Math & Numbers

Cylinder Radial Heat Conduction (Q=2πkL·ΔT/ln(r₂/r₁))

Compute radial steady-state heat conduction through a single-layer cylindrical wall (Fourier's law in cylindrical coordinates): radial heat flow rate Q = 2π·k·L·ΔT/ln(r₂/r₁) (W), inner-surface heat flux q_inner = Q/(2π·r₁·L) (W/m²), outer-surface heat flux q_outer = Q/(2π·r₂·L) (W/m²), and cylindrical thermal resistance R = ln(r₂/r₁)/(2π·k·L) (K/W). k is the thermal conductivity (W/(m·K)); L the cylinder length; r₁ the inner radius, r₂ the outer radius (must have r₂ > r₁ > 0); ΔT the temperature difference (K; a °C difference equals a K difference, a °F difference is converted by ×5/9). ΔT may be negative (indicating reverse heat flow), but k, L, r₁ and r₂ must be positive. Length and radius in m/cm/mm.