An integral relationship for a fractional one-phase Stefan problem

A one-dimensional fractional one-phase Stefan problem with a temperature boundary condition at the fixed face is considered by using the Riemann–Liouville derivative. This formulation is more convenient than the one given in Roscani and Santillan (Fract. Calc. Appl. Anal., 16, No 4 (2013), 802–815) and Tarzia and Ceretani (Fract. Calc. Appl. Anal., 20, No 2 (2017), 399–421), because it allows us to work with Green’s identities (which does not apply when Caputo derivatives are considered). As a main result, an integral relationship between the temperature and the free boundary is obtained which is equivalent to the fractional Stefan condition. Moreover, an exact solution of similarity type expressed in terms of Wright functions is also given.

Analysis of Dieless Drawing to Form the End of Metal Wires under Proportional Shape Evolution with Slab Method

This study is to set a goal to create a model solving the temperature distribution and its evolution for the process of dieless drawing metal wire parts by using slab method and postulating that the wire end suffers a proportional deformation. The results from using a SUS304 stainless wire in 5 mm diameter dielessly drawn show that the highest temperature locates on the symmetry plane at the process beginning, so that the necking takes place there and an end will be formed securely. As a result, the method proposed by this study is feasible. In addition, for a given final shape of the metal wire end, there are many possibilities to get different temperature distribution and its evolution by setting different temperature boundary condition. The higher the boundary temperature set, the higher the temperature distribution, but the lower the drawing force needed.