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Unformatted text preview: 16.21 Techniques of Structural Analysis and Design Spring 2005 Unit #4 - Thermodynamics Principles Raul Radovitzky February 22, 2005 First Law of Thermodynamics d K + U = P + H (1) dt where: K : kinetic energy U : internal energy P : Power of external forces H : hear exchange per unit time 1 u u 1 u i u i K = dV = dV (2) 2 V t t 2 V t t U = U dV = U dV (3) V V 1 where U , U 0 are the internal energy densities per unit mass and per unit volume, respectively. u u P = f dV + t dS (4) t S t V In components: u i u i P = f i dV + t i dS (5) t S t V Replacing t i = n j ji in this expression: u i u i P = f i dV + n j ji dS (6) t S t V Using Gauss Theorem: u i u i P = f i dV + ji dV V t V x j t ji u i u i = + f i + ji dV x j t x j t V 2 u i u i (why?) (7) t 2 t x j 2 u i u i u i = + ji dV t x...
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This note was uploaded on 11/07/2011 for the course AERO 16.21 taught by Professor Dffs during the Fall '10 term at MIT.
- Fall '10