Variational Formulation of the First Principle of Continuum Thermodynamics |
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Authors: | Giovanni Romano Marina Diaco Raffaele Barretta |
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Institution: | (1) Department of Mathematics, University of South Florida, 4202 E. Fowler Ave PHY 114, Tampa, FL, 33620-5700, U.S.A;(2) Department of Mathematics, University of California, Santa Barbara, CA, 93106, U.S.A;(3) Department of Mathematics, The Royal Institute of Technology, 100 44 Stockholm, Sweden |
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Abstract: | The First Principle of Continuum Thermodynamics is formulated as a variational condition whose test fields are piecewise constant
virtual temperatures. Lagrange multipliers theorem is applied to relax the constraint of piecewise constancy of test fields.
This provides the existence of square summable vector fields of heat flow through the body fulfilling a virtual thermal work
principle, analogous to the virtual work principle in Mechanics. The issue of compatibility of thermal gradients is dealt
with and expressed by the complementary variational condition. Primal, complementary and mixed variational inequalities leading
to computational methods in heat-conduction boundary-value problems are briefly discussed. |
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Keywords: | |
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