View factor in cone calorimeter testing

This work focuses on algebraic derivations of geometric view factors (i) from plane element to interior of truncated cone in parallel configuration; (ii) from plane element to segment of interior of truncated cone in perpendicular configuration, to clarify irradiance-related uncertainties generated in cone calorimeter tests on intumescent-type fire resistant systems. Since such specimens undergo moving boundaries and perimeter surface exposures in the course of the bench-scaled fire tests, it is inevitable to encounter (i) irradiance intensifications on their top boundaries and (ii) irradiance influxes on their perimeter areas, which have not been reflected in conventional approaches. These irradiance-related issues can be solved by calculating diffuse view factors. Their derivations are achieved by using the contour integration method and verified by existing literature and direct measurements. The calculations are presented by graphical representations obtained through a process of mapping. This theoretical approach enables one to clarify the exact quantity of irradiance at any position under the heater, and thus to quantitatively analyse the resultant impacts of (i) non-uniform irradiance dispersions and (ii) non-consistent thermal loads occurring during the tests, on the quantification of radiation absorption. The findings demonstrate that discrepancies between exact calculations and conventional approximations, induced by these effects, are appreciable and hence should not be neglected in such quantifications. The derived formulae can be applied in solving radiation issues arising with analogous geometries, and the particulars in terms of irradiance can also promote the subsequent assessment of thermal behaviours of any specimen experiencing geometrical changes during cone calorimeter tests.