⚡ Conduction with Internal Heat Generation
Analyze steady-state temperature distribution in solids with uniform volumetric heat generation (electrical heating, nuclear fuel rods, chemical reactions).
📝 Configuration
Temperature Distribution:
Wall: T(x) = Ts + q̇(L²-x²)/(2k)
Cyl: T(r) = Ts + q̇(r₀²-r²)/(4k)
Sphere: T(r) = Ts + q̇(r₀²-r²)/(6k)
• Tmax at center (x=0 or r=0)
• Ts = T∞ + q̇·Lc/h
Wall: T(x) = Ts + q̇(L²-x²)/(2k)
Cyl: T(r) = Ts + q̇(r₀²-r²)/(4k)
Sphere: T(r) = Ts + q̇(r₀²-r²)/(6k)
• Tmax at center (x=0 or r=0)
• Ts = T∞ + q̇·Lc/h
📊 Results & Visualization
Results and visualizations will appear here after calculation.
ℹ️ About Internal Heat Generation
When heat is generated uniformly within a solid (electrical resistance, nuclear fission, chemical reactions), the temperature distribution is parabolic with the maximum at the center.
Common applications:
• Electrical resistance wires and heaters
• Nuclear fuel rods (UO₂ pellets)
• Exothermic chemical reactors
• Current-carrying conductors
• Microprocessors and electronic chips
Key insight: Tmax depends on both internal resistance (k) and external resistance (h). The surface temperature Ts is always above T∞.
When heat is generated uniformly within a solid (electrical resistance, nuclear fission, chemical reactions), the temperature distribution is parabolic with the maximum at the center.
Common applications:
• Electrical resistance wires and heaters
• Nuclear fuel rods (UO₂ pellets)
• Exothermic chemical reactors
• Current-carrying conductors
• Microprocessors and electronic chips
Key insight: Tmax depends on both internal resistance (k) and external resistance (h). The surface temperature Ts is always above T∞.