surface heat transfer between the surface of the billet and the hydrostatic fluid medium.A similar expression can be written for the extruded rod: Extrusion die, billet die, and position coordinates referred to by Eqs. (2) through(5).…”