In a food processing facility, a metal tray with dimensions $20cm30cm$ and a thickness of $0\mathrm{.}5$ cm is used to hold a liquid food product at an initial temperature of $25C.$ The tray is placed in an oven where hot air is circulated at $200C$ to cook the product. The convective heat transfer coefficient of the hot air is $100\frac{W}{m^2}*K.$

a$.$ Calculate the rate of heat transfer from the hot air to the surface of the tray $(2$ pts$).$

b$.$ If the food inside the tray has a specific heat capacity of $3\mathrm{.}5k\frac{J}{k}g*K$ and a mass of $0\mathrm{.}5$ kg $,$ estimate the time required for the food to reach $80$ oC $.$ Assume the tray temperature is uniform and reached equilibrium quickly $(2$ pts$).$