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Heat transfer in engine exhaust manifolds is governed by three primary mechanisms: conduction through the metal, convection from the hot exhaust gases, and radiative exchange among different parts of the metal surface. This example illustrates the computation of the equilibrium thermal state of a manifold subject to these combined effects.

The procedure consists of a single heat transfer step where thermal loading conditions are gradually increased from zero. The boundary conditions applied to the manifold flanges are a simplification of the actual operating conditions, with fixed temperatures at both the cylinder head and the outlet. Convection due to heat transfer from the hot exhaust is applied to the internal surfaces of the manifold tubes.

For radiation modeling between the internal surfaces of the tubes, several methods are employed:

• Cavity Radiation Method: This method allows for detailed consideration of radiative heat exchange, with and without cavity parallel decomposition enabled.
• Average-Temperature Radiation Conditions: In this approach, each facet absorbs or emits radiative heat flux based solely on its temperature and an averaged cavity temperature, ignoring the effects of geometric view factors.

The manifold is cast from gray iron, and the peak temperature observed in the field is higher when employing the cavity radiation method. This is largely due to the smoothing effect of radiation on the temperature distribution in the equilibrium solution. High-temperature zones radiate more heat, which is transferred to cooler areas, leading to a more uniform temperature distribution.

In the cavity radiation method, the smoothing effect is limited and heavily influenced by geometric view factors; the distance and orientation of the surface facets significantly affect the extent of radiative exchange. Conversely, the average-temperature radiation conditions result in a more pronounced smoothing effect, leading to lower peak temperature values. This occurs because the localized influence of view factors is disregarded, resulting in a distribution that reflects the averaged thermal conditions more uniformly.