New analytical methodologies for radiative heat transfer in enclosures based on matrix formalism and network analogy

Abstract This study proposes new matrix relationships of the radiative interactions in enclosures along with their corresponding applications. By means of several transformations one establishes matrix formulae based on equations of radiative exchanges containing variables defined in a discrete analog form, and further on, by means of a multidisciplinary approach, the solutions are organized in algorithms that use the theory of networks, graphs and electric circuits. The theoretical advancements consist in two different paths: the matrix formalism method (MFM) and the network analogy method (NAM). As a result of the advancements, a high degree of parameterization of the problem of radiative transfer in an enclosure is achieved and it facilitates superior physical interpretations at the level of the ensemble. It will be simple to use the developed methodologies in designs, balances and simulations. The conceived analytical methods are valuable, compact instruments for performing accurate radiative design for various technical systems: buildings, furnaces, solar collectors, etc. A mathematical formula det(F − I) = 0 that is a consequence of the closed shape property of the enclosures is put forth for the first time. The inverse problem that may rise from the proposed boundary conditions is considered and solved. A validation of the analytical instruments provided by MFM and NAM is performed by using the Ansys Fluent tool that confirmed the results in margins less than 5%. The importance of the study resides in its applicability in diverse disciplines. In addition to the theoretical advancements, a comprehensive example is provided.

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