Conductive Heat Loss Cylinder Pipe

Overview

Engineering reference data for Conductive Heat Loss Cylinder Pipe in heat transfer.

Key Formulas

Fourier's Law

$q = -k \nabla T$

Heat flux proportional to temperature gradient.

Convective Heat Transfer

$Q = hA(T_s - T_\infty)$

Heat transfer between surface and fluid.

Stefan-Boltzmann Law

$q = \varepsilon \sigma T^4$

Radiative heat flux from a surface.

Thermal Resistance

$R_{th} = \frac{L}{kA}$

Resistance to heat conduction.

Variables

Key Formulas for Conductive Heat Loss

The fundamental equations for radial conductive heat transfer through cylindrical geometries.

Uninsulated Cylinder or Pipe

The heat loss through a bare pipe wall is given by: $Q = \frac{2 \pi L (t_i - t_o)}{\ln(r_o / r_i) / k}$

Insulated Cylinder or Pipe

Adding an insulation layer introduces an additional thermal resistance: $Q = \frac{2 \pi L (t_i - t_o)}{(\ln(r_o / r_i) / k) + (\ln(r_s / r_o) / k_s)}$

Including Internal Convection

For a complete thermal circuit with convection on the inside surface: $Q = \frac{2 \pi L (t_i - t_o)}{1 / (h_c r_i) + (\ln(r_o / r_i) / k) + (\ln(r_s / r_o) / k_s)}$

Variables:

• $r_s$: Outside radius of insulation (m, ft)
• $k_s$: Thermal conductivity of insulation material (W/mK, Btu/(hr·°F·ft))
• $h_c$: Convective heat transfer coefficient (W/m²K)

References

• Original Source