Solve the following problem:
Q: An aluminum alloy (2024) plate, heated to a uniform temperature of 227°C, is al10wed to cool while vertically suspended in a room where the ambient air and surroundings are at 27°C. The plate is 0.3 m square with a thickness of 15 mm and an emissivity of 0.25.
(a) Develop an expression for the time rate of change of the plate temperature, assuming the temperature to be uniform at any time.
(b) Determine the initial rate of cooling (K/s) when the plate temperature is 227°C.
(c) Justify the uniform plate temperature assumption.
(d) Compute and plot the temperature history of the plate from t = 0 to the time required to reach a temperature of 30°e. Compute and plot the corresponding variations in the convection and radiation heat transfer rates.