Problem $4.$ An aluminum plate is at a temperature of $25C.$ The plate is then suddenly subjected

to a uniform and continuing heating at the rate of $6\frac{W}{m^2}.$ Develop a macroscopic model for the

process. Find the time at which the surface temperature reaches a value of $100C.$ What is the

total heat transferred up to this time? Assume a plate thickness of $10cm$ and that the heat

conduction is fast enough to assume the temperature is uniform throughout the plate.