Transient heat conduction in a solidifying alloy

ABSTRACT
Alloys are combinations of two or more metals with the purpose of improving its mechanical and chemical properties, but majority of the time when combining these metals; a diversion from the supposed result is experienced. This diversion was majorly seen to occur during the process of solidification of the alloy, thereby making it paramount to study the solidification process of alloys since it differs from the solidification process of pure metals. The objective of this project is to study the temperature distribution in a solidifying alloy over a range of time and to also plot a graph of temperature against time.
In the course of studying the previous work done on same subjects and related projects, a discovery of how pertinent the situation is and how there hasn‟t been a major breakthrough in the subject. A lot of work has been done on the derivation of the heat flux and heat transfer coefficient of various alloys ranging from AL-SI alloys to MN-CU alloys. The three phases during solidification has also been studied; the solidus region, the liquidus region and the mushy region which is the region in-between the solid and the liquid region also fondly called the problem domain. The mass composition in this region has also been studied
The method adopted for this process is the finite difference approximation using the implicit method where the time steps that can be used in the calculations are unlimited. This mathematical modeling procedure involves the discretization of the length into nodal lengths at varying time steps. The higher the nodes the more accurate the results obtained will be. In this project, 50 nodes are used.
The result gotten shows a graph depicting the cooling pattern of alloys and suggested points of phase change which varies from one node to the other. This result will help in guiding
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experimental results that would be obtained during the process of carrying out this project experimentally.