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We have generalized, in the current study, the results of research presented earlier with the aim of obtaining an approximate solution for the creeping, plane-parallel flow of viscoplastic non-Newtonian fluid where the focus is on the study of rivulet fluid flows on an inclined surface. Namely, profiles of velocity of flow have been considered to be given in the same form as previously (i.e., Gaussian-like, non-stationary solutions) but with a novel type of pressure field p. The latter has been chosen for solutions correlated explicitly with the critical maximal non-zero level of stress τs in the shared plane layer of rivulet flow, when it begins to move as viscous flow (therefore, we have considered here the purely non-Newtonian case of viscoplastic flow). Correlating phenomena such as the above stem from the equations of motion of viscoplastic non-Newtonian fluid considered along with the continuity equation. We have obtained a governing sub-system of two partial differential equations of the first order for two functions, p and τs. As a result, a set of new semi-analytical solutions are presented and graphically plotted. [ABSTRACT FROM AUTHOR]

The effect of elasticity on the peristaltic flow of a micropolar fluid containing nanoparticles in a cylindrical tube is investigated using a mathematical model. The expressions for velocity and flux flow rate are determined by using Homotopy Perturbation method, under long wave length and low Reynold's number approximations. The variation of flux is calculated by Rubinow and Keller, Muzumdar methods. Different parameters' effects on velocity and flow have been discussed. For various settings, the trapping phenomenon is demonstrated. The flux increases as the elasticity parameters, micropolar parameter, thermophoresis parameter, and coupling number increase. The flux similarly reduces as the Brownian motion parameter is increased. The obtained results are same when we apply Rubinow and Keller, Muzumdar methods. [ABSTRACT FROM AUTHOR]

The processes of hydrodynamics and heat transfer during the flow of a non-Newtonian polymeric medium in a plane channel have been investigated with boundary conditions of the first kind. Consideration was given to a steady-state nonisothermal process with low values of the Reynolds number and high values of the Péclet number, which made it possible to neglect gravity and inertial forces, and also longitudinal thermal conductivity. The Ellis model with a viscosity dependent on temperature, pressure, and the degree of chemical transformation was used as the rheological model. A high-viscosity medium was investigated. Therefore, it is the dissipative term that was taken account of in the energy equation. With the above rheological model, an expression in explicit form was obtained from the equation of motion of such a medium for the velocity profile of its flow. It has been established that the dependence of the viscosity of a medium on its temperature, pressure, and the degree of transformation has an appreciable effect on the distribution of the temperature of the medium and the velocity of its flow along the channel's length. Taking account of the temperature dependence of the viscosity of the medium leads to a decline in the role of dissipation in the process of its warmup. The dependence of the medium's viscosity on pressure, conversely, considerably enhances the dissipative effect, which appreciably accelerates the course of a chemical reaction. [ABSTRACT FROM AUTHOR]

• The methane hydrate formation under the non-Newtonian fluid flowing condition is investigated experimentally. • A mass transfer hydrate formation model is developed with an empirical integrated hydrate formation coefficient. • The XG concentration and the fluid velocity are found as the key controlling factors for methane hydrate formation. Developing natural gas hydrates in deep water faces serious well control problem and flow assurance problem, induced by the reformation of gas hydrate in the drilling fluid. In order to solve this problem, developing a hydrate formation predicting model becomes necessary. In this work, the methane hydrate formation experiments are performed in the xanthan gum (XG) aqueous solution under flow velocities from 1.8 to 1.5 m/s, XG concentrations from 0.1 to 0.3% and void fraction of 4.5%. The hydrate formation rates decrease with the XG concentration increasing and increases with the flow velocity increasing. The hydrate formation rate at the moment of the experiment onset will decrease sharply due to the formation of hydrate shell on gas bubbles and gas hydrates will form at the almost constant rate, because the second growth of hydrate shells on the fractures of gas bubbles and collisions between gas bubbles enhances the hydrate formation rates. The hydrate formation rate increases rapidly when the hydrate formation process is near the end of hydrate formation since the breakage rates of gas bubbles increase the hydrate formation rates. A mass transfer model is developed to describe the methane hydrate formation under the non-Newtonian fluid flowing condition. Since the volumetric mass transfer coefficient closely depends on the rheological properties of carrying fluid, the rheological experiments for the XG aqueous solution are conducted and an empirical rheology model is developed correspondingly. An integrated constant is proposed to improve the accuracy of the model which reflects influences of the hydrate shell formation, the second growth of hydrate shell and the bubble breakage on methane hydrate formation. The correlations of the integrated constant are functions of the XG concentration, the flow velocity and the subcooling temperature. Through validation, the proposed mass transfer model shows good agreements with experimental data and the maximum discrepancy is 11.64%. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for modelling velocity profiles and suspended objects in non-Newtonian fluid environment. A setup is proposed to allow mimicking blood properties and arterial to venous dynamic flow changes. Navier-Stokes relations are employed followed by fractional constitutive equations for velocity profiles and flow. The theoretical analysis is performed under assumptions of steady and pulsatile flow conditions, with incompressible properties. The fractional derivative model for velocity and friction drag effect upon a suspended object are determined. Experimental data from such an object is then recorded in real-time and identification of a fractional order model performed. The model is determined from step input changes during pulsatile flow for velocity in the direction of the flow. Further on, this model can be employed for controller design purposes for velocity and position in pulsatile non-Newtonian fluid flow. [ABSTRACT FROM AUTHOR]

• MHD non-Newtonian fluid flow with CNTs and heat transfer across a linearly shrinking sheet. • An exact solutions are extracted for the governing equations of the aforesaid flow. • Two types of non-Newtonian fluids like second grade fluid and Walters' liquid B. • The existence of unique and dual solutions domains are traced by physical parameters. • Dual solutions exist for second grade fluid for both slip and no-slip restrictions. The present paper focuses on electrically driven magnetohydrodynamic non-Newtonian fluid flow (viscoelastic fluid)with CNTs and heat transmission across a linearly shrinking sheet. The flow is urged with the partial slip conditions, radiation and heat source/sink. Single walled and multi walled CNTs are considered in this analysis. An exact solution is extracted for the governing equations of the aforesaid flow of two types of non-Newtonian fluids like second grade fluid and Walters' liquid B with CNTs using similarity transformations. The flow velocity is pretentious due to many physical parameters like magnetic force, visco-elasticity, slip parameter, whereas the energy profile is pretentious due to Prandtl number, Biot number, heat sink/source parameter and radiation parameter. The existence of unique and dual solutions domains are traced by combining the above parameters and velocity, energy profiles and skin friction are explained using graphs. The results reveal that the dual solutions exist for both types of viscoelastic fluids under specific flow restrictions. In particular, dual solutions exist for second grade fluid for both slip and no-slip restrictions. And similar observations are found for Walters' liquid B fluid for unique slip flow when viscoelastic parameter value increases above a definite value. Inclusion of magnetic field terminates the ambiguity of existence of solution for different λ 1 values for both viscoelastic fluids. [ABSTRACT FROM AUTHOR]

The theory of rheology of non-Newtonian fluids is based on the generalized Newtonian hypothesis of viscosity. The viscometers for non-Newtonian fluids should implement fluid flows with the known stress and strain state parameters distributions. Ideally, the distributions should be homogeneous in the flow domain. The idea of the proposed method is based on a combination of a capillary and a rotational viscometers implemented in the torus-shaped capillary viscometer. Analysis of the mathematical model of the inertial non-Newtonian fluid flow in the torus allowed to determine the conditions of homogeneity of the mechanical and thermal parameters in the flow domain and to develop method of viscosity measurement. The measured values are the shear rate on the inner surface of the capillary and the flow rate. The measurements are implemented with the computer vision system that processes data obtained from the high speed CMOS camera that records inertial flow in the transparent capillary illuminated with laser. The computer vision system is based on the application of deep convolutional neural network for laser speckle contrast imaging processing. During the experiments, the proposed viscometer was compared with the Brookfield rotational viscometer. The relative error of the proposed viscometer and method is less than 2 %. The inertial viscometer is compact, it allows to study the wide range of shear rates per one test in automatic mode, and it has low fluid capacity of approximately 1.87 ml. That makes it possible to use the viscometer as a point on care testing device in medicine to study the rheology of physiological fluids, in particular blood. [Display omitted] • Inertial flow in a torus-shape capillary is perfectly symmetrical and homogeneous. • Laser speckle-contrast imaging allows one to see flow velocity on an image. • Artificial intelligence allows computer vision to see shear rate of the fluid flow. • Inertial viscometer could be a novel point on care testing device in medicine. [ABSTRACT FROM AUTHOR]

We study the pressure driven transport of a multilayer system consisting of alternate Newtonian and non-Newtonian fluids in the narrow fluidic configuration. We consider the power law model to describe the rheology of the non-Newtonian fluid in this study. The first part of the analysis, employing the assumptions routinely conferred in the literature, constitutes for an analytical solution of the transport equation resulting in the closed-form expressions of velocity field and net throughput. We demonstrate that the rheology driven modification in the flow velocity for a given strength of the applied forcing leads to the prolific amplification in micro-pumping phenomena. In the second part, the use of artificial neural network (ANN) is implemented to present an alternative solution for the problem undertaken in this study by using the analytical results from the first part. To make the prediction using ANN, various influential transport parameters are considered and their effects on the velocity and net throughput are analyzed. It is elucidated that an appropriately trained neural network can act as a good alternative for time-consuming calculations on the multi-layered fluid flow in micro channels. The flow configuration considered in this analysis alongside the findings of our work may provide a pathway of developing novel analytical platforms for precise loading and handling of chemical samples of biological fluids in a portable fluidic environment. [Display omitted] • Transport of Multilayer system comprising of alternate Newtonian and non-Newtonian fluids. • Closed-form expressions of velocity field and net throughput. • The use of artificial neural network (ANN) implemented to present an alternative solution. • Trained neural network as a good alternative on the multi-layered fluid flow analysis. [ABSTRACT FROM AUTHOR]

The flows of non-Newtonian fluid over upper horizontal surfaces of rockets, over bonnets of cars, and pointed surfaces of aircraft are of great importance to the experts in the field of space sciences, automobile construction, and aerodynamic industry where efficiency is dependent on the thickness of paraboloid of revolution, buoyancy, and autocatalysis. The purpose of this study is to present not only the nonlinear governing equation which models the transport phenomenon, but also to analyze the non-Newtonian Erying–Powell fluid flow within a thin layer formed on an object which is neither a perfect horizontal nor a vertical, and neither an inclined surface nor a cone/wedge. The governing equation suitable to model the transport phenomenon above for the case of equal diffusivity during quartic autocatalytic kind of chemical reaction was non-dimensionalized and solved numerically. The velocity of the flow along x − direction can be enhanced when thickness increases negligible but buoyancy forces increase significantly. The rate of increase in the velocity of the flow along the y − direction from the wall to the free stream is optimal when the thickness of the paraboloid of revolution is zero (objects with a uniform thickness) and buoyancy force is sufficiently large. The concentration of Erying–Powell fluid at the wall G (0) is a decreasing function of Prandtl number but an increasing property of Schmidt number. [ABSTRACT FROM AUTHOR]