Issues of the flat flow of pseudo-plastic fluid in a channel between parallel plates are presented in the paper. The problem was solved using the Ellis model. Based on the analytical solutions of movement equations, and with regard to the Ellis model equation, the velocity distribution in a flat channel was described.
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The convective stability of a horizontal layer of viscoelastic conducting liquid (Walters' liquid B') heated from below and rotating about a vertical axis in the presence of a magnetic field and thermal relaxation has been investigated. Linear stability theory and normal mode analysis are used to derive an eigenvalue system of eighth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers and wave numbers for the onset of instability are presented graphically as functions of Taylor number for various values of the Chandrasekhar number and the relaxation time at a Prandtl number Pr = l.
Flow of pseudo-plastic fluid through a circular channel is considered in the paper. The problem was solved using the Rotem-Shinnar model. The solution was obtained using an analytic method. As a result, a formula defining the velocity distribution in a channel was received.
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An analytical study has been performed to evaluate the flow of viscoelastic fluid through and past an infinite porous bed. A most general form of Darcy law has been taken into account when the free stream oscillates with or without a non-zero mean. In modeling the flow in the bed a separation of variable technique was utilized to represent the governing equations with appropriate boundary layer assumption. The effect of flow inertia was taken into consideration. Results obtained include velocity distributions of the fluid in the bed. The dependence of velocity profile on elasticity parameter of the fluid and permeability parameter of the medium with the variation of the time and position was also obtained and discussed graphically.
Przedstawiono równania i numeryczne rozwiązania oscylacji pęcherzyka kawitacyjnego w płynie nieniutonowskim lepkim i lepkosprężystym. Właściwości lepkie płynu opisano modelem potęgowym, a właściwoości lepkosprężyste modelem OWF (Oldroyda-Waltersa-Fridricksona). Uzyskane z obliczeń numerycznych charakterystyki oscylacji pojedynczego pęcherzyka kawitacyjnego różnią się dla cieczy niutonowskiej i nieniutonowskiej. Z przeprowadzonej analizy numerycznej wynika, że lepkość i sprężystość płynu w znaczny sposób ograniczają zjawisko kawitacji. Wskazują na to uzyskane charakterystyki zależności oscylacji prędkości i ciśnienia, wykazujące zmniejszenie amplitudy drgań pęcherzyka wraz ze wzrostem lepkości i sprężystości płynu.
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The paper presents the equations and numerical solutions of oscillation of the bubble cavitation in the non-Newtonian viscous fluid and viscoelastic fluid. The properties of viscous liquid were described by the involution model and the viscoelastic properties by the OWF (Oldroyd-Walters-Fridrickson) model. The characteristics of oscillation of a single bubble cavitation obtained from the numerical calculations are different for the Newtonian and non-Newtonian liquids. From the numerical analysis it follows that the viscosity and elasticity of fluid significantly limit the cavitation effect. The characteristics of velocity and pressure oscillation show the reduction of vibration amplitude of a bubble along with the increasing viscosity and elasticity of fluid.
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