A Heat Balance Integral Method for Estimating Practical Solidification Parameters

A heat balance integral technique based on an enthalpy formulationof a metallurgical solidification problem is presented. Unlikethe majority of previous heat balance integral methods the newtechnique can analyse situations in which the phase change takesplace over a temperature range. This means that solidificationparameters of practical significance may be efficiently estimated.An application of the new technique is made to a problem ofbinary alloy solidification. The results obtained are comparedwith existing numerical models.     

Monotonous enclosures for the Thomas-Fermi equation in the isolated neutral atom case

Please address any correspondence to: C. Grossmann, Department of Mathematics, Kuwait University, PO Box 5969, Safat 13060, Kuwait A numerical method for the generation of enclosures for thesolution of the Thomas–Fermi equation on a semi-infiniteinterval is proposed. The method is based on the monotone discretizationprinciple and on available global bounds for the solution. Theconvergence of the new method on refined and extended gridsis investigated where available bounds are used to increasethe local step size with increasing arguments.     

Implicit Finite--difference Solutions of the Enthalpy Formulation of Stefan Problems

When related to a phase-change problem, an implicit finite-differencediscretization of the enthalpy formulation results in a systemof non-linear equations at each time step. In this paper, variousnumerical enthalpy methods based on such discretizations areoutlined and examined. An alternative discretization for anenthalpy formulation is developed on separating the sensibleand latent heat terms. This approach also results in a non-linearsystem of equations but with the non-linearity isolated as asource term of nodal latent heat. This offers an advantage overthe previous techniques in that only one variable (i.e. temperature)is solved for in the resulting iterative scheme. Comparisonwith simple one- and two-dimensional test problems indicatethat the computing requirements, with the alternative discretization,are reduced by between 20 and 50%.