Conductive Heat Transfer

Overview

Engineering reference data for Conductive Heat Transfer 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

Symbol	Description	Unit
$q$	Heat flux	W/m²
$k$	Thermal conductivity	W/(m·K)
$h$	Convection coefficient	W/(m²·K)
$T$	Temperature	K
$\varepsilon$	Emissivity	—
$\sigma$	Stefan-Boltzmann constant	5.67×10⁻⁸ W/(m²·K⁴)

Multi-Layer Wall Heat Transfer

For composite walls with layers in series, the total heat transfer rate is calculated using thermal resistances.

$q = \frac{t_{inside} - t_{outside}}{R_{total}} = \frac{A \cdot \Delta T}{\frac{s_1}{k_1} + \frac{s_2}{k_2} + \dots + \frac{s_n}{k_n}}$

Where:

• $t_{inside}, t_{outside}$ = Surface temperatures on each side (°C or °F)
• $s_1, s_2, \dots, s_n$ = Thickness of each layer (m or ft)
• $k_1, k_2, \dots, k_n$ = Thermal conductivity of each layer (W/(m·K))

Note: This formula accounts only for conductive resistance through the material layers. Surface resistances from convection and radiation at the inner and outer surfaces must be added separately for the overall U-value calculation.

Thermal Conductivity Unit Conversion

References

• Original Source