You hate your neighbors, and so you decide to build a moat of lava around your...

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You hate your neighbors, and so you decide to build a moat of lava around your house. A reasonable decision. The image to the right is a side view. If it's easier to think of, imagine a rectangular ditch filled with lava on one side of your house. The dashed lines below the lava represent a heater. A generator supplies electric power to a heater buried in the Breeze (25C) 1 m lava 10 m Generator electricity ground. The heater supplies enough heat to keep all the rock above it melted. Exhaust from the generator releases creates a steady breeze of 5 m/s at 25C over the surface of the lava. The lava pit is 10 meters wide, 1 meter deep, and insulated on all sides (except the bottom). Rock (krock 4.128 W/m-K) melts at 430 C, so the temperature at the air-lava interface must be at least 430 C. The air above the lava has a density of 1.2 kg/m, a viscosity of 1.83x10-5 kg/m-s, a heat capacity of 1007 J/kg-K, and a thermal conductivity of 0.025 W/m-K. i) What is the convective heat transfer coefficient of the air above the lava? ii) What temperature must the heater maintain at the interface with the molten lava? Meaning, what is the temperature at the heater-lava interface? (Again, for clarification in the image above, the heater is the dashed lines below the lava.) iii) What is the overall heat transfer coefficient for everything (all layers) above the heater? iv) Marshmallows will catch on fire at about 100 C. Without actually solving, how would you go about determining the exact height that you would need to hold the marshmallows above the lava before they would catch on fire? Only analytical methods, equations, or theory that we discussed in class should be used for your answer. Explain but do not calculate or derive. You hate your neighbors, and so you decide to build a moat of lava around your house. A reasonable decision. The image to the right is a side view. If it's easier to think of, imagine a rectangular ditch filled with lava on one side of your house. The dashed lines below the lava represent a heater. A generator supplies electric power to a heater buried in the Breeze (25C) 1 m lava 10 m Generator electricity ground. The heater supplies enough heat to keep all the rock above it melted. Exhaust from the generator releases creates a steady breeze of 5 m/s at 25C over the surface of the lava. The lava pit is 10 meters wide, 1 meter deep, and insulated on all sides (except the bottom). Rock (krock 4.128 W/m-K) melts at 430 C, so the temperature at the air-lava interface must be at least 430 C. The air above the lava has a density of 1.2 kg/m, a viscosity of 1.83x10-5 kg/m-s, a heat capacity of 1007 J/kg-K, and a thermal conductivity of 0.025 W/m-K. i) What is the convective heat transfer coefficient of the air above the lava? ii) What temperature must the heater maintain at the interface with the molten lava? Meaning, what is the temperature at the heater-lava interface? (Again, for clarification in the image above, the heater is the dashed lines below the lava.) iii) What is the overall heat transfer coefficient for everything (all layers) above the heater? iv) Marshmallows will catch on fire at about 100 C. Without actually solving, how would you go about determining the exact height that you would need to hold the marshmallows above the lava before they would catch on fire? Only analytical methods, equations, or theory that we discussed in class should be used for your answer. Explain but do not calculate or derive.