nant variable. The objective function for optimization was defined as:
where and are the modelled and experimen-
tal (measured) temperature at the jth time step for the ith thermocouple. Iterations were performed to minimize F(x). The optimization problem was unconstrained to ensure that the design variables (i.e. heat transfer coefficient points) could be freely manipulated due to the physical action of pushing the chills closer to the casting during the experiments.
Effect of “Fixed Chill without Water Cooling” on Heat Transfer “Scenario A”
In this scenario, the heat transfer coefficient commences at 5000 W/m²K due to full initial contact between the chill and molten metal, but then decreases as the casting solidi-
Effect of “Fixed Chill with Water Cooling” on Heat Transfer “Scenario B”
As in the previous case, the heat transfer coefficient be- gins at 5000 W/m²K but decreases suddenly once the air gap is formed (i.e. after approximately 30 seconds from pouring). The heat transfer coefficient is lowered to 500 W/m²K. The overall interfacial heat transfer in this chill condition is less than the Scenario A trials. This con- firms previous discussions about an instant surface layer (skin) forming at the chill interface, thus causing shrink- age to occur in the casting earlier than in Scenario A (with no cooling).
HTC vs Time Trial A (Average) (Fixed Chill) (Without Cooling)
fies. In this case, the heat transfer coefficient decreases after the first cut-off (i.e. approximately 230 seconds). In other words, heat transfer decreases after the air gap is formed. This indicates that the chill is inefficient for the remaining duration of solidification.
Time, sec (a)
Trial A (Average) (Air Gap Signature)
Time, sec (b)
Objective Function F(x) vs Iteration
Time, sec (c)
Iterations (d)
Figure 8. (a) Measured vs. simulated temperature data; (b) Calculated heat transfer coefficients for trial A_Average; (c) Air gap signal; (d) Objective function vs. iteration.
International Journal of Metalcasting/Spring 11 71
Voltage, V
Temperature, C
F(x)
HTC (W/m2K)
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