Consider melted pure copper initially, Ti = 1300 OC, is being solidified in a large rectangular insulated ceramic vessel for which 1-D transient solidification (Neumann model) is applicable. The bottom of the container is made of a steel plate through which heat is being extracted by maintaining its temperature (Ts) at 50 C. Assume that the heat transfer resistance of the plate is negligible. By solving the transcendental equation for the problem (Neumann problem), the value of the root is found to be 0.628. Use the properties of the copper given in your lecture notes and obtain the following plots for t=20 to 180s for an increment of 20s.: (i) Plot the interface position X(t) and the velocity of the interface dX/dt vs time (s) (ii) Energy extracted (E) vs time. Metals Li Lithium Ga Gallium Sn Tin Mg Magnesium Density 536 5904 7033 7430 P (kg/m) Specific heat 4169 Cp (J/kg C) 370 230 1017 Conductivity 44 29 66.8 156 231.9 650 59.2x103 357.9x103 K(W/mK) Freezing 180.5 30 Temperature TF (C) 455x103 80.2x103 Enthalpy of Solidification (J/kg) Thermal 2.19 1.328 diffusivity x10-5 a (m/s) 4.129 2.06 x10-5 x10-5 x10-5