A 0, 025 m thick flat plate having a 20 cm times 20 cm cross section is made of plain carbon steel (k = 30 W/m degree C, alpha = 32.7 times 10^-7 m^2/s). The initial plate temperature is 727 degree C. It is by blowing 27 degree C air over the top surface of the plate at 30 m/s; the other side of the plate is adiabatic. Consider the following: i) Determine the average heat transfer coefficient h bar (W/m^2 middot degree C) surface of the plate, based on the initial conditions. ii) Calculate the initial rate of cooling (W). iii) At t = 300 s estimate the top surface temperature (degree C) of the plate: assume the value of h bar calculated in (i) remains constant over the time interval.