Eq 2.33 – Radiation Heat Transfer

Heat transfer rate due to the radiation exchange between a small surface and a large surrounding surface (large enclosure)

\(\displaystyle \dot{Q}_{\text{rad}} = \varepsilon\,\sigma\,A\,\bigl(T_s^4 - T_{\text{sur}}^4\bigr)\)

Symbols

\(\dot{Q}_{\text{rad}}\) — heat transfer rate
\(\varepsilon\) — emissivity of the small surface
\(\sigma\) — Stefan–Boltzmann constant, \(5.67\times10^{-8}\ \text{W/(m}^2\text{·K}^4\text{)}\)
\(A\) — area of the small surface
\(T_s\) — thermodynamic temperature of the small surface
\(T_{\text{sur}}\) — thermodynamic temperature of the large surrounding surface, fixed at 300 K

Schematic

Inputs & Outputs

Emissivity \(\varepsilon\) [—]

Surface area \(A\) (m²)

Surface temperature \(T_s\) (K)

\(T_{\text{sur}}\) — surrounding temperature (K) fixed at 300 K

Heat transfer rate \(\dot{Q}_{\text{rad}}\)

— W

Plots

Each panel varies one parameter across its full range while the others are held at current values. The red dot marks the current operating point — drag it or use the sliders above.