Determine the wall temperatures to be applied along ab bc

Question

Problem #: Casting

Solve the following manufacturing optimization problem using the computer code that you previously created to simulate solidification during casting processes.

The material is once again the well-known polymer known as PEEK (polyetheretherketone). The properties of this material are as follows:

k = 0.251 W/mK,      ρ = 1262 kg/m3, C_ps = C_pl = 1339 J/kgK

T_s = 330^oc = 603K, T_l = 345^oC = 618 K

h_s = Cp_sT_s = 807,417 J/kg, h_l = C_plT_l = 827,502 J/kg

Assume the two-dimensional configuration shown below. Also assume that T_initial = 650 K everywhere in the interior of the casting (i.e. the pouring temperature). At time t= 0 the wall temperature is to be set to T_wall = 425 K along the mold wall region AFED. Along this portion of the mold wall you have no control over this fixed mold wall temperature.

To make your manufacturing process adjustable, your mold has been designed to have the ability to adjust the three mold wall temperatures applied along boundary regions AB, BC, and CD respectively. The temperatures along these three wall segments can be set to any levels that you desire, but they have to remain constant throughout the product casting cycle.

Using an optimization methodology that you design, determine the wall temperatures to be applied along AB, BC, and CD so that 1) the last point to solidify in the casting is point P, and 2) the time for complete solidification of the product is as fast as possible.

Optimize this solidification problem numerically, and hand in the following:

- A description of the optimization methodology that you selected, and a listing of all of the wall temperature boundary condition sets that you simulated during the optimization process.

- A clear statement of the FINAL OPTIMAL THREE WALL TEMPERATURES that you determined.

- For the optimal conditions above, a plot of Tp versus time

- For the optimal conditions above, the total solidification time and final point of solidification within the product.

- For the optimal conditions above, a plot showing the temporal progression of solidus interface fronts during the casting process.

Attachment:- code.rar