When the molten metal solidifies, how the temperature will be distributed to solid cold metal? I need to know the mathematical modelling of such compound casting.
As a first approximation dT/dx can be taken as negative constant, with Tmax=Tm at the soild-liquid interface, Tmin will depend on thermal conductivity of the solid metal. Similarly, dT/dx in liquid can be considered as positive constant with Tmin=Tm at the soild-liquid interface and Tmax equals to the temperature of liquid metal.
It is better to do FEM analysis for more elaborate result and better understanding of solidification.
FEM analysis will help you to understand the heat distribution during solidification of molten metals as suggested by Chandra.
Law of Homogeneous Materials: - A thermoelectric current cannot be sustained in a single homogeneous material by the application heat alone, regardless of how it might vary in cross-section.
Law of Intermediate Material: - The algebraic sum of thermoelectric forces in circuit composed of any number of dissimilar materials is Zero if all of the circuit is at same temperature.
Law of Successive or Intermediate Temperature:- If two dissimilar homogeneous materials produces thermal (emf)1 when the junctions are T1 and T2 and produces thermal (emf)2 when the junction are at T2 and T3 the emf generated when the junction are at temperature T1 and T3 will be (emf)1 + (emf)2.
Use mid-wave infra-red camera (wavelength 1-4 microns) with cooled detector, e.g. FLIR SC7000 series. We observe similar cases during crystallization of arc melted metallic alloys.
https://books.google.com.tr/books?id=cYzNYwMtQHcC&pg=PA102&lpg=PA102&dq=the+intermediate+temperature+between+hot+liquid+and+cold+metal&source=bl&ots=6C-OdoUdt-&sig=fakX10Wr0reIua_ULQ5iG44zdAQ&hl=tr&sa=X&ved=0ahUKEwiEh_fi-JrYAhVH6RQKHSFOD3IQ6AEIOzAF#v=onepage&q=the%20intermediate%20temperature%20between%20hot%20liquid%20and%20cold%20metal&f=false
FEM analysis may help to understand the heat distribution of solidified molten metals. at the solid-liquid interface Tmax is the equal to the temperature of the liquid metal.
T1-T2/RA can be used for finding intermediate temperature in wall interface. R is the overall thermal resistance.
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