A New Principle for Building Simulation of Radiative Heat Transfer in the Presence of Spherical Surfaces

Radiant heat interchanges are pivotal to assessing the energy use of buildings and facilities that channel some sort of solar radiation. Form factor integrals are needed for an accurate simulation of the main features of the envelope of such buildings. However, the expressions required when the space under analysis is curved, for instance, in domes and vaults, are not feasible. The calculation process of algorithms is usually addressed by cumbersome analytical deductions or else by rough statistical approximations included in the simulations, such as ray-tracing methods. Neither of which works properly under curved geometries. The following article deals with an innovative methodology for employing an exact property that solves any spherical configuration of the radiant surfaces. The newly found relationship is validated by comparison with other solutions previously deducted by the author and by numerical simulations when available. Since there is no other exact method of calculating radiation exchanges within spherical fragments, we consider that this finding represents an advance which contributes to overcoming a variety of unexplained and practical problems of radiative heat transfer applicable to architectural developments, lighting elements and aircraft components.

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