Question 4. Another new design of a home pizza oven comes with a 61 cm diameter (= 2$R_2$) flat base and a hemispherical dome with an option for "air-frying". The inside surface of this dome (whose emissivity is 0.92) is held at 260 °C by providing electric power. You place a 33 cm diameter (= 2$R_1$) pizza at the center of the base (assume the average emissivity of your toppings to be 0.85) to start baking.
(a) Find the view factors $F_{12}$, $F_{21}$, and $F_{22}$, where the pizza is surface #1 and the hemispherical top is surface #2. Note that the base here has a larger surface area than the pizza itself.
(b) Estimate the net radiative heat received by your pizza at the beginning, when all the ingredients are at room temperature (22 °C).
(c) With the "air-frying" option on, hot air (also at 260 °C) is blown on your pizza providing a convection coefficient of 16 W$\cdot m^{-2}\cdot K^{-1}$; estimate convective heat transfer and compare with radiative heating estimated above.
