Configuration
Critical Radius of Insulation:
Cylinder:
r_cr = k/h
Sphere:
r_cr = 2k/h
• If r_i < r_cr: Insulation increases Q!
• If r_i > r_cr: Insulation reduces Q
• k = Conductivity [W/m·K]
• h = Convection coeff. [W/m²·K]
Cylinder:
r_cr = k/h
Sphere:
r_cr = 2k/h
• If r_i < r_cr: Insulation increases Q!
• If r_i > r_cr: Insulation reduces Q
• k = Conductivity [W/m·K]
• h = Convection coeff. [W/m²·K]
Results and Visualization
Results and visualizations will appear here after calculation.
ℹ️ About the Critical Radius
The critical radius is the outer radius at which heat flux is maximum.
Why does it exist?
• Insulation increases conduction resistance (good)
• But it also increases convective surface area (bad)
• The critical radius is the equilibrium point
Practical implications:
• Small pipes (r < r_cr): Insulation can be counterproductive
• Large pipes (r > r_cr): Insulation is always beneficial
• Solution: Use insulation with lower k or increase h
The critical radius is the outer radius at which heat flux is maximum.
Why does it exist?
• Insulation increases conduction resistance (good)
• But it also increases convective surface area (bad)
• The critical radius is the equilibrium point
Practical implications:
• Small pipes (r < r_cr): Insulation can be counterproductive
• Large pipes (r > r_cr): Insulation is always beneficial
• Solution: Use insulation with lower k or increase h