Casting a metal (Enthelpy of Fusion Question)

[360modina]

I want to take a liquid metal, Aluminum at 700^oC and pour it into a steel mold starting at 20^oC. For the purpose of the question let’s say that the heat transfer is 100% with no losses to the surroundings.

Here are some numbers:

Al
Mass = 200 g = 0.2 Kg
Ti, Al = 700^oC
Cp = 900 J/Kg-K
ΔHf = 10.67 kJ/mol
Melting point of Al = 660^oC

Steel
Mass = 3Kg
Ti, st = 20^oC

So the liquid aluminum will cool once it hits 660, but the steel mold should never change state due to its higher melting point.

At this point I want to find the final temperatures of the Aluminum and the Steel mold.

Here's what I have so far can someone please check my theory/number placement:

(900 J/Kg-K)(0.2Kg)(700^oC-660^oC)+(200g)(1 mol/26.96g) + (900 J/Kg-K)(0.2Kg)(T_{f, Al} - 20^oC)

= (486 J/Kg-K)(3Kg)(T_{f, St} - 20^oC)

So my guess is both final temperatures will be the same, I just wanted to know if this work looks correct or if I need to change/move some numbers.

 

[Astronuc]

This part (900 J/Kg-K)(0.2Kg)(Tf, Al - 20oC) is not correct. One is still cooling from Tmelt to Tf. The Al decreases in temperature while the Fe heats up.

At equilibrium Tf(Al) = Tf(Fe)

 

[360modina]

That's actually why I posted this, I had a feeling that using the 20^oC on the Aluminum side didn't make sense, so I think the left hand side should be changed to (900 J/Kg-K)(0.2Kg)(Tf, Al - 660^oC).

Is that correct, or am I still missing something else?

 

[Astronuc]

Try (660°C-T_f(Al)). The Al is cooling from 660°C to T_f, 660°C > T_f.

 

[360modina]

Ok, I reworked it again let me know what you link:

LHS (Aluminum)
(900 J/Kg-K)(0.2Kg)(700^oC-660^oC)+(200g)(1 mol/26.96g)(10.67 kJ/mol)+(900J/Kg-K)(0.2Kg)(660^oC - T_f)

RHS (Steel)
(486 J/Kg-K)(3Kg)(T_f - 20^oC)

I took the sum of the LHS and the RHS and put them both into excel

I set Tf as my variable on both sides of the equation and used goal seek to find Tf = 94.77^oC

With that LHS=RHS=109019.9

 

[Integral]

It is my experience that molten Al can do nasty things to Stainless. Even though you are well below SS melting point reactions can still occur. The fact that your steel is cool should help.

Good luck and dry molds.