Qualitative analysis of magnetohydrodynamics stagnation point flow with a novel numerical approach through Shifted Chebyshev collocation method

This paper investigates the third-order nonlinear boundary value problem, resulting from the exact reduction of the Navier-Stokes equation caused by the magnetohydrodynamics boundary layer flow near a stagnation point on a rough plate. The governing partial differential equations are transformed into a nonlinear ordinary differential equation and partial slip boundary conditions by an appropriate similarity transformation. In this previous work, the boundary value problem (BVP) was investigated numerically, and a lot of speculations regarding the existence and behavior of the solutions were carried out. The primary objective of this article is to verify these speculations mathematically. In this work, we have proved that there is a unique solution for all parameters values, and further, the solution has monotonic increasing first derivative. Moreover, the resulting nonlinear boundary value problem is solved by shifted Chebyshev collocation method. We compare the present numerical results with the previous results for the particular physical parameters, concluding that the results are highly accurate. The velocity profiles and streamlines are also plotted to address the significance of the parameters. Our manuscript is a judicial mix between mathematical and numerical methods.

Partial velocity slip effect on working magneto non-Newtonian nanofluids flow in solar collectors subject to change viscosity and thermal conductivity with temperature

Solar thermal collectors distribute, capture, and transform the solar energy into a solar thermal concentration device. The present paper provides a mathematical model for analyzing the flow characteristics and transport of heat to solar collectors (SCs) from non-Newtonian nanofluids. The non-Newtonian power-law scheme is considered for the nanofluid through partial slip constraints at the boundary of a porous flat surface. The nanofluid is assumed to differ in viscosity and thermal conductivity linearly with temperature changes and the magnetic field is appliqued to the stream in the transverse direction. The method of similarity conversion is used to convert the governing structure of partial differential formulas into the system of ordinary differential ones. Using the Keller box procedure, the outcoming ordinary differential formulas along with partial slip constraints are numerically resolved. A discussion on the flowing and heat transport characteristics of nanofluid influenced by power law index, Joule heating parameter, MHD parameter and slip parameters are included from a physical point of view. Comparison of temperature profiles showed a marked temperature increase in the boundary layer due to Joule heating. The thickness of the motion boundary-layer is minimized and the transport of heat through boundary-layer is improved with the partial slip velocity and magnetic parameters rising. Finally, With an increase in the Eckert number, the distribution of temperature within boundary layer is increased.

Partial Slip Impact on Double Diffusive Convection Flow of Magneto-Carreau Nanofluid through Inclined Peristaltic Asymmetric Channel

The significance of partial slip on double diffusive convection on magneto-Carreau nanofluid through inclined peristaltic asymmetric channel is examined in this paper. The two-dimensional and directional flow of a magneto-Carreau nanofluid is mathematically described in detail. Under the lubrication technique, the proposed model is simplified. The solutions of extremely nonlinear partial differential equations are calculated using a numerical technique. Graphical data are displayed using Mathematica software and Matlab to examine how temperature, pressure rise, concentration, pressure gradient, velocity profile, nanoparticle volume fraction, and stream functions behave on emerging parameters. It is noticed that as the velocity slip parameter is increased, the axial velocity at the channel’s center increases. Additionally, near the boundary, opposite behavior is observed. The temperature, concentration, and nanoparticle profile drops by increasing thermal slip, concentration slip, and nanoparticle slip parameter.

The Role of the Double-Layer Potential in Regularised Stokeslet Models of Self-Propulsion

The method of regularised stokeslets is widely used to model microscale biological propulsion. The method is usually implemented with only the single-layer potential, the double-layer potential being neglected, despite this formulation often not being justified a priori due to nonrigid surface deformation. We describe a meshless approach enabling the inclusion of the double layer which is applied to several Stokes flow problems in which neglect of the double layer is not strictly valid: the drag on a spherical droplet with partial-slip boundary condition, swimming velocity and rate of working of a force-free spherical squirmer, and trajectory, swimmer-generated flow and rate of working of undulatory swimmers of varying slenderness. The resistance problem is solved accurately with modest discretisation on a notebook computer with the inclusion of the double layer ranging from no-slip to free-slip limits; the neglect of the double-layer potential results in up to 24% error, confirming the importance of the double layer in applications such as nanofluidics, in which partial slip may occur. The squirming swimmer problem is also solved for both velocity and rate of working to within a small percent error when the double-layer potential is included, but the error in the rate of working is above 250% when the double layer is neglected. The undulating swimmer problem by contrast produces a very similar value of the velocity and rate of working for both slender and nonslender swimmers, whether or not the double layer is included, which may be due to the deformation’s ‘locally rigid body’ nature, providing empirical evidence that its neglect may be reasonable in many problems of interest. The inclusion of the double layer enables us to confirm robustly that slenderness provides major advantages in efficient motility despite minimal qualitative changes to the flow field and force distribution.

The Effect of Displacement Amplitude on Fretting Wear Behavior and Damage Mechanism of Alloy 690 in Different Gaseous Atmospheres

The effect of displacement amplitude on fretting wear behavior and damage mechanisms of alloy 690 in air and nitrogen atmospheres was investigated in detail. The results showed that in air, the friction coefficient gradually increased with the increase in displacement amplitude which conformed to the universal law. In nitrogen, however, it had the highest point at the displacement amplitude of 60 μm due to very strong adhesion. Whether in air or nitrogen, the wear volume gradually increased with the increase in displacement amplitude. The wear volume in air was larger than that in nitrogen except at 30 μm. At 30 μm, the wear volume in air was slightly smaller. With an increase in displacement amplitude, a transformation of fretting running status between partial slip, mixed stick-slip, and final gross slip occurred along with the change of Ft-D curves from linear, to elliptic, to, finally, parallelogrammical. Correspondingly, the fretting regime changed from a partial slip regime to a mixed regime to a gross slip regime. With the increase in displacement amplitude, the transition from partial slip to gross slip in nitrogen was delayed as compared with in air due to the strong adhesion actuated by low oxygen content in a reducing environment. Whether in air or nitrogen, the competitive relation between fretting-induced fatigue and fretting-induced wear was prominent. The cracking velocity was more rapid than the wear. Fretting-induced fatigue dominated at 30 μm in air but at 30–60 μm in nitrogen. Fretting-induced wear won the competition at 45–90 μm in air but at 75–90 μm in nitrogen.

Two-dimensional numerical studies of particle motion and deposition in the channel of diesel particulate filters

A numerical investigation on the soot laden flow of gas in a partial diesel particulate filter (PDPF) is presented based on solving the momentum equations for a continuous phase in the Euler frame and the motion equations for the dispersed phase in the Lagrangian frame. The interaction between the gas phase and the particles is considered as a one-way coupling for dilute particle concentration, while the interaction between particles and porous wall is implemented through user-definedsubroutines. To accurately track motion of nanoscale particles, the Brownian excitation and drag force as well as partial slip are taken into account in the particulate motion equation. Two methods are used to verify the gas flow model and reasonable agreements for both comparisons are observed. The effects of inlet velocity, wall permeability and particle size on the filtration efficiency and deposition distribution of the particles along with wall surface of inlet channel are quantitatively studied. The results show that (i) wall permeability plays the primary role in determining the filtration efficiency of PDPF, (ii) both upstream velocity and particle size have an effect on the initial deposition position of particles and (iii) filtration efficiency of PDPF is not markedly proportional to gas flow into inlet channels at a low wall permeability.