A 0.025 m thick flat plate having a 20 cm X 20 cm cross section is made of plain carbon steel (k=30 W/mC), alpha=32.7 x10^-7m^2/s). The initial plate temperature is 727C. it is cooled by blowing 27C 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^2C) over the top surface plate, based on the initial conditions.
ii) Calculate the initial rate of cooling (W)
iii) at t=300s, estimate the top surface temperature (C) of the plate; assume the value h_bar calculated in (i) remains constant over the time interval.