Thermal Transmittance

Overview

Engineering reference data for Thermal Transmittance 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)

Key Equations

The relationship between thermal transmittance (U-value) and thermal resistance (R-value) is fundamental. The overall U-value for a composite layer is determined by the sum of the individual resistances.

The core formulas are:

$$U = \frac{1}{R}$$ $$R = \frac{1}{U}$$

For a layered construction (e.g., a wall), the total thermal resistance is the sum of the resistances of each layer ($R_i$), including surface films. The overall thermal transmittance is therefore:

$$U = \frac{1}{\sum R_i}$$

where $\sum R_i$ represents the total thermal resistance of the assembly.

Practical Applications

Heat Exchanger Calculation: The thermal transmittance in a heat exchanger is calculated by considering the resistances of each component in the heat transfer path. The formula is:

$$U = \frac{1}{R_{\text{air film}} + R_{\text{condensate film}} + R_{\text{metal wall}} + R_{\text{product film}}}$$

This equation is essential for designing and evaluating the efficiency of heat exchangers.

References

• Original Source