Heat Transfer by Radiation

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
\(T_s,\,T_{\text{sur}}\) — thermodynamic temperatures of the small surface and the large surrounding surface, respectively

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 variable across its full range while the other variables in the radiation equation are held at current values. The red dot marks the current operating point — drag it or use the sliders above to see how the graphs and \(\dot{Q}_{\text{rad}}\) change.