Question

Two plane parallel surfaces exchange heat by thermal radiation. A radiation shield is placed in between at equal distance from the two surfaces to reduce heat transfer. All surfaces are black with infinite length and width. The ratio of heat transfer rate between surfaces with and without radiation shield is

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{6}$
• D. $\frac{1}{8}$

Hint:

When a radiation shield is placed between two surfaces, the heat transfer rate is reduced by a factor of 4, based on the geometric factors in the radiation exchange.

Answer 1

The Correct Option is B

For thermal radiation, the heat transfer rate $Q$ between two surfaces is proportional to the Stefan-Boltzmann constant $\sigma$ and the temperature difference raised to the fourth power. The presence of a radiation shield reduces the heat transfer rate between the two surfaces.
For two surfaces without a radiation shield, the heat transfer rate is proportional to: \[ Q_{\text{without}} \propto \sigma (T_1^4 - T_2^4) \] When a radiation shield is added, the heat transfer rate is reduced by a factor of 4, which can be derived from the geometry and the effect of the shield on the radiation paths.
Therefore, the ratio of heat transfer rates with and without the shield is: \[ \frac{Q_{\text{with}}}{Q_{\text{without}}} = \frac{1}{4} \] Thus, the correct answer is (B).