How should I cool a cast metal component if surface finish is my only priority?

Assume a perfectly smooth mold.

Answer:
It sounds like what you're doing is essentially permanent mold casting, and to achieve a smooth, pore-free surface, what you need is RAPID cooling against the mold wall. However, if your casting has intricately shaped and/or thin sections, you may run into problems with the melt starting to solidify before the mold is completely filled. In that case, superheating and/or pressurizing the melt (like die casting) should help. If possible, use an aluminum alloy designed for this kind of processing, such as A380 or A356. I'm not sure how your near-eutectic solder will behave under these conditions, but it should be alright.
depends on the metal. If strength and durability is not important, just let air cool and polish when you demold.

Generaly, the faster the better. Steel can be imersed in oil to cool it, or even water. I'm not sure about solder. I assume you're limited by the temperature your mold can withstand.that's why you're using solder? Why not try pewter.there are some good low temp lead free pewters out there, just web search for it.
very slowly, otherwise it will be very brittle and hard to file or sand.slower the better.
I'm not at all sure this is the right question. If you haven't even decided what metal you are using, cooling rate might be bit premature. Some other, possibly more important factors are mold temperature while injecting, injection speed and pressure.
I seems to me that the "surface" of your part will be be at the mold temperature almost immediately, and the rate that you cool the bulk of the part may have relatively little impact on the surface finish.
Over all, I suspect that fast cooling may be better, if you drip molten solder on a cold surface you get very shiny spatters, while slowly cooled solder sometimes has a somewhat crystallized in appearance. So a fast injection into a fairly cool mold may work. But I wonder what control you have over injection speed. If you are using solder as your material, one suspects you may be using a homemade, possibly hand operated machine.
Being a ChemE student, I cannot speak of the casting process. But I could have discussed the micro-structures if you would have specified the C % in the alloy. I am assuming that the component is Cast Iron. I think annealing would be the best option. All I know is Eutectic reaction occurs at 1148 C at 4.3 % C content. After that if we cool gradually another Eutectoid reaction occurs at 727 C at 0.8 % C. The matter below 727 C will now be a mixture of alpha Fe, alpha+Gamma Fe & alpha+Pearlite. This is thought to have good casting properties. I am not clear about the solder part of it. Anyways because you have ruled out abrasion, polishing etc. I would recommend a solution called Nital (It is a solution of 3-4% Nitric Acid in Ethanol or other spirit), when we observed slides for micro-structures of slow cooled steel this substance was used for etching. Nital etches hence it gives a very fine polish unattainable by mechanical processes. The other advantage I see with Nital is it can be used for unusual shapes too.

If slow cooling (annealing) is used a combination of cementite and ferrite results. If it is cooled rapidly martensite will be formed instead of pearlite. Now martensite does not have good casting properties.

Maybe your question is outside my scope. Anyways I know one thing for sure almost all properties depend on the C %
cool it in an naturally but in a gas or liquid that is inert

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