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A mathematical model and robust numerical solution algorithm for radiator heating of an arbitrary room is presented in this paper. Three separate and coupled transient thermal energy equations are solved. A modified transient heat conduction equation is used for solving the heat transfer at multi-layer outer walls and room assembly. Heat exchange between the inner walls and the observed room are represented with their own transport equation and the transient thermal energy equation is solved for radiators as well. Explicit coupling of equations and linearization of source terms result in a simple, accurate, and stabile solution algorithm. Verification of the developed methodology is demonstrated on three carefully selected test cases for which an analytical solution can be found. The obtained results show that even for the small temperature differences between inner walls and room air, the corresponding heat flux can be larger than the transmission heat flux through outer walls or windows. The benefits of the current approach are stressed, while the plans for the further development and application of the methodology are highlighted at the end.

This article presents a method for calculation of the complete casting process, including the pouring of the liquid metal into the mold, its solidification, the deformation of the solidified cast, the formation of airgaps between the cast and the mold and their influence on the heat transfer, and the residual stresses. An original phase-change procedure is developed, valid for an arbitrary number of pure metals and=or alloys. A collocated version of a segregated finite-volume method is used to calculate both the liquid metal flow and the deformations and stresses in solids.

In this article, the numerical method proposed in Part I is validated by applying it to relatively simple validation test cases with phase change as well as to real-life problems. First, the results of the 1-D calculations are compared with the analytical solutions for the Stefan problem with mushy zone. Then, the 2-D and 3-D calculations of the Bridgman crystal growth are compared with available experimental results. The ability to predict the residual stresses is demonstrated on an academic 2-D example. Finally, the results of calculation for two real-life industrial cases, injection casting and solidification of a multicomponent metal drill head, are presented and discussed.

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