The stability of plane flow for a non-Newtonian fluid obeying a rheological power law

With respect to small perturbations, we examine the stability of a steady flow (with a gradient) of a non-Newtonian fluid obeying a rheological power law in a flat channel. We have found the neutral stability curves for various values of the exponent n in the rheological law.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 5, pp. 793–797, May, 1969.     

Electrodynamic flows of media obeying a nonlinear rheological law

Examples of the one-dimensional, steady-state electrodynamic flow of liquids characterized by power-type rheological laws and Shvedov-Bingham plastics in channels with dielectric walls in a uniform longitudinal electric field are considered.     

On a boundary layer theory for non-Newtonian fluids

Theoretical support for the existence of a boundary layer theory, similar ⁺o the classical boundary layer theory for linearly viscous fluids, is offered in the case of the non-Newtonian fluid of second grade. It is also pointed out that unless certain assumptions are made regarding the flow, assumptions which are not alluded to in earlier work in this area, in addition to the assumptions usually made in the case of the linearly viscous fluid, the theory so developed might have inherent flaws.     

On some similarity solutions to shear flows of non-Newtonian power law fluids

Summary The nonlinear rheological effects of non-Newtonian power law fluids on some shear flows are addressed. Exact similarity solutions to Stokes' first problem for unsteady flow generated by the vertical motion of a slender cylinder in an unbounded fluid are presented. The nonlinear effects on the velocity and shear stress distributions are shown and discussed. These reveal the existence of traveling wave characteristics for a shear thickening fluid, which determine a moving shear front for which the shear disturbances propagate with a finite velocity.     

Peristaltic flow of a non-Newtonian liquid with a power-type rheological law in a slot channel

The peristaltic motion of a non-Newtonian liquid with a power-type rheological law in a slot channel with elastic, deformable walls is considered. Using the asymptotic method of narrow bands, the velocity distributions in the channel are derived in terms of certain defining parameters.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 26, No. 2, pp. 245–251, February, 1974.     

Simulation of ultrasound pulse propagation in lossy media obeying a frequency power law

A method is proposed to simulate the propagation of a broadband ultrasound pulse in a lossy medium whose attenuation exhibits a power law frequency dependence. Using a bank of Gaussian filters, the broadband pulse is first decomposed into narrowband components. The effects of the attenuation and dispersion are then applied to each component based on the superposition principle. When the bandwidth of each component is narrow enough, these effects can be evaluated at the center frequency of the component, resulting in a magnitude reduction, a constant phase angle lag, and a relative time delay. The accuracy of the proposed method is tested by comparing the model-produced pulses with the experimentally measured pulses using two different phantoms. The first phantom has an attenuation function which exhibits a nearly linear frequency dependence. The second phantom has an attenuation function which exhibits a nearly quadratic frequency dependence. In deriving the dispersion from the measured attenuation, a nearly local model and a time causal model are used. For linear attenuation, the two models converge and both predict accurately the waveform of the transmitted pulse. For nonlinear attenuation, the time causal model is found more accurate than the nearly local model in predicting the waveform of the transmitted pulse     

Boundary layer at a plate with an arbitrary injection mode

A sufficiently general solution is obtained, applicable to a boundary layer with any injection mode (up to a certain limit).Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 4, pp. 720–726, October, 1972.     

Flow of a non-Newtonian power law lubricant through the conical bearing gap

Summary The hydrodynamic theory of lubrication for non-Newtonian power law lubricants has been recently developed by I. Teipel et al. [1], [2], and K. Wierzcholski [3]. They restricted, however, their investigations to the cylindrical journal bearings only. Moreover, the authors assumed the width of the bearing to be infinite in order to reduce a three-dimensional problem to the two-dimensional one. In this paper an attempt is made to study the non-isothermal flow of a power law lubricant through the gap of a conical journal bearing. At first, the more general equations in curvilinear coordinates are derived which describe the flow of a power law lubricant in the bearing gap of a quite arbitrary geometry. Afterwards, as a special case, a conical bearing gap is considered. It seems to the authors that they succeeded in omitting the necessity of using numerical procedures and obtained a relatively simple, analytical solution to the problem discussed.With 5 Figures     

New evolution equations for turbulent boundary layers in arbitrary pressure gradients

A new approach to the classical closure problem for turbulent boundary layers is presented. This involves using the well-known mean-flow scaling laws such as Prandtl’s law of the wall and the law of the wake of Coles together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially, closure is done here empirically from the data but the framework is most suitable for applying the attached eddy hypothesis in future work. How this might be done is indicated here.     

Thermal boundary layer on a plate in a non-Newtonian fluid with nonlinear heat conduction law

The flat-plate boundary layer equation for a rheological power law and a proposed nonlinear law of heat conduction is reduced to an ordinary differential equation, which is solved in quadratures using previously calculated [2] velocity profiles. Graphs of the temperature and heat transfer coefficient profiles are presented.     

J-integral evaluation for U- and V-blunt notches under Mode I loading and materials obeying a power hardening law

The paper deals with calculations of the J-integral for a plate weakened by U- and V-blunt notches under mode I loading in the case of a linear and nonlinear elastic material. The main aim of the study is to suggest simple equations suitable for rapid calculations of the J-integral. The semicircular arc of the notch, which is traction free, is assumed as integration path and the J-integral is given as a function of the strain energy over the notch edge. For a numerical investigation of the strain energy density distribution on the notch edge the equation W(θ)=W_max cos^δ(θ) has been assumed, where δ has been determined from finite element analyses. In particular, the following values of the notch acuity a/ρ and the opening angle 2α have been analyzed: 4 ≤ a/ρ ≤ 400 and 0 ≤ 2α ≤ 3π /4. Considering plates weakened by lateral and central notches under symmetric mode I loading, the approximate relationships for the strain energy density, which require the presence of a non zero notch radius for their application, and the J-integral are discussed firstly considering a linear elastic material and then a material obeying a power hardening law during the loading phase. The predicted results of the J-integral are consistent with those directly obtained from finite element analyses.     

Solution of the boundary layer equation for a power law fluid in magneto-hydrodynamics

Summary The problem of a non-Newtonian power law conducting fluid past a semi-finite plate, in the presence of an external electromagnetic field, is studied. The electric conductivity is taken as a function of the velocity. The method of expansion for a small parameter is used to obtain the solution and for a special form of the free stream velocity, the method of similarity solutions is used to obtain the exact solutions of the boundary layer equations associated with this problem in a closed form. It was found that the presence of the electromagnetic field reduces the velocity of the fluid.     

Nonsteady flow of non-Newtonian fluids through a porous medium

In this paper, the nonsteady flow of power-law fluids with a yield stress through a porous medium is investigated. In order to illustrate the rheological behaviour effects on pressure and flow rate distributions, a flow system of practical interest was analysed. The approximate solutions in a closed form were obtained by using the integral method. For a short time, these have been formulated in terms of a moving boundary problem. The flow deviation from Newtonian behaviour was emphasized by means of several dimensionless groups. These have been found to be relevant in evaluating the rheological effects on steady and nonsteady flow behaviour through a porous medium.     

Turbulent to laminar transition of a boundary layer under large negative pressure gradients

Results are shown of an experimental study concerning the development of a laminar sub-layer in a turbulent boundary layer under large negative longitudinal pressure gradients.Translated from Inzhenerno-Fizicheskii Zharnal, Vol. 24, No. 2, pp. 276–281, February, 1973.     

Spreading of a horizontal layer of non-Newtonian liquid

The flow of a layer of non-Newtonian liquid in an open volume is investigated numerically.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 48, Np, 6, pp, 950–957, June, 1985.     

Boundary-layer equations for a power-law shear-driven flow over a plane surface of non-Newtonian fluids

We study the boundary-layer similarity flow driven over a semi-infinite flat plate by a power-law shear with asymptotic velocity profile u _e (y) = βy ^α (y → ∞, β > 0), for fluids both Newtonian and non-Newtonian. Theoretical analysis is reported to derive a range of exponents α and amplitudes β for which similarity solutions exist. The shear stress parameter f′′(0) is determined as a function of α and β.