In the heat-transfer analysis of a solidification process, the effective specific heat method is conceptually simple to apply while dealing with the latent heat problem. The implementation of computer program is very easy for this method. However, in a time step, if a nodal temperature enters, leaves or jumps over the artificial mushy zone of a pure substance, it cannot calculate the released or absorbed latent heat correctly. If the latent heat is large or the temperature variation is very large, the discontinuity of the effective specific heat will make the iterative convergence difficult to reach. In this work, a modified method is proposed to solve these problems. The method modifies the relation between the temperature and effective specific heat for a solidification process by considering the effect that the temperature at either of two successive time steps is in the mushy zone. The Stefan and Neumann problems with exact solutions were used to test the modified method. The computing results will be compared with those of the effective specific heat method and the enthalpy method. Finally, the feasibility of the modified method is further testified by using a crystal growth problem of GaAs in a Bridgman furnace.

In a directional solidification process, since the liquid solubility is higher than the solid one, the surplus solute will be released from the solid/liquid interface into the liquid, which is the main source of increasing the liquid solute. The release of solute at the moving interface is like that of latent heat. Except the growth rate, the release of extra solute also depends on the liquid concentration at the interface, which is not fixed. Consequently, the numerical treatment of the solute release is not so easy as that of the latent-heat one. If the effect of solute release is not handled appropriately, the concentration solutions will diverge very easily. In this paper, extra nodes added on the solid/liquid interface in a fixed grid system are proposed to solve the mass transfer problem in the directional solidification process. A one-dimensional problem is firstly used to test the proposed method. The computing results are compared with those of other fixed grid methods and the analytical solutions from the literature. Finally, the feasibility of the proposed method is further testified by applying it to solve the concentration field of the crystal growth of GaAs in a Bridgman furnace.

With a varus deformity, repairs of proximal humeral fractures frequently fail after screws pull out due to lack of medial support. Indirect intramedullary grafts have been used to prevent such complications. A biomechanical study was performed to investigate the role of an intramedullary bone peg (strut) in fractures fixed with conventional and locking plates. Twenty artificial proximal humerus specimens were divided into four groups. Group 1 specimens were fixed with convention plates and group 2 specimens were fixed with the addition of a bone peg. Groups 3 and 4 specimens were fixed using locking plate and additional bone peg, respectively. All specimens were tested with a static loading test, and the axial stiffness and maximal load were recorded. Locking plates with inlay graft were the most rigid of the four groups. When an intramedullary graft was introduced, the maximal load increased by more than 200%, whether conventional or locking plates were used. The maximal load of a conventional plate with inlay graft was more than twice of that of the locking plate only. Indirect medial support acts as an anti-bending device, reducing the tension on the plate. It also decreases varus deformity and loosening of screws. Locking plate stabilize the plate-bone interface. Locking plate with indirect medial support is thus recommended for patients withsevere osteoporotic or medial comminuted proximal humeral fractures.