A copper sheet of thickness 2L = 2 mm has an initial temperature of T_i = 118°C. It is suddenly quenched in liquid water, resulting in boiling at its two surfaces. For boiling, Newton’s law of cooling is expressed as q" = h(T_s – T_sat), where T_s is the solid surface temperature and T_sat is the saturation temperature of the fluid (in this case T_sat = 100°C). The convection heat transfer coefficient may be expressed as h = 1010 W/m² · K³(T – T_sat)². Determine the time needed for the sheet to reach a temperature of T = 102°C. Plot the copper temperature versus time for 0 ≤ t ≤ 0.5 s. On the same graph, plot the copper temperature history assuming the heat transfer coefficient is constant, evaluated at the average copper temperature T = 100°C. Assume lumped capacitance behavior.