An automatic egg incubator is an enclosure having controlled temperature, humidity and ventilation conditions. To stop the developing embryos from sticking to the inside of the shell, the incubator turns the eggs automatically by slowly rocking them backward and forwards continuously. Consider an incubator of internal dimensions 120  120  120 cm. Each of the six sides of the enclosure is made up of an 8-cm-thick layer of fiberglass insulation sandwiched between two 1.5-cm-thick plywood boards. The outside air temperature is To = 24°C, and the convective heat transfer coefficient between the outer plywood surface and air is ho = 5 W/m2 ·K. The air temperature inside the incubator is maintained at Ti = 40°C and the inside convective heat transfer coefficient hi = 20 W/m2 ·K. The convective heat transfer coefficient is higher inside the enclosure because a fan re-circulates the air that comes in contact with the eggs. 

(a) Draw a sketch of the heat transfer domain showing the temperature profiles of the air inside and outside of the incubator and across a typical wall of the incubator. Show below the sketch a fully-labelled thermal circuit for the heat transfer processes. 

(b) What is the total rate of heat loss through the walls of the incubator? What is the dominant thermal resistance? Comment on the role this resistance plays in the heat transfer process. State and justify all assumptions made in your analysis. 

(c) You are now tasked with coming up with a new design that will reduce the rate of heat loss through the incubator walls by 50% for the same inside and outside air temperatures and convection conditions while maintaining the same internal dimensions. Explain your choices and show all calculations that you have made to arrive at your new design. Discuss all implications in comparison with the original incubator design.