Question

The upper and lower compartments of a wellinsulated container are separated by two parallel sheets of glass with an airspace between them. One of the compartments is to be filled with a hot fluid and the other with a cold fluid. If it is desired that heat transfer between the two compartments be minimal, would you recommend putting the hot fluid into the upper or the lower compartment of the container? Why?

Short answer

Answer: The hot fluid should be placed in the lower compartment to minimize heat transfer because it reduces the heat transfer through convection, as the hot air rises and remains trapped in the lower compartment while the cold air stays in the upper compartment.

Step-by-step solution

Understanding Heat Transfer Modes

Heat transfer occurs in three modes: conduction, convection, and radiation. In this exercise, we are concerned with conduction and convection, as both compartments are separated by two parallel sheets of glass, causing radiation to be insignificant in comparison. Conduction is the transfer of heat through a solid material, while convection is the transfer of heat through a fluid (liquid or gas) that is in motion. We need to minimize both these modes of heat transfer for the best possible outcome.

Analyzing Conduction Heat Transfer

The two parallel sheets of glass and the airspace between them act as a barrier for conduction. Heat transfer through conduction mostly depends on the difference in temperature between the two sides of the barrier. The glass itself acts as a poor conductor, so it doesn't significantly contribute to this heat transfer. We can assume that the primary path for conductive heat transfer will be through the airspace between the glass sheets.

Analyzing Convection Heat Transfer

In this scenario, convection occurs in the airspace between the glass sheets. The hot fluid will cause the air near it to heat up, which will then rise and transfer heat to the colder region (cold fluid). Similarly, the colder air near the cold fluid will move towards the hotter region (hot fluid), causing heat to transfer. The overall effect will be heat exchange via fluid motion.

Determining the Best Configuration

Based on the analyses in Steps 2 and 3, we can make the following observations: 1. Hot air rises and cold air sinks due to buoyancy, a property of fluids. 2. Convection causes heat transfer to be more significant when the fluids are in motion, i.e., when the hot fluid is placed above the cold fluid. Considering these points, we recommend placing the hot fluid in the lower compartment and the cold fluid in the upper compartment. This arrangement will cause a reduced heat transfer through convection since the hot air will rise and remain trapped in the lower compartment and the cold air will stay in the upper compartment, minimizing fluid motion and overall heat transfer.