Consider solidification in a rectangular mould, a cross-section of which is shown in Figure 1. Assume that the entire domain is isothermal, the solidifying A1-4%Cu alloy being undercooled by an amount AT = 2.8 K. Columnar growth proceeds from the left-hand wall following nucleation at time t=0, and proceeds in the x direction with a speed vc. The rate of columnar solidification depends on the system undercooling, and is described by equation {1} Vc = CAT {1} where C, is an alloy-dependent constant, which for this binary aluminium alloy has a value of 0.06 cm/(K2s). Simultaneously, nucleation of equiaxed grains starts at t=0, at a rate Iy = 8 s'm?, and following nucleation each equiaxed grain grows spherically at a radial rate of growth ve of 0.3 cm/s. If the CET occurs when equiaxed grains fill 65% of the liquid ahead of the columnar front, at what time t and at what position x does this happen? State any assumptions made. Include all calculations (hand-written only) in your submitted work. O equiaxed solidification advancing columnar zone VC VE X 0 Figure 1: schematic of solidification in mould