Williamson Model Research Articles

Involvement of temperature dependent thermal conductivity and diffusion coefficient on bio-convective flow partial differential equations of Williamson model with radiation phenomenon

The Williamson nanofluid flow via a nonlinear stretching plate is examined in this work. Unlike the literature analysis for a linear stretching situation, which focuses on the local impact of Williamson parameter, this analysis will examine the global influence of λ. Furthermore, the characteristics of activation energy are also considered in this review. It is still unclear how the proposed model and ensuing similarity transformation are viewed. Analytical solutions are found for the altered partial differential equations. Figures illustrate the effects of embedding factors on the temperature, concentration, density microorganisms, and velocity curves. Tables are also used to illustrate how embedded characteristics affect mass transfer, heat transfer, and skin friction.

Preparation and characterization of dressing-type emulsions formulated with hydrocolloids from the mango (Mangifera indica) peel

Mango is a popular tropical fruit known worldwide and mango peel is a waste product worthy of valorization. This study explores the stabilizing effect of hydrocolloids extracted from mango peel in dressing-type emulsions (DE). Emulsions stabilized with different ratios of mango (Mangifera indica) peel-derived hydrocolloids (PE) and guar gum (1 % wt. total concentration) were prepared and characterized: DE1 (0.25/075), DE2 (0.5/0.5), DE3 (0.75/0.25) and DE4 (1/0). Particle size distribution, ζ-potential, proximal composition, color, microstructure, and rheological properties were evaluated. All the samples showed similar proximal compositions. However, PE/guar gum ratio influences color parameters. For the microstructural analysis, Sauter's mean droplet size ranged from 6.41 to 11.11 µm. The ζ- potential values ranged from −18.03±0.21 to −16.97 mV. Emulsions exhibited shear thinning responses that can be well described by the Williamson model, and gel-like viscoelastic character with G’ higher than G”. The activation energy values (Eα) deduced from the application of an Arrhenius model to the viscous flow behaviour of the emulsions ranged from 108.46 to 143.44 Kj/mol. From the microstructural analysis and the rheological characterization, it can be inferred that PE favors the flocculation of the emulsion droplet in high concentrations. Overall, this research contributes to the sustainable exploitation of a mango waste material, such as the peel, in food emulsions.

Optimal homotopic strategy for thermal and mass transport in Williamson model flow PDEs under heat generation/absorption and Joule heating

In current paper, we considered the 3-D occurrence of magneto Williamson fluid subjected to linear penetrating expanding sheet. The Williamson liquid is taken into account under the essence of bio convection bordering with Joule heating, heat production. Moreover, Brownian movement combined with thermophoresis diffusion was also analyzed in current study. Central PDEs are modified into system of ODEs on the basis of appropriate similarity transformation utilization. For solution purpose, an optimal approach namely HAM was opted. The critical review based on all involved multifarious constraints across the non- dimensional velocity contour [Formula: see text] energy and concentration distribution. Moreover, across the motile organism distribution was also conducted graphically and depicts total covenant with the former published research work. The drag force effect, Nusselt number, Sherwood number, and motile organism density in tabular form is also proposed in this study. Moreover, Motile organism profile graphically demonstrates decreased demeanor for considered bio convection Lewis number, Peclet number, and also temperature difference constraint whereas results of motile organism density augmented in tabular version for the considered bio convection Lewis number, Peclet number, and also temperature difference constraint.

Thermophoretic particle deposition and double-diffusive mixed convection flow in non-Newtonian hybrid nanofluids past a vertical deformable sheet

PurposeThermophoresis deposition of particles is a crucial stage in the spread of microparticles over temperature gradients and is significant for aerosol and electrical technologies. To track changes in mass deposition, the effect of particle thermophoresis is therefore seen in a mixed convective flow of Williamson hybrid nanofluids upon a stretching/shrinking sheet.Design/methodology/approachThe PDEs are transformed into ordinary differential equations (ODEs) using the similarity technique and then the bvp4c solver is employed for the altered transformed equations. The main factors influencing the heat, mass and flow profiles are displayed graphically.FindingsThe findings imply that the larger effects of the thermophoretic parameter cause the mass transfer rate to drop for both solutions. In addition, the suggested hybrid nanoparticles significantly increase the heat transfer rate in both outcomes. Hybrid nanoparticles work well for producing the most energy possible. They are essential in causing the flow to accelerate at a high pace.Practical implicationsThe consistent results of this analysis have the potential to boost the competence of thermal energy systems.Originality/valueIt has not yet been attempted to incorporate hybrid nanofluids and thermophoretic particle deposition impact across a vertical stretching/shrinking sheet subject to double-diffusive mixed convection flow in a Williamson model. The numerical method has been validated by comparing the generated numerical results with the published work.

Boundary layer analysis on magnetohydrodynamic dissipative Williamson nanofluid past over an exponentially stretched porous sheet by engaging OHAM

PurposeThis investigation delves into the rationale behind the preferential applicability of the non-Newtonian nanofluid model over alternative frameworks, particularly those incorporating porous medium considerations. The study focuses on analyzing the mass and heat transfer characteristics inherent in the Williamson nanofluid’s non-Newtonian flow over a stretched sheet, accounting for influences such as chemical reactions, viscous dissipation, magnetic field and slip velocity. Emphasis is placed on scenarios where the properties of the Williamson nanofluid, including thermal conductivity and viscosity, exhibit temperature-dependent variations.Design/methodology/approachFollowing the use of the OHAM approach, an analytical resolution to the proposed issue is provided. The findings are elucidated through the construction of graphical representations, illustrating the impact of diverse physical parameters on temperature, velocity and concentration profiles.FindingsRemarkably, it is discerned that the magnetic field, viscous dissipation phenomena and slip velocity assumption significantly influence the heat and mass transmission processes. Numerical and theoretical outcomes exhibit a noteworthy level of qualitative concurrence, underscoring the robustness and reliability of the non-Newtonian nanofluid model in capturing the intricacies of the studied phenomena.Originality/valueAvailable studies show that no work on the Williamson model is conducted by considering viscous dissipation and the MHD effect past over an exponentially stretched porous sheet. This contribution fills this gap.

Конвективные режимы псевдопластической жидкости в квадратной полости при воздействии высокочастотных вибраций в условиях пониженной гравитации

In this paper, we investigate convective modes of pseudoplastic fluid in a square cavity with solid perfectly heat-conducting boundaries under reduced gravity. The cavity performs vertical linearly polarized high-frequency vibrations. Between the vertical walls of the cavity a temperature drop is prescribed in the direction perpendicular to vibrations and the field of gravity. The fluid rheology is described using the Williamson model. The problem is solved based on the averaged thermovibration convection equations for nonlinear viscous fluids. The vibration intensity is determined by the vibration parameter V, which is proportional to the ratio of the amplitude of the vibration acceleration to the free-fall acceleration and does not depend on the temperature difference. The problem is found to have two types of solutions, which we call Newtonian and non-Newtonian modes. These solutions correspond to different convective structures, for which the dependences of the maximum of the stream function and the Nusselt number on the Grashof number are derived. We use these dependences for determining at different values of rheological parameters the threshold values of the Grasgof numbers, corresponding to the change in the modes of stationary averaged convection and the critical Grasgof numbers, corresponding to the loss of stability of stationary averaged flow and the occurrence of oscillatory modes of averaged convection. The structures of different modes of averaged stationary and oscillatory convection are studied. The results obtained for the Newtonian mode have shown that at small values of the Grasgoff number, a slow one-vortex stationary convective flow is realized in the cavity. With increasing the Grasgoff number it transforms into a three-vortex flow. A further increase in the Grasgoff number results in the appearance of a four-vortex convective flow, which eventually transforms again into a three-vortex motion. At even greater Gr, the stationary averaged motion becomes unstable and the oscillatory modes appear in the cavity. For the non-Newtonian mode, a stationary convective flow is the basic flow pattern detected in the cavity; the oscillatory modes are not observed in the whole investigated range of the Grasgoff numbers.

Mango (Mangifera indica) seeds and peel-derived hydrocolloids: Gelling ability and emulsion stabilization

Mango is a tropical fruit that is consumed worldwide and is distinguished by its sweet and juicy flesh. Unfortunately, the peels and seeds of mango fruit are often discarded despite the fact that they contain compounds that can be valorized for certain applications. In this study, a physicochemical and hydrodynamic characterization of hydrocolloids extracted from the peel and seeds of mango fruit was performed and the impact on the microstructure and rheological behavior of derived gels, as well as the ability to form emulsions, were analyzed. The physicochemical parameters and proximate compositions of the different samples showed that the hydrocolloids extracted from the seeds are rich in proteins whereas those from the peel are rich in carbohydrates. The molecular weights calculated from the hydrodynamic characterization (Mv) are 101515 g/mol and 102,580 g/mol for hydrocolloids extracted from the peel and seeds, respectively. Dispersions of these hydrocolloids in water produced hydrogels upon heating, which exhibited a shear thinning response that can be described by the Williamson model. The ability of these hydrocolloids to form thermally-induced strong gels was monitored and analyzed by means of curing tests. Throughout thermal treatments, the storage modulus showed a significant increase, especially at concentrations greater than 2.5 wt%. Mango seeds and peel-derived hydrocolloids are also able to stabilize o/w emulsions. Derived emulsions showed D50 mean diameters and zeta potential values (ζ) in the ranges from 10.04 to 82.52 μm and from -17.63 to -11.12 mV, respectively. On the basis of the observed rheological behavior of hydrogels and emulsion-forming ability, the hydrocolloids derived from mango seeds and peels possess suitable characteristics to be potentially implemented in diverse food matrices, offering functional and nutritional benefits to final consumer products.

Characterization of contact evolution on sand grain surfaces and their time-dependent contact properties based on Greenwood and Williamson model

This paper focuses on the microscopic roughness of silica sand grain, and its morphological evolution (contact maturing) under a constant load. The surface topology with rich texture is obtained by Atomic Force Microscopy and various roughness parameters are investigated by statistical approaches. The surface profiles in the same contact region before and after being subjected to sustained loading are both measured to identify time-dependent morphological changes on the contact surface. The two congruent surface topologies, initial and mature surfaces, not only show the delayed fracturing of contact asperities, but also present quantitative differences in the spatial roughness parameters over time. These differences are intensified with consideration of upper profiles only, indicating that asperities with higher elevations are susceptible to the contact maturing process. With the geometric information obtained from the same region at two different measurement times, the Greenwood and Williamson asperity model of rough surface is used to estimate contact proximity, real area of the load-bearing contacts, and the number of contact spots. The model results of the post-loaded surface incorporated with true surface profiles show an increased number of contact points as well as the true contact area under constant loading. It is expected that subcritical fracturing of contact asperities leads to closer proximity of contact entities when loaded by prolonged loading, resulting in firmer and stiffer intergranular contact. This may very well be the reason for time effects in sand assemblies.

Multi-optimization of rod fastened rotor on the distribution of bending stiffness and unbalance

A rod fastened rotor (RFR), which contains serial disks, rods (or a rod), and a torque tube, is the main form of heavy duty gas turbines and light duty aero engines. The roughness of the interface is the main parameter affecting the bending stiffness of RFR, and the jumpiness of the disks is the intuitive representation of the unbalance of the rotor. In this paper, a multi-optimization algorithm, NSGA-Ⅱ, was used to improve the vibration behavior of the RFR-bearing system. First, the quantitative relation between the bending stiffness of the rotor and the roughness of the interface was set up by combining the Persson contact theory and the Greenwood–Williamson model, and the nondimensional bending stiffness (NS) was proposed as the optimization objective of roughness. Then, the optimization objective of the jumpiness of the disk, (A + B), was rendered based on the minimum unbalance force. Finally, the multi-optimization on the roughness and jumpiness of the RFR was carried out, and the vibration behavior was improved greatly. In addition, this multi-optimization method was applied to a practical RFR, and the experimental results showed that the vibration amplitude was reduced by about 82%. The work in this paper can provide the guidance for vibration reduction of the rotor system.

Flow analysis of Williamson model over a moving surface with nonlinear convection/diffusion and variable thermal conductivity

This article analyses the flow across a moving surface using the magnetohydrodynamic (MHD) Williamson fluid model in detail, accounting for the effects of diffusion, nonlinear convection, and variable thermal conductivity. The heat transmission within the system is impacted by the changing thermal conductivity, which can also significantly alter the flow behavior. The effects of the moving surface on flow forms in porous media are explained here using the Darcy model. The similarity transformations are used to convert the underlying nonlinear partial differential equations into a collection of ordinary differential equations. The work uses a numerical RK4 technique to examine the complex incompressible fluid flow behavior on a moving surface. The study’s conclusions provide insight into the intricate flow patterns and shear layer forms brought on by the interaction of fluid and surface motion while taking varied thermal conductivity into account. The findings give important information for the design and optimization of engineering applications involving changeable thermal characteristics and advance our understanding of fluid dynamics in geophysical and atmospheric systems. Physical descriptions are used to depict how flow parameters behave in relation to velocity, temperature, and concentration distributions.

Effect of inclined Lorentzian force on radiated nanoflow Williamson model under asymmetric energy source/sink: Keller box method

An asymmetric energy source/sink can be designed to efficiently convert ambient energy into usable forms; this could have applications in micro-/nanoscale power generation, i.e., energy harvesting. The asymmetric energy source/sink and inclined Lorentzian force could be used to control the flow of fluids within these devices. This study numerically investigates the model of a Williamson nanofluid influenced by an angled magnetic force and an asymmetric energy input/output on a stretching surface with a convective wall boundary condition. The partial differential equations connected to the momentum, energy, and concentration equations are transformed into nonlinear ordinary differential equations (ODEs) by applying relevant similar variables. The obtained ODEs are handled by the Thomas algorithm and a finite difference in the Keller box method. A thorough examination of a change in velocity, temperature, and concentration is done for all the relevant parameters. A higher buoyancy ratio parameter lowers the streamline density. As far as the numerical method is concerned, the Keller box method gives the highest convergence value when compared to other methods, so we use this method to investigate the sleeping behavior of the Williamson nanofluid. The energy source decreases the non-Newtonian passing surface friction. The concentration gradient increases for an increasing value of the chemical reaction parameter. A decreased diffusion rate is seen for increasing Brownian number, while the opposite behavior is noticed for the thermophoretic parameter. The wall friction coefficient increases for augmenting We but decreases for the angled Lorentzian force. Except for radiation, energy transfer is high in all other flows, affecting parameters such as A, B, Nb, Nt, and Pr. By controlling the magnetic field, MHD heat exchangers can manipulate heat transfer rates for various industrial applications. In fusion reactors, strong magnetic fields confine hot plasma, and understanding the interaction between the field and heat sources is crucial for efficient energy generation.

Improved mesh stiffness model of spur gear considering spalling defect influenced by surface roughness under EHL condition

Gear tooth spalling is a typical tooth surface defects in gear transmission. The accurate calculation of the time-varying mesh stiffness of the gear pair with spalling defect under mixed elastohydrodynamic lubrication (EHL) plays an important role in tooth damage prediction and fault feature analysis. In this work, an improved time-varying mesh stiffness (TVMS) model of spalling faulty gear in mixed EHL line contact considering the coupled effect of rough surface topography is established. The proposed model considers the combined effect of spalling defect, surface roughness topography, and lubrication on the contact characteristics of the meshing interface to obtain a revised contact stiffness, which is further used to determine the comprehensive TVMS. The cylindrical contact coefficient for curved meshing interface with spalling fault is derived and incorporated into the statistical micro-contact Greenwood and Williamson model (GW model) to obtain the asperity contact stiffness. The revised contact stiffness at the rough faulty gear interface is obtained from the parallel action of the asperity contact stiffness and oil film stiffness under load-sharing concept. The dynamic responses of the gear system are analyzed using the established mesh stiffness model through the six degrees of freedom translational-torsional dynamic model, in which the dynamic meshing force is calculated iteratively using the transit surface topography and geometrical parameters along the line of contact instead of a quasi-static meshing force. Effects of multi-parameters as surface roughness, spalling fault size, and lubricant on the mesh characteristics and dynamic responses of the gear system are further investigated and discussed.

Analysis of the discrete contact characteristics based on the Greenwood-Williamson model and the localization principle

The contact of a rigid body with nominally flat rough surface and an elastic half-space is considered. To solve the contact problem, the Greenwood-Williamson statistical model and the localization principle are used. The developed contact model allows us to investigate the surface approach and the real contact area with taking into account the asperities interaction. It is shown that the mutual influence of asperities changes not only contact characteristics at the macroscale, but also the contact pressure distribution at the microscale. As follows from the results, the inclusion in the contact model of the effect of the mutual influence of asperities is especially significant for studying the real contact area, as well as the contact characteristics at high applied loads. The results calculated according to the proposed approach are in a good agreement with the experimentally observed effects, i.e., the real contact area saturation and the additional compliance exhaustion.

Elastic Contact for Rock Fractures under Compressive Loading: Revisiting Greenwood and Williamson Model with Interacting and Coalescing Hertz Asperities

Elastic Contact for Rock Fractures under Compressive Loading: Revisiting Greenwood and Williamson Model with Interacting and Coalescing Hertz Asperities

Effect of Hexagonal Boron Nitride on Morphology, crystallinity and internal Exfoliation properties of Polypropylene melt and solid phases

ABSTRACT Polypropylene (PP) is one of the most important polymers widely used in different industries due to its many superior properties. Hexagonal boron nitride (hBN) is generally used in the electronic packaging industry and insulator material production due to its high thermal conductivity and low electrical conductivity. However, the lubrication properties have not yet been examined in the polymer matrix. The main purpose of this study is to examine the lubricating properties of hBN in the PP matrix and to expand its application areas. In this research, hBN/PP composites have been produced and characterized by scanning electron microscopy with an energy dispersive X-ray detector (SEM-EDX) and the differential scanning calorimeter (DSC), respectively. The linear viscoelastic behaviors (LVBs) and rheological properties of the hBN/PP composites have been investigated at 190°C by hybrid rheometer which had high temperature plate-plate geometry system; furthermore, the SEM has been used for searching hBN particles deformation, which was mechanical deformation and distribution into the PP. The oscillation sweeps tests have shown that the critical strain values and the gelation point of composites decreased with the increasing of the hBN content into the composites. Over the 10%, hBN addition into the PP elevated internal lubrication by the exfoliation of hBN plaques. The Williamson model and the discrete retardation spectrum (DRS) equation has been applied on the hBN loaded PP composites and the PP.

Analysis of heat and mass transfer in magnetic fluid flux (MHD) using Williamson's model over an expanded surface with thermal and nonlinear radiation effects

This study investigates the heat and mass transfer characteristics of Williamson MHD fluid flow over a stretching surface with variable thickness, considering the effects of Lorentz forces, nonlinear thermal radiation, and cross-diffusion phenomena. The governing equations for momentum, energy, and concentration are derived and transformed into dimensionless coupled nonlinear ordinary differential equations using similarity transformations. These equations are solved numerically using a fourth-order Runge-Kutta method coupled with shooting techniques. The analysis incorporates the effects of thermal and concentration slip conditions, magnetic field intensity, and electrical conductivity. Results are presented graphically and in tabular form to illustrate the influence of key parameters, such as the magnetic field parameter, thermal radiation, Eckert number, and Soret and Dufour numbers, on velocity, temperature, and concentration profiles. Additionally, the study evaluates skin friction coefficients, Nusselt numbers, and Sherwood numbers under varying conditions. The findings highlight the complex interplay between magnetic, thermal, and mass diffusion effects, offering valuable insights for industrial applications such as polymer processing, glass manufacturing, and heat exchangers

Thermally Radiation of MHD Two-Phase Williamson Fluid with Newtonian Heating (NH)

Due to the unique qualities in its behaviours that study the solid and fluid aspects, a study on two-phase flow (solid and liquid) is deemed to be supplementary trustworthy in describing the application of liquid in industrial sectors. Over the past few decades, several non-Newtonian fluid models have been found, but the Williamson model stands out as the most intriguing. The Williamson flow model will be more fascinating to study when the existing particles are considered. Therefore, the purpose of this article is to investigate Williamson fluid with dust particles under the existing MHD and heat radiation. To make inquiry more intriguing, the analysed model also included a Newtonian heating (NH) condition. After employing similarity transformation, the resultant equations, as in Ordinary Differential Equations (ODEs), are solved using the Runge-Kutta Fehlberg (RKF45) method. The findings showed that the presence of fluid-particle interaction (FPI) influenced the fluid velocity, subsequent in a declining the fluid movement and an increase in particle motion.

Non-linear Dynamic Characteristics of High-Speed Wheel-Rail Interface Considering Surface Topography and Liquid Medium

In this work, the force-deflection characteristics, and the nonlinear vibration of the wheel-rail interaction with surface roughness and liquid medium are studied. The statistical micro-contact Greenwood and Williamson model is used to characterize the rough surface. The load sharing theory is used to determine the analytical elastic contact force-deflection and damping force-deflection relationships, which are further approximated by power law functions. The nonlinear contact stiffness and damping characteristics are illustrated for different rough surface topographies and running speeds. The natural frequency is solved by assuming small covariates and defining time variables of different scales. Effects of surface topography and liquid medium on the natural frequency of the wheel-rail interface system are studied. The first-order harmonic responses under harmonic excitation are further determined as well as the jump-up and jump-down responses for different rough surface topographies, excitation loads, liquid mediums and running speeds. It is shown that the resonance region and the peak value of the vibration amplitude increase as the surface roughness, running speed and excitation load increase; whilst the jump-up and jump-down frequencies decrease. In addition, the system can change from a monostable to a bistable structure when surface roughness and excitation force increase and large limit cycle oscillation can occur.

Quantification of viscous and damage dissipation of bituminous binder and mastic using White-Metzner model

ABSTRACT Bituminous pavement layers are composite in nature, consisting of binder, filler, and aggregates. Understanding the mechanical behaviour of bituminous layers demands investigation of their different material scales, such as the binder, mastic, and mixture scales. While substantial investigation has been carried out on binder and mixture related to fatigue damage, not much research is carried out on mastic. Of the methods used to characterise fatigue damage, energy dissipation is widely used; however, it is complicated due to the presence of other modes of dissipation, such as viscous dissipation. In this study, an attempt is made to separate viscous dissipation and dissipation due to damage for both binder and mastic using a nonlinear viscoelastic fluid model. For this purpose, six types of materials were tested at temperatures of 20 ∘ C and 25 ∘ C, 10 Hz frequency, and five different strain levels spanning the linear and non-linear regimes, for 20,000 cycles. Material parameters for the non-linear White-Metzner model incorporated with the Williamson model were determined for an initial cycle and using these parameters, the viscous component of energy dissipation was determined. Dissipation due to damage was estimated by separating viscous dissipation from total dissipation at every 2000th cycle and based on the evolution of viscous and damage dissipation across cycles, three trends were observed. Based on the trends observed, the influence of strain amplitude, temperature and modifiers on the fatigue resistance of the materials was ascertained.

Enhancement of physical properties of thermoplastic polyurethanes by blending with cyclic olefin copolymer elastomer

AbstractIn this study, two different thermoplastic polyurethanes (TPUs), a poly(ester)‐based TPU including aromatic diisocyanate units (TPU1) and a poly(ester‐ether)‐based TPU including aliphatic diisocyanate units (TPU2) were blended with a cyclic olefin copolymer (COC) elastomer to prepare TPU‐rich blend films via melt compounding in a twin screw extruder equipped with a slit die and film casting rollers. Morphological features and viscoelastic properties of blend films were characterized with scanning electron microscope analysis, different test protocols in melt rheology measurements, and dynamic mechanical analyzer tests, in detail. Viscoelastic properties of blend films were quantified with various mathematical approaches such as Williamson model, discrete retardation spectrum (DRS), Burger, and Findley equation. It was found that COC phase dispersed more homogenously into TPU1 matrix than TPU2. COC elastomer addition significantly increased the melt viscosity and melt elasticity of TPUs and improved the creep strength.Highlights COC addition enhanced the viscosity and elasticity of TPUs in melt state. The creep strains of TPUs decreased by 65% with addition of 40 wt% of COC.