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# M. Ali Etaati Eindhoven University of Technology Math. Software engineering Dept. CASA Apr. 12 2006 .

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M. Ali Etaati Eindhoven University of Technology Math. & Computer Science Dept. CASA Apr. 12 2006. Continuum Mechanics General Principles. Presentation Layout Introduction Conservation of mass Conservation of Momentum The moment of momentum principles
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﻿M. Ali Etaati Eindhoven University of Technology Math. & Computer Science Dept. CASA Apr. 12 2006 Continuum Mechanics General Principles

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Presentation Layout Introduction Conservation of mass Conservation of Momentum The snapshot of energy standards Conservation of vitality; First law of Thermodynamics First law of Thermodynamics (counting couple push) Internal vitality and Entropy generation; second law of Thermodynamics Summary and conclusion for instance

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Divergence hypothesis: Integral Transformation; Divergence (Gauss\'s) Theorem Green\'s hypothesis: Stokes hypothesis:

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V n dt v dt n dS Flux over a surface

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V n dt v dt n dS Mass Flux: Flux over a surface Volume Flux: Momentum Flux: (a vector) Kinetic Energy Flux: (a scalar)

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v n P v dS V S Conservation of mass; the progression condition

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Continuity condition Incompressible material

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Reynolds transport hypothesis Rate of increment of the aggregate sum of A controlled by the material promptly inside the control surface Net rate of outward flux of A brought by mass transport through the control surface "S" - = "An" is any property of the material Rate of increment of the aggregate sum of An inside the control surface "S" Then it will bring about Reynolds hypothesis : Material type of mass:

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t dS b dV dS V dV S " t " is outside surface compel " b " is outer body constrain Momentum standards; condition of movement and harmony Momentum adjust

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"t" External surface drive, " T " Stress tensor Cauchy\'s conditions of Motions Equilibrium conditions (no speeding up)

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x 2 x 1 x 3 The snapshot of force standards or (Symmetrical Stress Tensor)

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x 2 x 1 x 3 " m " Average couple traction,(per unit zone) " M " couple tensor , " c " Average aggregate body couple (per unit mass) Momentum condition; Couple stretch

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Which " l " turn rakish force (per unit mass) Momentum condition; Rotational force guideline Which brings about (Non-symmetrical Stress Tensor)

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Thermodynamic framework ( shut framework for consistent matter ) Power input Conservation of vitality Heat input " q " warm flux vector " r " conveyed inward warmth source per unit mass (conceivably from a radiation field)

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First law of Thermodynamics " u " particular interior vitality and , the rate of disfigurement Finally brings about ( the nonpolar case ): Remark on inner vitality

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Power of couple push Such that First law of Thermodynamics (counting couple push) Energy condition with couple stresses

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Reversible and irreversible procedures Second law of Thermodynamics

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Entropy in traditional thermodynamics Ideal gas Second law of Thermodynamics (entropy) (Constant volume) (Entropy as a state work)

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Gibbs connection Enthalpy Second law of Thermodynamics (entropy) Then,

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" the rate of increment of the framework\'s entropy " r " dispersed inside warmth source per unit mass (perhaps from a radiation field) " entropy creation rates because of inner irreversible procedures " q " the outward warmth flux vector Or better to say: Second law of Thermodynamics (entropy creation) " v " is an arrangement of " n " factors including all the mechanical and electrical state factors for continuum thermodynamics

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Summary for instance

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