Understanding Non-Equilibrium Thermodynamics - Springer 2008 Episode 7 ppt

... β  =0means absence of coupling in (7. 47) – (7. 49) and similarly in (7. 43) of J s ,which boils down to the classical result J s = q/T . To identify the coefficients appearing in (7. 47) – (7. 49) in physical terms, consider ... Equations (7. 47) – (7. 49) then reduce to ∇T −1 − T −1 α 1 ˙ q =(λT 2 ) −1 q, (7. 50) −T −1 ∇·v −T −1 α 0 ˙p v =(ζT) −1 p v , (7. 51) −T −1 0 V − T −1 α 2 ( 0 P v )...

Ngày tải lên: 12/08/2014, 08:22

... of non-equilibrium thermodynamics have been the subject of several books (Katchalsky and Curran 1965; Nicolis and Prigogine 1 977 ; Hill 1 977 ; Caplan and Essig 1983; Westerhoff and van Dam 19 87; ... a gradient of concen- tration as evidenced by (3.48) is the Dufour’s effect. It should be observed that the cross-coefficients D T and D F are much smaller than the direct co- efficients like the...

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... eliminating J s between (8 .71 ) and (8 .73 ); making use of (8 .72 ) and introducing a pseudo- enthalpy function ˜ h = T ˜s + µ, it is found that q = −λ∇T + ˜ hJ + η(u −v) ·∇u. (8 .77 ) For pure heat conduction, ... is of prime importance in non-equilibrium thermodynamics. In addition, it was proved that the entropy used in rational thermodynamics is not unique. Meixner (1 973 a, 1 973...

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... and tools from equilibrium thermodynamics but transposed at a local scale because non-equilibrium states are usually in- homogeneous. The objective is to cope with non-equilibrium situations where basic ... coupling be- tween thermal, mechanical, chemical, and electromagnetic effects, as the Soret (1 879 ) and Dufour (1 872 ) effects, coupling heat, and mass transport, and the 37 2.4 Ge...

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... of variational principles in non-equilibrium thermodynamics. 2.5.1 Minimum Entropy Production Principle Consider a non-equilibrium process, for instance heat conduction or thermod- iffusion taking place ... (2 .71 )–(2 .73 ) in (2 .70 ) of the entropy production, one obtains σ s = λ T 2 (∇T ) 2 + ζ T (∇·v) 2 + 2η T ( 0 V : 0 V ) ≥ 0. (2 .74 ) Positiveness of σ s requires that λ>0,ζ>...

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... 19 87; Parmentier et al. 1993; Madruga et al. 2003), convection in porous media, which is of interest in the mineral oil industry, thermal con- vection in rotating systems (Busse 1 978 ; Davis 19 87) , ... illustrations, we will dis- cuss in the next sections the Lotka–Volterra and the Brusselator models (Prigogine and Lefever 1968; Nicolis and Prigogine 1 977 ). To maintain non- equilibrium...

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... connection be- tween dynamics and thermodynamics should be underlined. EIT enlarges the range of applicability of non-equilibrium thermodynamics to a vast do- main of phenomena where memory, non-local, ... the 215 7. 2 One-Component Viscous Heat Conducting Fluids 199 By setting α 1 = τ 1 (λT ) −1 ,α 0 = τ 0 ζ −1 ,α 2 = τ 2 (2η) −1 , (7. 53) µ 1 =(λT 2 ) −1 ,µ 0 =(ζT) −1 ,µ 2 =(2ηT) −1...

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... 149, 176 Newton–Stokes’ law, 37, 199 non-equilibrium entropy, 180, 2 07, 2 57, 279 , 289, 304 non-equilibrium temperature, 189, 190, 1 97, 250, 255, 2 57, 277 , 291, 295, 301 Non-Fickian diffusion, 273 , ... coefficient, 85 membranes, 54, 69, 70 , 83, 85– 87, 89, 102, 292, 2 97 memory, 179 , 181, 206, 2 07, 219, 2 37, 240, 241, 2 47, 251, 2 57, 286, 2 87, 300, 304 mesoscopic, 275 , 27...

Ngày tải lên: 12/08/2014, 08:22

Ngày tải lên: 12/08/2014, 08:22