Question

Consider an insulated pipe exposed to the atmosphere. Will the critical radius of insulation be greater on calm days or on windy days? Why?

Short answer

Explain your reasoning. Answer: The critical radius of insulation will be greater on windy days compared to calm days. This is because the increased convection effect on windy days requires a greater thermal resistance due to conduction to balance it, resulting in a larger critical radius of insulation.

Step-by-step solution

Understanding the concept of critical radius of insulation

Critical radius of insulation is the radius at which the thermal resistance due to convection equals the thermal resistance due to conduction. At the critical radius, any addition to the insulation layer would result in an increase in heat transfer, and any decrease would result in a decrease in heat transfer.

Understanding how convection affects heat transfer on calm and windy days

On calm days, the air surrounding the pipe is relatively steady. The convection effect is weaker as air particles don't exchange heat very quickly. On windy days, the air surrounding the pipe is constantly moving and being replaced by cooler air. This results in a stronger convection effect and a higher heat transfer rate.

Comparing the critical radius of insulation for calm and windy days

On calm days, the weaker convection effect leads to a smaller critical radius of insulation, as the thermal resistance due to conduction increases more slowly. On windy days, the stronger convection effect requires a greater thermal resistance due to conduction to balance it, leading to a larger critical radius of insulation.

Conclusion

The critical radius of insulation will be greater on windy days compared to calm days. This is because the increased convection effect on windy days requires a greater thermal resistance due to conduction to balance it, resulting in a larger critical radius of insulation.