Laminar MHD natural convection of nanofluid containing gyrotactic microorganisms over vertical wavy surface saturated non-Darcian porous media

Magnetohydrodynamic （MHD） bioconvection of an incompressible electrically conducting nanofluid near a vertical wavy surface saturated porous medium containing both nanoparticle and gyrotactic microorganisms is investigated. The nanofluid is represented by a model that includes both Brownian motion and thermophoresis effects. A suitable set of non-dimensional variables are used to transform the governing boundary layer equations into a dimensionless form. The resulting nonlinear system is mapped to the vertical flat plate domain, and a non-similar solution is used to the obtained equations. The obtained non-similar system is then solved numerically using the fourth-order Runge-Kutta method. The influence of various physical parameters on the local Nusselt number, the local Sherwood number, the local density number of the motile microorganisms, the dimensionless velocity, the dimensionless temperature, and the rescaled density of motile microorganisms is studied. It is found that the local Nusselt number, the local Sherwood number, and the local density number of the motile microorganisms decrease by increasing either the Grashof number or the magnetic field parameter.

Natural Convection of MHD over a Vertical Wavy Surface in Presence of Porous Media

This paper shows the natural convective heat transfer in porous media over the vertical wavy surface and it assumes that the fluid is viscous and in-compressible. This model shows the effects of the inverse of Darcy number. The dimensional partial differential equations are converted into a dimensionless form. The non-linear system of equations is obtained and these equations are solved numerically by the finite difference method. The results are obtained for inverse Darcy number, magnetic parameter, Prandtl number, amplitude of surface, parameter of heat generation and parameter of thermal conductivity, and their effects on the velocity, temperature of the fluid and Nusselt number.

Reflection and Refraction of Gaussian Beam on Wavy Surface in Airborne Ocean Lidar

According to the statistical description of direction distribution on wavy surface by Cox, we have set up a physical model of reflection and refraction of Gaussian beam on wavy surface, derived that a beam reflected and refracted by wavy surface is also a Gaussian beam when the incident beam is a Gaussian beam, and set up the relationship between Gaussian beam's light spot size and wind speed over sea surface.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Effect of thermal radiation on mixed convection of a nanofluid from an inclined wavy surface embedded in a non-Darcy porous medium with wall heat flux

This article focuses on the effect of radiation on mixed convection in a nanofluid along an inclined wavy surface embedded in a non-Darcy porous medium.A coordinate transformation is employed to transform the complex wavy surface to a smooth surface.The governing equations are transformed into a set of partial differential equations using the nonsimilarity transformation and then a local similarity and non-similarity method is applied to obtain coupled ordinary differential equations.These resulting equations are linearized using the successive linearization method and then solved by the Chebyshev spectral method.The effects of radiation,non-Darcy parameter,Brownian motion parameter,thermophoresis parameter,the amplitude of the wavy surface,angle of inclination of the wavy surface on the non-dimensional heat and nanoparticle mass transfer rates are studied and presented graphically.

Modeling of Mixed Convection in a Lid Driven Wavy Enclosure with Two Square Blocks Placed at Different Positions

The purpose of this paper is to investigate the simulation of mixed convection in a lid-driven wavy enclosure with blocks positioned at various positions. This study also examined the impact of the longitudinal position of the heated block on heat transfer enhancement. The Galerkin weighted residual finite element method is employed to computationally solve the governing equations of Navier-Stokes, thermal energy, and mass conservation. The enclosure consists of two square heated blocks strategically placed at different heights—firstly, one set is closer to the bottom surface;secondly, one set is nearer to the middle area and finally, one set is closer to the upper undulating surface of the enclosure. The wavy top wall’s thermal insulation, along with active heating of the bottom wall and blocks, generates a dynamic convective atmosphere. In addition, the left wall ascends as the right wall falls, causing the flow formed by the lid. The study investigates the impact of the Richardson number on many factors, such as streamlines, isotherms, dimensionless temperature, velocity profiles, and average Nusselt numbers. These impacts are depicted through graphical illustrations. In all instances, two counter-rotating eddies were generated within the cage. Higher rotating speed consistently leads to improved performance, irrespective of other characteristics. Furthermore, an ideal amalgamation of the regulating factors would lead to increased heat transmission.

Investigation of Surface Micro Waviness in Single Point Diamond Fly Cutting

Single point diamond fly cutting is widely used in the manufacture of large-aperture ultra-precision optical elements. However,some micro waviness( amplitude about 30 nm,wavelength about 15 mm) along the cutting direction which will decrease the quality of the optical elements can always be found in the processed surface,and the axial vibration of the spindle caused by the cut-in process is speculated as the immediate cause of this waviness. In this paper,the analytical method of dynamic mesh is applied for simulating the dynamic behavior of the vertical spindle. The consequence is then exerted to the fly cutter and the processed surface profile is simulated. The wavelength of the simulation result coincides well with the experimental result which proves the importance of the cut-in process during the single point diamond fly cutting.

3D surface topography formation in ultra-precision turning

The generation process of 3D surface topography in ultra-precision turning is analyzed, as the result of superimposing between actual roughness surface,waviness surface and geometrical form texture surface. From the viewpoints of machine technical system and manufacturing process,factors influencing on roughness surface, waviness surface and geometrical form texture surface in ultra-precision turning are discussed further.The 3D topography of ideal roughness surface and actual surface affected by cutting vibration are simulated respectively.

Surface Waviness in Grinding of Thin Mould Insert Using Chilled Air as Coolant

On going trend of miniaturization in electronic rel at ed parts, which is an average of two times in every 5～7 years introduce grindin g challenges. In grinding process, the surface waviness control of thin parts is an ardent task due to its warpage, induced by the high specific grinding energy (2～10 J/mm 3). Therefore, coolant is often used to avoid thermal damage, obtai n better surface integrity and to prolong wheel life. However coolant, the incomp ressibility media introduce high forces at the grinding zone creating dimensiona l as well as shape instability. In view of these situations chilled air was ap plied in place of conventional coolant. The chilled air is produced using a two -stage vapor compression refrigeration cycle with characteristics of: temperatu re -35 ℃, pressure 0.2～0.3 MPa and flow rate 0.4 m 3/min. Also traces of eco - oil mist that encompass the chilled air are supplied to the grinding zone. B oth chilled air and eco-oil mist are applied through two independent paths of a specially designed twin compartment nozzle for maximizing the penetration. This paper investigates the grinding characteristics of mold insert which is closer to M2 tool steel (component widely used in connector industries) when using chil led air as coolant media. Grinding experiments were conducted using a vitrified bond CBN wheel (B91N100V) and a surface grinder. Initial study was focussed on establishing the most suita ble clamping method for the thin mold insert. FEM analysis and grinding experime nt studies were performed to quantitatively analyze the clamping induced deflect ion. Waviness value (W t) of (24～62) μm was achieved for resin clampi n g whereas (4～8) μm, (4～6) μm were achieved for magnetic and wax clamping res pe ctively. Wax clamping is predominantly used in all the grinding experiments that characterize the grinding process, which use chilled air as the coolant media. Between 0.15 to 0.9 mm 3/mm.s of specific material removal rate, ground sur face temperature of mold insert was increased from 0.3 ℃ to 59.7 ℃ for chi lled air. For the similar grinding conditions with the coolant fluid an increase from 0.9 ℃ to 14.4 ℃ was recorded. With increase of specific material removal rate from 0.15 to 0.65 mm 3/mm.s, F t/F n ratio was increased from (0.2 to 0.4), (0.6 to 1.67) for wet coolant and chilled air respectively. Despite of high F t/F n ratio and ground surface temperature, chilled air method has shown a surface waviness, W t from (2 to 5.6) μm. Microstructure examination of chilled air produced ground surface was comparable to those of using coolant fluids. Surface finish, R a of (0.45～0.7) μm was achieved for mold insert . This work will enable to have clear understanding about the quantitative influe nce of chilled air as well as the clamping method against the surface waviness o f thin mold insert.

Heat Transfer Characteristics of Wavy-Wall Channels in Micropolar Fluids

Forced convection flow through a sinusoidally curved converging diverging channel in micropolar fluids has been investigated numerically. A simple coordinate transformation is employed to transform the complex wavy wall channel to a parallel plate channel, and the cubic spline alternating direction implicit method is then used to solve the flow patterns and heat transfer characteristics. The effects of the wavy geometry, vortex viscosity parameter and Reynolds number on skin friction coefficient and Nusselt number have been examined in detail. Results show that the flow through a sinusoidally curved converging diverging channel forms a strong forward flow and a reticular vortex within each wave for larger Reynolds number and wavy amplitudes. The heat transfer rate of a micropolar fluid is smaller than that of a Newtonian fluid, but the skin friction of a micropolar fluid is larger than that of a Newtonian fluid. Moreover, both Reynolds number and wavy amplitude tend to enhance the total heat transfer rate, irrespective of whether the fluids are Newtonian fluids or micropolar fluids.

A comparative study of surface waviness models for predicting vibrations of a ball bearing

Surface waviness models utilized to describe the excitation events in the ball bearings(BABs) play an important role in predicting the vibrations of the ball bearing systems. This work proposes a comparative study on the most relevant existing surface waviness models. One model is named as time-varying displacement(TVD) model, which can only describe the time-varying displacement excitation(TDIE). Another model is named as TVDS model, which can describe the TDIE and time-varying contact stiffness coefficient excitation(TCSE). The influences of the wave number, maximum amplitude, nonuniform distribution on the contact stiffness coefficients are studied, as well as vibrations of the BAB. The comparative results demonstrate that the time-varying displacement and stiffness(TVDS) model can provide a more accurate impulses caused by the uniform and nonuniform surface waviness on the races of the BABs. It also seems that the surface waviness distribution has a significantly influence on vibrations of the BABs.

Formation mechanism and modeling of surface waviness in incremental sheet forming

mproving and controlling surface quality has always been a challenge for incremental sheet forming (ISF), whereas the generation mechanism of waviness surface is still unknown, which impedes the widely application of ISF in the industrial field. In this paper, the formation mechanism and the prediction of waviness are both investigated through experiments, numerical simulation, and theoretical analysis. Based on a verified finite element model, the waviness topography is predicted numerically for the first time, and its generation is attributed to the residual bending deformation through deformation history analysis. For more efficient engineering application, a theoretical model for waviness height is proposed based on the generation mechanism, using a modified strain function considering deformation modes. This work is favorable for the perfection of formation mechanism and control of surface quality in ISF.