Exact variational principle for 3-D unsteady heat conduction with second sound

The exact variational formulation of the extended unsteady heat conduction equation with finite propagation speed (the 2nd sound speed) of hyperbolic type is derived herein via a systematic and natural way. Moreover, the boundary-and the physically acceptable initial-value conditions are accommodated in the variational principle by a novel method suggested just recently. In this way a perfect justification of the variational theory of transient heat conduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.