Discusssed are dissipation of kinetic energy due to viscosity and radial distributions of velocity and entropy. The viscous dissipation
Wν and the function
fν related to the radial distribution of velocity are discussed using a linearized form of the Euler equation with a long-wave approximation The radial distribution of entropy
fα is discussed using linearized form of the general equation of heat transport with a long-wave approximation. These distribution functions depend on geometry of the flow channel. Analytic solutions are obtained for a parallel plane case and a circular cylinder case. Corresponding to the thermal diffusivity α and the kinematic viscosity ν, two characteristic times τ
α≡
r02/2α and τ
ν≡
r02/2ν are introduced, ωτ
α=0 corresponds to the quasistatic limit, and for finite ωτ
α the distribution of entropy is inhomogeneous because of the irreversible process due to thermal diffusion. For large ωτ
ν the distribution of velocity is homogeneous except for near the solid wall, and for small ωτ
ν the distribution of velocity is parabolic, similarly to the case of stationary flow. After discussions on χ
ν≡‹
fν›
r and χ
α≡‹
fα›
r, the function
g≡‹
fα(1-
fν+)/(1-χ
ν+)›
r is discussed. Main results are followings: using
Yλ≡(1+
i)(ωτ
λ)
1/2(λ=α and ν),
fλ=cosh(
Yλr/
r0)/cosh(
Yλ) and χ
λ≡‹
fλ›
r=tanh(
Yλ)/
Yλ for a parallel plane case having separation of 2
r0, and
fλ={
J0(
iYλr/
r0)}/{
J0(
iYλ)} and χ
λ≡‹
fλ›
r={2
J1(
iYλ)}/{
iYνJ0(
iYλ)} for a circular cylinder case having diameter of 2
r0. For both cases
g=(χ
α-χ
ν+)/{(1+σ)(1-χ
ν+)} where σ≡ν/α is the Prandtl number.
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