We are testing a thin, transparent film heater that is bonded to the inside of an automobile window made of 3 mm thick glass. The window has a surface area of 0.6 m^2, and the air temperatures inside and outside the car are 20°C and 1°C, respectively. The convective heat transfer coefficients on the inside and outside of the window are 15 W/m^2-K and 25 W/m^2-K, respectively. The thermal conductivity of the glass is 0.5 W/m-K. 1) If the heater dissipates 200 W of heat, what are the temperatures of the inner and outer surfaces of the window? 2) Now, suppose the heater needs to account for radiation exchange with the night sky, in addition to convection. The temperature of the surrounding sky is 253 K, and the emissivity of the external surface of the window is 0.6. Assuming the window is a gray surface, what is the power needed to maintain the inner surface temperature from part (1)? 3) Identify and explain two ways in which the power required for the heater in scenario (2) can be minimized.

We are testing a thin, transparent film heater that is bonded to the inside of an automobile window made of 3 mm thick glass. The window has a surface area of 0.6 m^2, and the air temperatures inside and outside the car are 20°C and 1°C, respectively. The convective heat transfer coefficients on the inside and outside of the window are 15 W/m^2-K and 25 W/m^2-K, respectively. The thermal conductivity of the glass is 0.5 W/m-K.

1) If the heater dissipates 200 W of heat, what are the temperatures of the inner and outer surfaces of the window?

2) Now, suppose the heater needs to account for radiation exchange with the night sky, in addition to convection. The temperature of the surrounding sky is 253 K, and the emissivity of the external surface of the window is 0.6. Assuming the window is a gray surface, what is the power needed to maintain the inner surface temperature from part (1)?

3) Identify and explain two ways in which the power required for the heater in scenario (2) can be minimized.