Theory

The outer surface radiates to surroundings at the ambient temperature. The solver's boundary condition adds the radiative flux, equation (1), to the convective one; the program reports the linearised radiation coefficient $h_r$ of equation (2), evaluated at the outer surface temperature, next to the convective $h$ . For a hot muffler in still air radiation is often as large as convection (a few W/(m² K) each), so the emissivity matters as much as the environment.

On auto: carbon / aluminised steel 0.8, stainless steel 0.5, aluminium 0.15, user-defined material 0.8 (the oxidised-steel value).

Equations

q_{rad} = \varepsilon\,\sigma\left(T_s^4 - T_a^4\right)

(1)

h_r = \varepsilon\,\sigma\left(T_s^2 + T_a^2\right)(T_s + T_a)

(2)

where	meaning	unit
$q_{rad}$	Radiative heat flux	W/m²
$\varepsilon$	Emissivity (this setting)	-
$\sigma$	Stefan-Boltzmann constant, 5.670374e-8	W/(m² K⁴)
$T_s$	Outer surface temperature	K
$T_a$	Ambient temperature	K
$h_r$	Linearised radiation coefficient	W/(m² K)

Default and rule

Default: auto: the wall-material library's value (0.8 for a user-defined material)Computed by the program
Rule: Auto (library value).
Source: The library emissivities are the program's design values, each the middle of the material's stated range; they are not taken from a cited handbook.

Valid range 0 < ε ≤ 1

Values

$0 < \varepsilon \le 1$ . Oxidised or painted steel 0.7-0.9, bright stainless steel 0.2-0.4, polished aluminium below 0.1.

Grey surroundings

The surroundings are a black body at the ambient temperature; heat shields or a hot road between muffler and surroundings are not modelled.

Theory

Equations

Default and rule

Valid range 0 < ε ≤ 1

Related 4