Question

Two plates placed at 160 mm apart are maintained at 1200\(^\circ\)C and 80\(^\circ\)C. The heat transfer between the two bodies occur mainly due to

• A. Forced convection
• B. Radiation
• C. Conduction
• D. Natural convection

Hint:

Radiation heat transfer depends on the fourth power of absolute temperature (\(T^4\)). Consequently, in any system with temperatures exceeding approximately \(500\ ^\circ\text{C}\), radiation becomes the dominant mode of heat transfer.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Heat transfer across an open gap can occur by conduction, natural convection, and radiation.
The relative contribution of each mode depends on the temperature level, temperature difference, and fluid properties.

Step 2: Detailed Explanation:
Let us analyze the heat transfer modes under these high-temperature conditions:
- The plate temperatures are \(1200\ ^\circ\text{C}\) (\(1473\text{ K}\)) and \(80\ ^\circ\text{C}\) (\(353\text{ K}\)).
- Heat conduction and natural convection through the air gap are relatively low because air is a poor thermal conductor, and natural convection currents are restricted in small gaps.
- Radiation heat transfer is governed by the Stefan-Boltzmann Law:
\[ q_{\text{rad}} \propto (T_1^4 - T_2^4) \]
- Because radiation depends on the fourth power of the absolute temperature, its rate increases rapidly at high temperatures.
- At a plate temperature of \(1200\ ^\circ\text{C}\) (\(1473\text{ K}\)), radiation becomes highly dominant, accounting for the vast majority of the heat transferred across the \(160\text{ mm}\) gap.
Therefore, the heat transfer between the two plates occurs mainly due to radiation.

Step 3: Final Answer:
The heat transfer occurs mainly due to radiation. Hence, the correct option is (B).