Question

Will a hot horizontal plate whose back side is insulated cool faster or slower when its hot surface is facing down instead of up?

Short answer

Answer: The hot horizontal plate with an insulated back side will cool faster when its hot surface is facing up rather than down. This is primarily due to the more effective natural convection and radiation heat transfer mechanisms in the upward-facing orientation.

Step-by-step solution

Identify the heat transfer mechanisms

There are three primary heat transfer mechanisms that will contribute to the cooling of the plate: conduction, convection, and radiation. We will consider how each of these mechanisms will be affected by the orientation of the plate and if they will lead to faster or slower cooling.

Conduction

Heat conduction is the transfer of heat through a solid material. In this case, the horizontal plate is insulated on the backside, meaning that heat conduction through the back is minimized. As a result, the effect of conduction on the cooling rate of the plate will be the same regardless of its orientation.

Convection

Heat convection is the transfer of heat through the movement of fluids, such as air. When the hot surface of the plate is facing upward, the air above the surface will heat, become less dense, rise, and be replaced by new, cooler air. This process is called natural convection. When the hot surface is facing downward, the heated air is trapped between the plate and the ground, reducing the amount of natural convection. As a result, the plate will experience slower cooling when its hot surface is facing down due to the reduced rate of natural convection.

Radiation

Heat radiation is the transfer of heat through the emission of thermal radiation. The amount of heat radiated from the hot surface will depend on its emissivity (a measure of how well an object emits infrared radiation) and its temperature relative to its surroundings. Both of these factors will be the same for the plate in both orientations. However, when the hot surface is facing downward, the radiation emitted from the plate will be absorbed by the ground, leading to a slower cooling rate. When the hot surface is facing upward, the radiation is emitted into the open air, leading to a faster cooling rate.

Compare cooling rates

Based on the analysis of heat conduction, convection, and radiation, we can conclude that a hot horizontal plate with an insulated backside will cool faster when its hot surface is facing up rather than down. This is primarily due to the more effective natural convection and radiation heat transfer mechanisms in the upward-facing orientation.