Generate a computer code to simulate the following solidification situation during a casting process:

The material is a 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      =330⁰C =    603K, T_l =345⁰C  =618 K

                h_s = CpsTs =807,417 J/kg, h_l C_pl T_l  = 827,502 J/kg

Assume that T_initial = 650 K everywhere (the pouring temperature) and that at time = 0 the wall temperatures on walls AB, BC, AD, and DC are set to T_wall = 290 K (the mold temperature).  Study this solidification problem numerically, and hand in the following:

• A copy of your source code

• Plots of T_center versus time and T_p versus time

• The total solidification time and final point of solidification within the product.

• Contour plots of solidus and liquidus interfaces for a selected time.

• A plot showing the temporal progression of solidus interface fronts during the casting process.

Run your code several times with a deceasing mesh cell size.  For each of these mesh cell sizes, report on the following:

• The total solidification time and final point of solidification within the product.

From this mesh size sensitivity analysis suggest an optimal mesh size to address this type of problem.

δ^2*T/δx^2

Δ/Δx * ΔT/Δx