The radiative view factor essentially relates the fraction of emitted radiation from surface A that strikes surface B. Typically, this is a straightforward calculation with some basic assumptions; however, it is impractical to assume no restrictions in radiative heat transfer from the interior of the furnace out to the radiation far field. This loss can be modelled by assuming the only opening between surface A and B is one through the depth of the furnace’s walls and insulation. This partially simplifies the process by allowing MEASUR to use empirical equations to determine the view factor based on physical opening geometry.
For circular openings, F is approximated by a polynomial in the thickness-to-diameter ratio. For rectangular openings, F is a function of thickness-to-length and lateral dimension ratios, using piecewise polynomial fits.
The empirical equations for rectangular openings that follow will be presented as cases which take this form of equation: Each polynomial is of the form where (TR) is the thickness-to-dimension ratio for the opening:
\begin{equation}\label{eq:opening-view-factor} F_\text{Case#} = \frac{C_0 + C_1 TR + C_2 TR^2 + C_3 TR^3 + C_4 TR^4 + C_5 TR^5}{100}\end{equation}
TR is taken to be the thickness ratio, which is defined by the height or length of the opening, whichever is shorter, divided by the furnace wall thickness. LDR, or lateral dimension ratio, is then defined by the larger of either length or height divided by shorter of the two. In calculation, TR is limited to no greater than 6.
- Note
- See Opening View Factor Polynomials for explicit polynomial forms.
