MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon

The problem of non-Newtonian Casson thin film flow of an electrically conducting fluid on a horizontal elastic sheet was studied using suitable dimensionless transformations on equations representing the problem. The thin film flow and heat mechanism coupled with mass transfer characteristics are basically governed by the slip velocity, magnetic field, and the dissipation phenomenon. The present numerical analysis by the shooting method was carried out to study the detailed, fully developed heat and mass transfer techniques in the laminar thin film layer by solving the competent controlling equations with eight dominant parameters for the thin liquid film. Additionally, the predicted drag force via skin-friction coefficient and Nusselt and Sherwood numbers were correlated. In view of the present study, a smaller magnetic parameter or a smaller slip velocity parameter exerts very good influence on the development of the liquid film thickness for the non-Newtonian Casson model. Furthermore, a boost in the parameter of unsteadiness causes an increase in both velocity distribution and concentration distribution in thin film layer while an increase in the same parameter causes a reduction in the film thickness. Likewise, the present results are observed to be in an excellent agreement with those offered previously by other authors. Finally, some of the physical parameters in this study, which can serve as improvement factors for heat mass transfer and thermophysical characteristics, make nanofluids premium candidates for important future engineering applications.

Outer Acoustic Streaming Flow Driven by Asymmetric Acoustic Resonances

While boundary-driven acoustic streaming resulting from the interaction of sound, fluids and walls in symmetric acoustic resonances have been intensively studied in the literature, the acoustic streaming fields driven by asymmetric acoustic resonances remain largely unexplored. Here, we present a theoretical and numerical analysis of outer acoustic streaming flows generated over a fluid–solid interface above which a symmetric or asymmetric acoustic standing wave is established. The asymmetric standing wave is defined by a shift of acoustic pressure in its magnitude, i.e., S0, and the resulting outer acoustic streaming is analyzed using the limiting velocity method. We show that, in symmetric acoustic resonances (S0 = 0), on a slip-velocity boundary, the limiting velocities always drive fluids from the acoustic pressure node towards adjacent antinodes. In confined geometry where a slip-velocity condition is applied to two parallel walls, the characteristics of the obtained outer acoustic streaming replicates that of Rayleigh streaming. In an asymmetric standing wave where S0 ≠ 0, however, it is found that the resulting limiting velocity node (i.e., the dividing point of limiting velocities) on the slip-velocity boundary locates at a different position to acoustic pressure node and, more importantly, is shown to be independent of S0, enabling spatial separation of acoustic radiation force and acoustic streaming flows. The results show the richness of boundary-driven acoustic streaming pattern variations that arise in standing wave fields and have potentials in many microfluidics applications such as acoustic streaming flow control and particle manipulation.

Analytical Investigation of Roller Skew and Tilt in a Spherical Roller Bearing

The objective of this investigation was to analytically investigate the performance of a spherical roller bearing operating under various loading and speed combinations. In order to achieve the objective, a full six degree of freedom spherical roller bearing dynamic model was developed. The model was corroborated with results in open literature. An adaptive slicing method was developed to optimize the accuracy and computational effort of the roller force, skew, and tilt calculations. A comprehensive roller-race contact analysis in terms of slip velocity and contact area was then carried out to identify how bearing load and inner race speed variations change slip velocity and skew at the roller-race contact. The results from this investigation demonstrate that roller skew increases with inner race speed, while the roller tilt remains relatively constant. The inner race speed and roller slip velocity correlate well, which causes the traction force to increase and therefore produce greater skew. Skew and tilt angles also increase with applied axial load. However, at a certain load the skew angle begins to decrease.

Slow periodic oscillation without radiation damping: New evolution laws for rate and state friction

Summary The dynamics of sliding friction is mainly governed by the frictional force. Previous studies have shown that the laboratory-scale friction is well described by an empirical law stated in terms of the slip velocity and the state variable. The state variable represents the detailed physicochemical state of the sliding interface. Despite some theoretical attempts to derive this friction law, there has been no unique equation for time evolution of the state variable. Major equations known to date have their own merits and drawbacks. To shed light on this problem from a new aspect, here we investigate the feasibility of periodic motion without the help of radiation damping. Assuming a patch on which the slip velocity is perturbed from the rest of the sliding interface, we prove analytically that three major evolution laws fail to reproduce stable periodic motion without radiation damping. Furthermore, we propose two new evolution equations that can produce stable periodic motion without radiation damping. These two equations are scrutinized from the viewpoint of experimental validity and the relevance to slow earthquakes.

The Impact of Variable Fluid Properties on Biomagnetic Maxwell Fluids Past a Stretching Sheet with Slip Velocity and Heat Generation/Absorption

The impact of variable fluid properties (viscosity and thermal conductivity) and magnetic dipole on biomagnetic Maxwell fluid past a stretching sheet with slip velocity and heat generation/absorptionhave been studied. Similarity transformation technique is adopted to obtain the self-similar coupled nonlinear ordinary differential equations. Using similarity variable, the basic governing equations with boundary conditions are transformed and solved in bvp4c technique with MATLAB software. The contribution of different pertinent parameters such as viscosity, thermal conductivity and ferromagnetic parameter on the flow profiles with physical quantities are analyzed and examined through graphically. Results shown that with increasing ferromagnetic parameter, slip parameter, Maxwell parameter, velocity decreases but temperature increases. For accuracy of the proposed model to compare our numerical results in numerically and graphically with the previousliterature under some limiting cases and a good agreement is found. Dhaka Univ. J. Sci. 69(2): 109-115, 2021 (July)

Experimental and Numerical Investigation of Tire Tread Wear on Block Level

Tread wear appears as a consequence of friction, which mainly depends on surface characteristics, contact pressure, slip velocity, temperature and dissipative material properties of the tread material itself. The subsequent description introduces a wear model as a function of the frictional energy rate. A post-processing as well as an adaptive re-meshing algorithm are implemented into a finite element code in order to predict wear loss in terms of mass. The geometry of block models is generated by image processing tools using photographs of the rubber samples in the laboratory. In addition, the worn block shape after the wear test is compared to simulation results.

Effective Slip Lengths for Stokes Flow over Rough, Mixed-Slip Surfaces

<p>In this thesis, homogenization and perturbation methods are used to derive analytic expressions for effective slip lengths for Stokes flow over rough, mixed-slip surfaces, where the roughness is periodic, and the variation in slip length has the same period. If the classical no-slip boundary condition of fluid mechanics is relaxed, the slip velocity of the fluid at the surface is non-zero. For simple shear flow, the slip velocity is proportional to the shear rate. The constant of proportionality has dimensions of length and is known as the slip length. Any variation in the slip length over the surface will cause a perturbation to the flow adjacent to the surface. Due to the diffusion of momentum, at sufficient height above the surface, the flow perturbations have diminished, and flow is smooth and uniform. The velocity and shear rate at this height imply an effective slip length of the surface. The purpose of this thesis is to predict that effective slip length. Homogenization is a technique for finding approximate solutions to partial differential equations. The essence of homogenization is to construct a mathematical model of a physical problem featuring some periodic heterogeneity, then generate a sequence of models such that the period in question reduces with each increment in the sequence. If the sequence is appropriately defined, it has a limit model in the limit of vanishing period, for which a solution can be found. The solution to the limit system is an approximation to the solutions of systems with a finite period. We use homogenization to find the effective slip length of a system of Stokes flow over a periodically rough surface, described by periodic function h(x; y), with a local slip length b(x; y) varying with the same period. For systems where the period L is smaller than both the domain height P and typical slip lengths, the effective slip length bₑff is well-approximated by the harmonic mean of local slip lengths, weighted by area of contact between liquid and surface: [See 'Thesis' document below for equation.] We further use a perturbation technique to verify the above expression in the special case of a flat surface, and to derive another effective slip length expression: For a flat surface with local slip lengths much smaller than the period and domain height, the effective slip length bₑff is well-approximated by the area-weighted average of local slip lengths: [See 'Thesis' document below for equation.]</p>