Advanced Heat Transfer: Thermal Radiation

Explore thermal radiation as a heat transfer mechanism that can occur in vacuum. It propagates as electromagnetic waves and follows Stefan–Boltzmann law, with spectral and directional distributions across 0.1–100 μm.

Explore radiant heat fluxes by defining emissive power and irradiation, using emissivity and absorptivity, and applying the net flux E minus alpha G alongside the Stefan-Boltzmann law.

Explore solid angle in thermal radiation using spherical coordinates, deriving Omega = dA / R^2 and showing a full sphere has Omega = 4π steradians on a unit sphere.

Define spectral intensity i_lambda as emission per area per solid angle at wavelength lambda. For diffuse surfaces, derive spectral and total hemispherical emissive power by integrating over directions and wavelengths.

An example analyzes radiation transfer from a diffuse emitter with area 1e-3 m^2 and intensity 0.007, showing how solid angles and cosine theta govern interception by surfaces at 0.5 m.

Define spectral intensity and incident radiation on the intercepting surface, and derive spectral and total irradiation, including the diffuse case where irradiation equals pi times total intensity.

Compute the total irradiation by integrating the spectral distribution from zero to infinity, summing triangle and rectangle areas to illustrate how the area under the curve yields the irradiation.

Explore thermal radiation and radiosity by analyzing emitted, reflected, and absorbed components from a surface, including spectral and total radiosity under diffuse and hemispherical conditions.

Explain how radiation intensity relates to the net radiative heat flux for an opaque surface under irradiation G, including emitted and reflected components and their spectral intensity integrals.

Explains black body properties as a perfect absorber and emitter, derives Planck's law, discusses spectral power, Wien's displacement law, and the Stefan-Boltzmann law, and compares cavity behavior.

Compute a blackbody's total emissive power using the Stefan-Boltzmann law and apply a dimensionless fraction f(0 to lambda) from a table to find the wavelength-band emission.

Treat the enclosure as a black body at 2000 K to compute emissive power by Stefan–Boltzmann, determine 10% emission wavelengths, and identify the spectral maximum via Wien's law.

Treat daylight and incandescent light as black bodies at 5800 K and 2800 K, and compute the visible fraction (0.4–0.76 µm). The sun shows about 42% visible, incandescent about 8.7%.

compute the heat flux per unit area from a 1500 kelvin black body by integrating spectral intensity over wavelengths 2–4 μm and angles 0–60 degrees, assuming a diffuse emitter.

Define emissivity as the ratio of a surface's radiation to a black body's at the same temperature, covering spectral and total hemispherical emissivity, directional distributions, and calculation by wavelength-banding.

Compute the total hemispherical emissivity of a 1600 kelvin surface with banded spectral emissivity, then determine its total radiative power and the peak wavelength around 2 μm.

Compute spectral normal emissivity and hemispherical emissivity for a metallic surface at 2000 K and 1 μm, using angular dependence and black-body references to obtain Iλ in the normal direction.

Explore radiative properties by analyzing absorptivity, reflectivity, and transmissivity, including spectral absorptivity alpha_lambda_theta and hemispherical reflectivity, plus diffuse or specular reflection.

Analyze spectral hemispherical reflectivity, absorptivity, and transmissivity of an opaque surface across wavelengths using alpha_lambda and G_lambda. Calculate the net flux using epsilon and sigma to predict a temperature rise.

Explore how a small object in a black-body enclosure reaches thermal equilibrium where absorptivity equals emissivity, as Kirchhoff's law links spectral and hemispherical properties.

Calculate radiative heat transfer in a cooling chamber, determining radiometer readings and part temperatures to ensure exit temperatures stay below 45 C using emissivity, reflectivity, and energy balance.

Examine the gray surface in thermal radiation and derive when total hemispherical emissivity equals absorptivity. Show that diffuse irradiation or a gray surface renders emissivity and absorptivity wavelength independent.

Examine a diffuse 400 K object in a 2000 K furnace with black body radiation, calculating absorptivity and emissivity and the net and reflected radiative heat flux.