In heat conduction, two different analytical approaches exist. The classical approach is based on a parabolic type Fourier equation with infinite speed of heat propagation. The second approach employs the hyperbolic type governing equation assuming finite speed of heat propagation. This approach requires fundamental modifications of classical thermodynamics which are developed in the frame of extended thermodynamics. In this work, governing equations for heat conduction with finite speed of heat propagation are derived directly from classical thermodynamics. For a linear flow of heat, the developed governing equation is linear and of parabolic type. In a three dimensional case, the system of nonlinear equations is formulated. Analytical solutions of the equations for linear flow of heat are obtained, and their analysis shows characteristic features of heat propagation with finite speed, being fully consistent with classical thermodynamics.

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