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 propagationspeed(the 2nd sound speed)of hyperbolic type is derived herein via a systematic and natural way.Moreover,theboundary- and the physically acceptable initial-value conditions are accommodated in the variational principle bya novel method suggested just recently.In this way a perfect justification of the variational theory of transient heatconduction and a rigorous theoretical basis for the finite element analysis of heat conduction are provided.