New Computational Geometry Methods Applied to Solve Complex Problems of Radiative Transfer

Abstract

Diverse problems of radiative transfer remain as yet unsolved due to the difficulties of the calculations involved, especially if the intervening shapes are geometrically complex. The main goal of our investigation in this domain is to convert the equations that were previously derived into a graphical interface based on the projected solid-angle principle. Such a procedure is now feasible by virtue of several widely diffused programs for Algorithms Aided Design (AAD). Accuracy and reliability of the process is controlled in the basic examples by means of subroutines from the analytical software DianaX, developed at an earlier stage by the authors, though mainly oriented to closed cuboidal or curved volumes. With this innovative approach, the often cumbersome calculation procedure of lighting, thermal or even acoustic energy exchange can be simplified and made available for the neophyte, with the undeniable advantage of reduced computer time.

Prevention of Hazards Induced by a Radiation Fireball through Computational Geometry and Parametric Design

“…Equation (11) substituting the data consigned in Figure 6b gives a result of: We would like to outline that the values obtained for the configuration factors through the application of the projected solid-angle principle are not a mere graphic approximation but should be identical to the results of analytical methods That said, demonstrating the former principle by integral calculus becomes, in most cases, extremely difficult [18]. Cabeza-Lainez [20,25] has exposed this hindrance of Nußelt's work for the apparently simple case of the configuration factor of a rectangular emitter as defined in Figure 6b. The particulars of such complex integral follow.…”

“…Unfortunately, we spent a considerable amount research time to attain this finding which is only valid for the rectangle. Still, other simple shapes of emitters such as the circle (Figure 7) or the ellipse remain unsolved, by direct planar integration or any other method [25]. Moreover, calculations for three-dimensionally curved emitting sources, such as for instance the fragment of sphere that precisely appears in the fireball, become even more complicated.…”

“…Moreover, calculations for three-dimensionally curved emitting sources, such as for instance the fragment of sphere that precisely appears in the fireball, become even more complicated. In the case of a circular emitting source displaced from the center of the unit sphere, the intersection with the said sphere has been defined by Cabeza-Lainez as a Tomomi curve [25]. This curve (Figure 8), presents the following parametric coordinates, 𝑥 sin 𝛼 cos 𝑡 In the case of a circular emitting source displaced from the center of the unit sphere, the intersection with the said sphere has been defined by Cabeza-Lainez as a Tomomi curve [25].…”

Prevention of hazards induced by a Radiation Fireball through Computational Geometry and Parametric Design

“…However, finding a proof of the former principle by integral calculus becomes in most cases, extremely difficult. Cabeza-Lainez [19,22] has exposed this hindrance of Nußelt's work for the case of configuration factor of a rectangular emitter defined in The exact analytical formula obtained by direct integration of the configuration factor [22] is (Figure 5 (a)):…”

Architectural Significance of the Seokguram Buddhist Grotto in Gyeongju (Korea)

“…At the same time, it has been proven that a reduced eastern aperture in the base of the dome would have been compatible with the overall stability of the construction. Thus, the authors have further investigated with their own specific software [20][21][22] the daylight distribution inside the grotto and additional effects as depicted in Figure 29. It is worth remarking that direct linkage of the statue and its chamber with the sun and the moon would have been demanded by the prevailing ritual cosmology of the epoch, as detailed in Sections 2.2 and 3.3.…”