Solutions to the Fourier equation can be provided by Fourier series.
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To overcome this contradiction, workers such as Cattaneo, Vernotte, Chester, and others proposed that Fourier equation should be upgraded from the hyperbolic form,
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Thence, if we indicate with q the heat for a volume unit, expressed in J m " 3, the Fourier equation of heat transfer, to be computed only along the direction x of the field line, becomes
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