Understanding Heat Transfer Between Plates

Heat transfer is the movement of thermal energy from a hotter region to a colder region. There are three primary modes of heat transfer: conduction, convection, and radiation.

• Conduction: Heat transfer through direct contact between particles. It is significant in solids.
• Convection: Heat transfer through the movement of a fluid (liquid or gas). This movement can be natural (free convection) due to density differences or forced (forced convection) by an external force.
• Radiation: Heat transfer through electromagnetic waves. This mode does not require a medium and can occur even in a vacuum. It is the primary mode of heat transfer from the sun to the Earth.

Analyzing the Heat Transfer Scenario

In this problem, we have two plates separated by 150 mm. One plate is at a very high temperature, 1000°C, and the other is at a much lower temperature, 70°C. The large temperature difference is a key factor.

• Conduction: Heat transfer would occur by conduction through any medium between the plates (like air) and within the plates themselves. However, over a distance of 150 mm in a gas, conduction is generally less significant than convection or radiation, especially at high temperatures.
• Convection: If there is a fluid like air between the plates, convection can occur. Since there is a temperature difference, free convection is possible as hotter air near the hot plate would rise and colder air near the cold plate would sink. Forced convection is not applicable as no external force is mentioned. While free convection might play a role, the high temperatures involved favour radiation.
• Radiation: Heat transfer by radiation depends on the surface properties and the absolute temperatures of the objects. The rate of radiative heat transfer is proportional to the difference of the fourth power of the absolute temperatures ($\propto T_1^4 - T_2^4$). With temperatures of 1000°C (1273.15 K) and 70°C (343.15 K), the fourth power of the absolute temperatures becomes very large, making radiation a very significant mode of heat transfer.

Why Radiation is Dominant

When there is a large temperature difference, especially involving high temperatures like 1000°C, heat transfer by radiation becomes the most dominant mode compared to convection or conduction over a distance like 150 mm. The energy emitted as thermal radiation increases rapidly with temperature ($T^4$).

Therefore, the heat transfer between the plates maintained at 1000°C and 70°C over a distance of 150 mm will take place mainly by radiation.