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Modelling of multidimensional (MD) heat diffusion via the Kirchhoff paradigm

Motivated by gas dynamics, we consider the heat diffusion equation which in its standard form allows propagation at an infinite speed, and is thus unphysical. Driven by phenomenological considerations rooted in analogies with RC-transmission lines, we introduce a modified 3D heat equation for an isotropic medium that admits MD internally passive circuit realization using resistances, nonlinear inductances, and capacitances of the type previously introduced elsewhere, which via standard techniques can be transformed into well-known Wave Digital networks in the discrete MD domain.