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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

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

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

V n dt v dt n dS Flux over a surface

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

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

Continuity condition Incompressible material

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:

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

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

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

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

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

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)

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

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

Reversible and irreversible procedures Second law of Thermodynamics

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

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

" 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

Summary for instance