PSI - Issue 24

Federica Fiorentini et al. / Procedia Structural Integrity 24 (2019) 569–582 Federica Fiorentini et al. / Structural Integrity Procedia 00 (2019) 000 – 000

574 6

p  = = c

Pr

6, 23

(11)

k

w

4014,8 D  

Re

= =

(12)

Nusselt number becomes equal to 35 and ℎ = 7 / 2 . Analytically, the evolution of the temperature on insert surface is given by integration for variable separation of the amount of heat transferred from the molten metal, Matisková et al. (2013). In the time dt , the amount of heat transferred on insert surface is: ( ) m s p dQ hS T T dt mc dt =  − = − (13)

So

( d T T − m s

hS

)

T

t





m

Q

dt

=

= −

(14)

m s T T −

mc

T

0

s

p

( ) s m T t T e −   = −  1

   

p hS t

mc

(15)



A schematic representation of this phase is shown in Figure 4.

Fig. 4. Schematization of heat transfer mechanism, Krishnan and Sharma (1996).

The conductive heat exchange phenomenon, which takes place into a solid body when a temperature gradient is present, is modelled by Fourier’s law: Q kA T = −  (16) To determine the features required to the cooling system, considering for an aluminum-silicon alloy casting an extraction temperature = 250 ° , = 700 ° , a mass = 20 , a latent heat of solidification