Thermal Slip Flow of a Three-Dimensional Casson Fluid Embedded in a Porous Medium with Internal Heat Generation

Present assessment is considered to analysis flow as well as heat characteristics of steady, thermal slip flow of three-dimensional Casson fluid embedded in a porous medium with internal heat generation. Geometry of the present analysis is linearly stretched surface. Later, all the PDEs corresponding to the study are altered to set of nonlinear equations ODEs by means of appropriate similarity transformations. An efficient numerical scheme of spectral relaxation method (SRM) is applied to solve the nonlinear ordinary system. Variations of Nusselt number, temperature, velocity, and local skin friction coefficient with fluid parameters exhibited by graphs and tables. Spectral relaxation method gives an exact convergence to the nonlinear boundary value problems compare with general methods. In this study, to improve the precision and accuracy of the SRM successive over-relaxation (SOR) strategy is utilized. Proposed method as well as outcomes is checked with the comparison. A sensible connection is acquired between the current outcomes and accessible outcomes in writing. Some of the observations are skin friction coefficient raises and velocities decreases by the magnetic field strength. Skin friction and Local Nusselt number at the surface is more pronounced for non-Newtonian case than that of Newtonian case.

The second rise of general relativity in astrophysics

The field equations, which are the mathematical basis of the theory of general relativity, provide us with a much larger variety of solutions to model the neutron stars and other compact objects than are used in the current astrophysics. We point out some important consequences of the new kind of solutions of the field equations, which can be obtained if the astrophysical usage of general relativity is not constrained, and outline an impact of these solutions on the models of internal structure of compact objects. If general relativity is not constrained, it enables to construct the stable object, with the outer surface above the event horizon, of whatever large mass. A new concept of relativistic compact object is a consequence of newly discovered property of gravity, yielded by the field equations in a spherically symmetric configuration of matter: in comparison with the Newtonian case, a particle is more effectively attracted by a nearer than a more distant matter.

Non-Newtonian Film Thickness Formation in Ultra-thin Film

This paper aims to show the characteristics of ultra-thin films for non-Newtonian fluid using Ree-Eyring model where intermolecular forces of solvation and Van der Waal's are considered in addition to the hydrodynamic action to fulfill an identified need for such a conjunction. In this case, the film thickness and pressure distribution are obtained by simultaneous solution of the modified Reynolds’ equation incorporating the effect of non-Newtonian fluid, film thickness equation including elastic deformation caused by all contributing pressures and the load balance equation using Newton-Raphson method with Gauss-Seidel iterations. Effect of changing the operating conditions of speed, load, Eyring shear stress and slide-roll ratio on the characteristic of the contact has been studied. The results show that, for the case where the hydrodynamic action is the only pressure acting to support the applied load capacity, the film thickness and the pressure gradient at the exit of the contact obtained using non-Newtonian model is different than that formed using the Newtonian model especially for the increased value of slide-roll ratio. The main results of this study are that for ultra-thin film, the film thickness formed using non-Newtonian model is smaller compared to that obtained using Newtonian case and the discretization of the film thickness as the gap is reduced occurs similar to the results obtained using Newtonian model. The pressure shape shows no difference compared to that formed using the Newtonian case in which an oscillation around the Hertizan contact pressure shape due to the solvation effect appears. The results also show that for ultra-thin film, changing the Eyring shear stress does not affect the film thickness formation.

A Numerical Study of Particle Migration and Sedimentation in Viscoelastic Couette Flow

In this work, a systematic investigation of the migration of sedimenting particles in a viscoelastic Couette flow is presented, using finite element 3D simulations. To this end, a novel computational approach is presented, which allows us to simulate a periodic configuration of rigid spherical particles accurately and efficiently. To study the different contributions to the particle migration, we first investigate the migration of particles sedimenting near the inner wall, without an externally-imposed Couette flow, followed by the migration of non-sedimenting particles in an externally-imposed Couette flow. Then, both flows are combined, i.e., sedimenting particles with an externally-imposed Couette flow, which was found to increase the migration velocity significantly, yielding migration velocities that are higher than the sum of the combined flows. It was also found that the trace of the conformation tensor becomes asymmetric with respect to the particle center when the particle is initially placed close to the inner cylinder. We conclude by investigating the sedimentation velocity with an imposed orthogonal shear flow. It is found that the sedimentation velocity can be both higher or lower then the Newtonian case, depending on the rheology of the suspending fluid. Specifically, a shear-thinning viscosity is shown to play an important role, which is in-line with previously-published results.

Numerical simulation of physiologically relevant pulsatile flow of blood with shear-rate-dependent viscosity in a stenosed blood vessel

Pulsatile flow of blood in a blood vessel having time-dependent shape (diameter) is investigated numerically in order to understand some important physiological phenomena in arteries. A smooth axi-symmetric cosine shaped constriction is considered. To mimic the realistic situation as far as possible, viscosity of blood is taken to be non-uniform, a shear-thinning viscosity model is considered and a physiologically relevant pulsatile flow is introduced. Taking advantage of axi-symmetry in the proposed problem, the stream function–vorticity formulation is used to solve the governing equations for blood flow. Effect of different parameters associated with the problem on the flow pattern has been investigated and disparities from the Newtonian case are discussed in detail.

Effect of viscosity variation on non-Newtonian lubrication of squeeze film conical bearing having porous wall operating with Rabinowitsch fluid model

In this study, the effect of viscosity variation of non-Newtonian lubrication on squeeze film characteristics with porous and Rabinowitsch fluid for conical bearings is analyzed. The modified Reynolds equation representing the characteristics of non-Newtonian fluid with viscosity variation on the porous wall followed by the cubic stress law condition is invoked. For lubricant flow in a bearing clearance and in a porous layer Morgan–Cameron approximation is considered. A small perturbation technique is used to compute the pressure generation using modified Reynolds equation of lubrication. Approximate analytical solutions have been obtained for the squeeze film pressure, load-carrying capacity, squeeze film time, and center of pressure. The outcomes are displayed in diagrams and tables, which show that the effect of viscosity variation and porous wall on the squeeze film lubrication of conical bearings decreases film pressure, load-carrying capacity, and response time for the Newtonian case in comparison to the non-Newtonian case.

Onset of transition in the flow of polymer solutions through microtubes

Experiments are performed to characterize the onset of laminar–turbulent transition in the flow of high-molecular-weight polymer solutions in rigid microtubes of diameters in the range $390~\unicode[STIX]{x03BC}\text{m}{-}470~\unicode[STIX]{x03BC}\text{m}$ using the micro-PIV technique. By considering flow in tubes of such small diameters, the present study probes higher values of elasticity numbers ($E\equiv \unicode[STIX]{x1D706}\unicode[STIX]{x1D708}/R^{2}$) compared to existing studies, where $\unicode[STIX]{x1D706}$ is the longest relaxation time of the polymer solution, $R$ is the tube radius and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the polymer solution. For the Newtonian case, our experiments indicate that the natural transition (without the aid of any forcing mechanism) occurs at Reynolds number ($Re$) $2000\pm 100$. As the concentration of polymer is increased, initially there is a delay in the onset of the transition and the transition Reynolds number increases to $2500$. Further increase in concentration of the polymer results in a decrease in the Reynolds number for transition. At sufficiently high concentrations, the added polymer tends to destabilize the flow and the transition is observed to happen at $Re$ as low as $800$. It is also observed that the addition of polymers, regardless of their concentration, reduces the magnitude of the velocity fluctuations after transition. Dye-stream visualization is further used to corroborate the onset of transition in the flow of polymer solutions. The present work thus shows that addition of polymer, at sufficiently high concentrations, destabilizes the flow when compared to that of a Newtonian fluid, thereby providing additional evidence for ‘early transition’ or ‘elasto-inertial turbulence’ in the flow of polymer solutions. The data for the transition Reynolds number $Re_{t}$ from our experiments (for tubes of different diameters, and for two different polymers at varying concentrations) collapse well according to the scaling relation $Re_{t}\propto 1/\sqrt{E(1-\unicode[STIX]{x1D6FD})}$, where $\unicode[STIX]{x1D6FD}$ is the ratio of solvent viscosity to the viscosity of the polymer solution.

Visco-instability of shear viscoelastic collisional dusty plasma systems

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjee et al.’s work (Banerjee et al., New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.

Control of viscous instability by variation of injection rate in a fluid with time-dependent rheology

Using variational calculus, we investigate the time-dependent injection rate that minimises the growth of the Saffman–Taylor instability when a finite volume of fluid is injected in a finite time, $t_{f}$, into a Hele-Shaw cell. We first consider a planar interface, and show that, with a constant viscosity ratio, the constant injection rate is optimal. When the viscosity of the displacing fluid, $\unicode[STIX]{x1D707}_{1}(t)$, gradually increases over time, as may occur with a slowly gelling polymer solution, the optimal injection rate, $U^{\ast }(t)$, involves a gradual increase in the flow rate with time. This leads to a smaller initial value of flow rate than the constant injection rate, finishing with a larger value. Such optimisation can lead to a substantial suppression of the instability as compared to the constant injection case if the characteristic gelling time is comparable to $t_{f}$. In contrast, for either relatively slow or fast gelling, there is much less benefit in selecting the optimal injection rate, $U^{\ast }(t)$, as compared to the constant injection rate. In the case of a constant injection rate from a point source, $Q$, then with a constant viscosity ratio the fastest-growing perturbation on the radially spreading front involves axisymmetric modes whose wavenumber increases with time. Approximating the discrete azimuthal modes by a continuous distribution, we find the injection rate that minimises growth, $Q^{\ast }(t)$. We find that there is a critical time for injection, $t_{f}^{\dagger }$, such that if $t_{f}>t_{f}^{\dagger }$ then $Q^{\ast }(t)$ can be chosen so that the interface is always stable. This critical time emerges from the case with an injection rate given by $Q^{\ast }\sim t^{-1/3}$. As the total injection time is reduced to values $t_{f}<t_{f}^{\dagger }$, the system becomes progressively more unstable, and the optimal injection rate for an idealised continuous distribution of azimuthal modes asymptotes to a flow rate that increases linearly with time. As for the one-dimensional case, if the viscosity of the injection fluid gradually increases over time, then the optimal injection rate has a smaller initial value but gradually increases to larger values than for the analogous constant viscosity problem. If the displacing fluid features shear-thinning rheology, then the optimal injection rate involves a smaller flow rate at early times, although not as large a reduction as in the Newtonian case, and a larger flow rate at late times, although not as large an increase as in the Newtonian case.