On the Implications of Exponentially Decaying Internal Heat Generation on Mixed Convection Flow from a Vertical Porous Plate Influenced by Hydrodynamics and Thermal Partial Slip

For the first time, an analytical solution has been derived for Stokes flow through a conical diffuser under the condition of partial slip. Recurrent relations are obtained that allow determination of the velocity, pressure and stream function for a certain slip length λ . The solution is analysed in the first order of decomposition with respect to a small dimensionless parameter ${\lambda }/{r}$ . It is shown that the sliding of the liquid over the surface of the cone leads to a vorticity of the flow. At zero slip length, we obtain the well-known solution to the problem of a diffuser with a no-slip boundary condition corresponding to strictly radial streamlines. To solve that problem, we use an alternative form of the general solution of the linearised, stationary, axisymmetric Navier–Stokes equations for an incompressible fluid in spherical coordinates. A previously published solution to this problem, dating back to the paper by Sampson (1891 Phil. Trans. R. Soc. A , vol. 182 , pp. 449–518), is given in terms of a stream function that leads to formulae that are difficult to apply in practice. By contrast, the new general solution is derived in the vector potential representation and is simpler to apply.

Impact of Partial Slip Condition on Forced Convection of Nanofluid in a Channel with Wavy Porous Layer

Hydrogenation influence on crack initiation and fretting corrosion mechanism of zirconium alloy under partial slip regime in high temperature pressurized water environment

Abstract An electrically conducting Reiner–Rivlin nanoliquid flow is considered over a rough, infinitely spinning disk based on a von Kármán model. The flow incorporates partial slip conditions and a temperature jump at the disk surface. This investigation seeks to establish a more precise and practical framework for advanced thermal-fluid systems, with specific relevance to microscale heat management and electrohydrodynamic technologies. The novelty lies in addressing the comparative appraisal of quartic and cubic chemical reactions as these possess pivotal applications, including advanced cooling systems, corrosion and material processing, electromagnetic and MHD applications, and aerospace and turbomachinery. Additionally, Brownian motion and thermophoresis effects are included owing to nanoparticles. The 3-stage Lobatto IIIa method of MATLAB software is applied to compute the numerical solution of the present model. Results are demonstrated in the form of illustrations and tables. The velocity and temperature profiles display contrasting trends for the slip parameter. The fluid concentration decreases with the Reiner–Rivlin parameter and the Schmidt number. In addition, the heat flux rate is higher for a quartic chemical reaction than for a cubic chemical reaction. This study can be applied to microfluidic devices, rotary heat exchangers, and rotating machinery in aerospace and biomedical systems, where enhanced heat transfer, complex fluid behavior, and realistic boundary effects like slip, roughness, and magnetic fields are critical. A validation of the presented data is also a part of this study. To draw the graphs and for the tabulated values, the assumed ranges of the involved parameters are as follows: 2 ≤ Pr ≤ 20 , 0.1 ≤ γ ≤ 0.5 , 5 ≤ M ≤ 15 , 0.2 ≤ α ≤ 0.6 , 4 ≤ N b ≤ 6 , 0.1 ≤ N t ≤ 0.3 , 0.3 ≤ K ≤ 0.4 , 2.5 ≤ S c ≤ 3.5 . \begin{array}{c}2\le \Pr \le 20,\hspace{.5em}0.1\le \gamma \le 0.5,\hspace{.5em}5\le M\le 15,\hspace{.5em}0.2\le \alpha \le 0.6,\\ 4\le {N}_{\text{b}}\le 6,\hspace{.5em}0.1\le {N}_{\text{t}}\le 0.3,\hspace{.5em}0.3\le K\le 0.4,\hspace{.5em}2.5\le Sc\le 3.5.\end{array}

Dexterous manipulations rely on tactile feedback from the fingertips, which provides crucial information about contact events, object geometry, interaction forces, friction, and more. Accurately measuring skin deformations during tactile interactions can shed light on the mechanics behind such feedback. To address this, we developed a novel setup using 3-D digital image correlation (DIC) to both reconstruct the bulk deformation and local surface skin deformation of the fingertip under natural loading conditions. Here, we studied the local spatiotemporal evolution of the skin surface during contact initiation. We showed that, as soon as contact occurs, the skin surface deforms very rapidly and exhibits high compliance at low forces (<0.05N). As loading and thus the contact area increases, a localized deformation front forms just ahead of the moving contact boundary. Consequently, substantial deformation extending beyond the contact interface was observed, with maximal amplitudes ranging from 5% to 10% at 5N, close to the border of the contact. Furthermore, we found that friction influences the partial slip caused by these deformations during contact initiation, as previously suggested. Our setup provides a powerful tool to get new insights into the mechanics of touch and opens avenues for a deeper understanding of tactile afferent encoding.

Elastic, flat and rounded finite contacts in partial slip: A novel solution based on wedge and half-plane formulations

Boundary layer formation over a stretchable cylinder in a viscoelastic fluid with partial slip and viscous dissipation effects

CFD analysis of cavitated flow in multi-groove water lubricated bearings with partial and full slip effects

A review of partial slip solutions for elastic contacts

A novel scenario for the yielding of three-dimensional crystals in the quasistatic limit is presented. To this end, a face-centered cubic Lennard-Jones crystal under deformation and periodic boundary conditions is studied using Monte Carlo simulation in combination with successive umbrella sampling. As a reaction coordinate, a non-affinity parameter X is introduced. In terms of this parameter, the yielding of the crystal can be described as a phase transition, where at the system-size-dependent yield strain ɛ(y), a deformed crystal, the "N phase," transforms into a nearly stress-free state, the "M phase." The N-M phase transition is dominated by the long-ranged elasticity of the crystal. As a consequence, there are no mixed states of both phases. Moreover, the free energy barrier between them is not associated with interfacial contributions, but rather scales with the total volume V of the crystal, implying non-convexity of the X-dependent free energy F(X). On the path from the N to the M phase with increasing X, the free energy F(X) develops two kinks that are associated with jumps of a field conjugate to the non-affinity parameter X. At the first kink, corresponding to the maximum of F(X), there is the nucleation of a partial slip plane, associated with the formation of a stacking fault that is circumvented by a loop of Shockley partial dislocations. At the second kink, at a lower free energy, the dislocations are annihilated leaving behind the stacking fault around now fully developed slip planes. The resulting M phase is inhomogeneous with periodically repeating stacking faults around the fully developed slip planes (here, the distance between the slip planes is determined by the periodic boundary conditions and the initial orientation of the crystal in the simulation box).

Numerical and regression study of Bödewadt flow with partial slips and variable thermal conductivity under a horizontal magnetic field

Surface bubble lifetime is determined by the thin liquid film drainage, which is driven by pressure gradients within the film. Traditional models consider gravity- and surface-tension-driven drainage for large and small bubbles, respectively. However, gravitational effects remain significant in small bubbles within highly viscous liquids because of the increased film thickness. Many models neglect the film pressure or estimate it solely based on the Young–Laplace equation, overlooking the pressure gradients along the liquid film. Moreover, despite the presence of partial slip behavior in microscale systems, which can influence film drainage rates, idealized boundary conditions such as slip or no-slip at the gas–liquid interface are often assumed. To enhance predictive accuracy, this study proposes a model that incorporates both gravity- and surface-tension-driven drainage, considers pressure gradients along the film, and applies partial-slip boundary conditions. Three key model variables—film pressure, film thinning rate, and tangential film drainage velocity—were determined by simultaneously solving three governing equations: (1) the Stokes equation for the liquid film under partial-slip conditions, (2) mass conservation equation that relates film thinning rate to film drainage velocity, and (3) force balance at the deformed free surface. The model was validated across various liquids, including water, perfluorocarbon liquid (PP11), and polydimethylsiloxane (PDMS) liquids with viscosities of 10, 100, and 1000 Pa s, yielding mean absolute percentage errors of 10.2%, 36.4%, 33.6%, 24.9%, and 32.9%, respectively. The model, derived from first principles, provides consistent and interpretable predictions across various liquids without relying on empirical fitting, demonstrating its general applicability.

Surface tractions for unsymmetrical nominally flat contacts under partial reverse slip conditions

The paper presents the results of long-term operation, improvement and modernization of a specialized friction machine designed and manufactured to study fretting wear of materials and coatings in gross slip regime. Four different regimes of friction contact surfaces behavior during fretting are known: full stick (seizing) and partial slip (stick-slip) regimes, which are characterized by fatigue failure and cracking, and regimes of gross slip and its transition to reciprocating sliding, for which the main damage contacting surfaces is wear process. It is typical for friction units in which moving contacts of friction surfaces are limited or specially designed, inherent in a large number of plants, machines and mechanisms, and in particular, friction units of gas turbine engines (GTE) and power plants based on them. The work examines not only the stages of modernization of a specialized friction machine, but also presents the main results obtained from studies of fretting wear of various friction units at each stage. The advantages of this machine are determined not only by the ability to control one of the main wear fretting factors — the amplitude of sliding (relative cyclic motion), but also, thanks to the use of collet clamps for fastening experimental samples, to test various forms of friction contacts, such as sphere – plane, plane – plane, cylinder – cylinder, cylinder – plane and others. At all stages of modernization of a specialized friction machine, various coating designs were developed and tested for fretting resistance to protect against fretting wear the friction surfaces, in particularly, of fan blade locks and friction pairs of the mid-span shrouds of gas turbine engine blades operating in gross slip regime. A comparison of the linear and volumetric fretting wear values of various coating options and their components made it possible to establish that the developed and proposed coatings have a good fretting resistance under the operating conditions specified and implemented on the friction machine. Using an analysis of variants of the dependences of the tangential friction force on the displacement values (amplitudes) of gross slip, the values of dissipation energy (friction energy) were obtained and fretting hysteresis loops were constructed. They made it possible to estimate the service life of each of the coatings under consideration with its known thickness and a given displacement, and by comparing the energy coefficients of volumetric wear to determine the most effective coating in terms of fretting resistance and service life. Based on the results of testing materials and coatings under plane-to-plane friction conditions at temperatures of 175 – 180°C, recommendations were developed for the utilization of these materials and technologies for use in friction pairs of mid-span shrouds of gas turbine engine blades. Thus, the considered and implemented capabilities of the modernized friction machine make it possible, under laboratory evaluation conditions, to study various materials and coatings under fretting wear conditions in model friction units of various power plants, machines and mechanisms under given operating conditions at normal and elevated temperatures.

This research examines the numerical study of a two-dimensional magnetohydrodynamic Williamson nanofluid flow in the presence of a magnetic field over a radially stretching surface. In this context, the fluid flow over a moving surface in the radial direction incorporates velocity slip and normal flux of the Williamson nanofluid. The impact of Magnetohydrodynamic flow on surface temperature, along with considerations of partial velocity slip, is given particular emphasis. Additionally, convective boundary conditions are included in the boundary layer fluid flow analysis, with modeling of key fluid field parameters such as concentration, temperature, and momentum of the Williamson nanofluid. The governing partial differential equations for axisymmetric flow are reduced to a set of nonlinear ordinary differential equations using appropriate similarity transformations and are mathematically solved using the Spectral Quasilinearization Method. A significant numerical study was conducted, with results compared to recent research, demonstrating its relevance to industrial applications. Moreover, key parameters such as the Weissenberg parameter, magnetic field, Eckert number, Prandtl number, thermophoresis parameter, and radiation parameter are shown to have important effects on velocity, temperature, and concentration profiles, as illustrated through various graphs. The Spectral Quasilinearization Method is employed to obtain a convergent series solution, with the influence of various parameters on the Magnetohydrodynamic Williamson nanofluid under thermal radiation depicted in the graphs. The velocity profile is to decrease 90% with an increment in the value of the Weissenberg parameter.

Purpose: Pulled elbow is a common injury found in children below 5 years of age. This condition occurs because of a sudden pull on the outstretched arm, which facilitates partial slipping of the head of the radius out of the ligamentous constricted annular ligament. This study identified knowledge gaps and areas that require improvement in the medical curriculum by assessing medical students’ understanding of the diagnosis, clinical presentation, and management of the condition.Methods: A 6-month cross-sectional analytical study was conducted between July 2024 and December 2024, which included 196 medical students at Batterjee Medical College, using a validated questionnaire. Chi-square tests examined the associations between past training, knowledge, and independent variables. Binary logistic regression identified the predictors of high knowledge levels. Odds ratios (ORs) and 95% confidence intervals (CIs) were also determined. Statistical significance was set at P&lt; 0.05.Results: Most students rated their knowledge as ‘poor’ (31.1%) or ‘very poor’ (27.0%) regarding the diagnosis and management of pulled elbow. Only 6.1% rated their knowledge as ‘good’ or ‘very good.’ Chi-square analysis showed significant associations between knowledge and gender (P = 0.020), as well as academic year (P = 0.001). Binary logistic regression revealed that male students were significantly more likely to report good knowledge (OR, 0.102; 95% CI, 0.019 to 0.562; P= 0.009), as were clinical-year students (OR, 3.051; 95% CI, 1.011 to 9.222; P= 0.048) and those with high self-rated knowledge (OR, 5.101; 95% CI, 1.301 to 20.101; P= 0.019). Workshop participation was strongly associated with prior exposure to pulled elbow cases (OR, 0.066; 95% CI, 0.010 to 0.423; P= 0.004) and high self-rated knowledge (OR, 4.251; 95% CI, 1.142 to 15.793; P= 0.031).Conclusion: There are serious knowledge gaps among medical students regarding the diagnosis and management of pulled elbow, a common pediatric condition. Despite the prevalence of this condition, exposure to real-life cases and structured pediatric rotations remains limited, with only 2.5% of students undergoing relevant training.

Fretting causes steep stress gradients, which can lead to premature crack initiation or wear across the surface of contacting parts. Both damage modes are activated depending on the slip condition, which can be defined as partial or gross slip based on relative displacement amplitude and normal load. This article investigates the effect of relative displacement on fretting behavior, as well as the impact of slip conditions on contact stresses. A cylinder/plane contact configuration involving AISI 5200 / Ti − 6 Al − 4 V is considered. Fretting tests are conducted up to 25,000 cycles, within the range of relative displacements from 10 to 50 µm, covering both partial and gross slip conditions. The contact stresses (including contact pressure, shear traction, and stress components) are evaluated using finite-element analysis (FEA), and validated against the classical Hertz–Mindlin theory, as well as equations recently developed by Vázquez for stress components. The findings indicate that an initial increase in the tangential force amplitude Q ∗ , followed by stabilization, is characteristic of a partial slip condition. In contrast, a continuous increase in Q ∗ throughout the fretting loading suggests a gross slip condition. Therefore, the Q ∗ –number of cycles curve serves as a reliable indicator for identifying the sliding condition. Finally, unlike in fretting fatigue, gross slip in plain fretting does not shift the peak stress locations. Furthermore, the stress magnitudes vary from partial slip to gross slip.

The Black Metal Tribometer: High-resolution measurement of normal load-indentation curves and partial slip hysteresis cycles

This study investigates the influence mechanisms of temperature on the tensile properties of Mg-Zn-Ca alloys, with a focus on the activation differences of slip systems at room temperature (RT) and high temperature (HT), and their effects on work hardening behavior. Observations using electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) reveal that Mg-Zn-Ca alloy deformation predominantly relies on basal slip and partial pyramidal slip at RT. The decomposition of pyramidal <c + a> into basal <c + a> dislocations enhance dislocation interactions, which increases the work hardening rate and tensile strength. In contrast, more non-basal and multi-slip systems are activated at HT, reducing dislocation interactions and leading to a decrease in the work hardening rate. The HT samples exhibit lower tensile strength but higher elongation. This study reveals the regulatory mechanism of pyramidal <c + a> dislocation slip decomposition and dislocation interactions at different temperatures, providing a theoretical foundation for designing high-strength, high-ductility magnesium alloys.