抄録
In order to discuss small cycles for different r collectively, the energy conversion and the energy flux are studied in a Lagrange system having an average velocity ‹u›r. In the beginning discussed are quasistatic small cycles for which variations of entropy are homogeneous in the flow channel, and later discussed are general small cycles for which variations of entropy aye inhomogeneous in the flow channel. Introducing a distribution function of velocity 1-fν and a distribution function of entropy fα and using their average over the cross-sectional area χν≡‹fν›r and χα≡‹fα›r, the work source W is, neglecting terms more than 4th order of p and (∇Tm)‹ξ›r; W=Wprog+Wstand+WP+Wν; Wprog≡β(∇Tm)FSχα′‹p⋅‹u›r›t; Wstand≡-β(∇Tm)FSχα″ω‹p⋅‹ξ›r›t; WP≡(KT-KS)FSχα″×ω‹p⋅p›t; Wν≡«u⋅∇p»; where FS is a measure of entropy exchange between solid wall and oscillating fluid. The work flux is I=‹p⋅‹u›r›t and the heat flux is, neglecting terms more than 3rd order of p and (∇Tm)‹ξ›r; Q=Qprog+Qstand+QD; Qprog≡-βTmFSg′‹p⋅‹u›r›t; Qstand≡-βTmFSg″ω‹p⋅‹ξ›r›t; QD≡ρmCP∇TmFSg″ω‹‹ξ›r⋅‹ξ›r›t; where g≡‹fα(1-fν+)/(1-χν+)›r=g′+ig″ and superscript+indicates complex conjugate of quantity without the superscript.
