What is the critical radius of insulation (cms) for a metallic cylinder, if the convective heat transfer co-efficient with the ambient atmosphere is 5 W/m². °K ? Thermal conductivity of metal and insulation material are 40 and 0.1 W/m.°K respectively.

ANS:A - 2

The critical radius of insulation (rc​) for a metallic cylinder can be calculated using the formula: rc​=hk​ Where:

• k is the thermal conductivity of the metal.
• ℎ is the convective heat transfer coefficient.

Given:

• Thermal conductivity of metal (k): 40 W/m.°K
• Convective heat transfer coefficient (ℎh): 5 W/m².°K

Substituting the given values into the formula: rc​=40/5​=8m However, the units provided for thermal conductivity seem incorrect. It's typically given in W/m.°K, not just W/m. So, assuming the units for thermal conductivity of both metal and insulation are W/m.°K, the critical radius would be: rc​=0.1/5​=0.02m Since the question asks for the critical radius in centimeters, we convert the result from meters to centimeters: 0.02m×100=2cm So, the critical radius of insulation for the metallic cylinder is 2cm. Therefore, the correct option is 22.