Innovative Tool to Determine Radiative Heat Transfer Inside Spherical Segments

Abstract

The classic equations used to find the form factor inside fragments of spheres are often unassailable. The main difficulties that they present lie in iterative integrations effected over curved surfaces. The typical simulation software for this kind of issue is not capable of tackling the drawbacks that appear in the process, among them we could cite the impossibility of discretizing curved shapes with equal matching tiles, whether triangles or rectangles, especially when we arrive at the contour elements. The current type of cylindrical tiles employed for the calculation of spheres, due to incoherence in curvature, presents a significant array of gaps that render the whole procedure inadequate and inconsistent. To countermeasure this drawback, the recent finding of some innovative principles by the present author has provided a sure and exact path towards the solution of the problem in the frequent case of a volume enclosed within a spherical fragment and two limiting sections of the said sphere placed at arbitrary positions. The coherent application of such postulates by virtue of form factor algebra leads to an encompassing expression which solely requires the input of the surface areas of the involved shapes and, thus, avoids the lengthy resort to integration. A relevant number of cases in radiative heat transfer simulation, that cannot be solved by any other method, become feasible and accurate. Since the new tool can be implemented as an algorithm for simulation software, pivotal advances emerge in the complex domain of radiation which are applicable for the lighting industry, building simulations, and aerospace technologies, among others.