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Experimental work to investigate plane Couette flow has been performed in the Reynolds number range of $750\,{\leq}\,\hbox{\it Re}\,(\,{=}\,hU_b/(2\nu))\,{\leq}\, 5000$ or $50\,{\leq}\, \hbox{\it Re}_*\,(\,{=}\,hu_*/\nu)\,{\leq}\, 253$, where $U_b$, $u_*$ and $h$ are moving wall speed, friction velocity and channel half-height, respectively. The low-Reynolds-number effect on the wall friction coefficient $C_f$, mean velocity profile and statistical turbulence quantities is discussed in relation to the turbulent Poiseuille flow properties. Since the shear stress is constant in Couette flow, the flow is free from the effect of shear stress gradient and the Reynolds number effect therefore can be seen explicitly, uncontaminated by this effect. A flow region diagram is given to show how the low-Reynolds-number effect penetrates into the wall region. The area of the buffer region is contracted by the low-Reynolds-number effect when $\hbox{\it Re}_*\leq 150$, so that the additive constant $B$ of the log law decrease as $\hbox{\it Re}_*$ decreases. Also, $C_f$ has a larger value than in Poiseuille flow in the low $\hbox{\it Re}_*$ range. The log-law area in Couette flow is 2–3 times as wide as that in Poiseuille flow. The defect law is $\hbox{\it Re}_*$-dependent and the non-dimensional velocity gradient at the core, $Rs=({\rm d}U_1/{\rm d}x_2)(h/u_*)$, increases from 3 to 4.2 as $\hbox{\it Re}_*$ increases from 50 to 253. The peak value of streamwise turbulence intensity $u_{1p}^+$ has a constant value of 2.88 but decreases sharply as $\hbox{\it Re}_*$ reduces below 150.The large longitudinal vortices extending the entire height of the channel are shown to be sustained in Couette flow that is oscillating around their average position. This causes a slow fluctuation with large amplitude in the streamwise velocity component. These vortices make the Couette flow three-dimensional and the skin friction coefficient varies 20% sinuously in the spanwise direction, for example. Also, the zero-crossing time separation of streamwise velocity auto-correlation $R_{11}(\tau)$ becomes longer as $\tau=40h/U_b$, which is 3 times as long as that in Poiseuille flow.

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The subloops in the shape memory alloys, the stress-strain-temperature hysteresis loops due to the incomplete transformation, are analyzed from the phenomenological point of view. The transformation kinetics formulated by the same authors is generalized by introducing the transformation start conditions, both martensitic and reverse, which are assumed to be dependent on the extent of prior transformation and be determined from the isothermal or isostatic experiment. The theory developed is successfully applied to the simulations on the subloop behavior in the alloys under the various mechanical and/or thermal loads.

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A simple mathematical model for discharge characteristics in lithium ion batteries is developed based on a novel multiphase fluids model. The species of lithium, lithium ion, anion, and the electron are considered in the present model for transport phenomena. Maxwell's equations for an electric field and the Butler–Volmer equation for electrochemical reaction are also included. The numerical code based on the finite differential technique and the implicit successive overrelaxation (SOR) scheme is developed here and numerical solutions of discharge phenomena are obtained successfully for a wide range of operating conditions. Furthermore, comparisons of discharge characteristics between experimental and numerical results are performed in detail. They are in good agreement from the viewpoint of engineering applications. Consequently, it is concluded that numerical scheme proposed here is sufficiently practical for computer-aided design of lithium ion rechargeable batteries.

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