This study undertakes a detailed examination of steady, two-dimensional boundary layer flow of a tangent hyperbolic nanofluid past a stretching sheet embedded within a porous medium, subjected to the action of a transverse magnetic field. The mathematical formulation accounts for the effects of velocity slip, viscous dissipation, Joule (Ohmic) heating, first-order homogeneous chemical reactions and wall heat transfer governed by Newtonian convective cooling. Furthermore, the thermodynamic irreversibilities resulting from fluid friction, heat transport and magnetic field effects are evaluated by entropy production and Bejan number analyses. While previous studies have examined Newtonian and conventional non-Newtonian nanofluid flows, the combined influence of electromagnetic forces, non-Newtonian rheology, slip mechanisms, reactive transport, convective thermal conditions and thermodynamic irreversibility for tangent hyperbolic nanofluids remains largely unexplored—a gap addressed in this work. The governing partial differential equations are reduced to a system of ordinary differential equations through similarity transformations and solved numerically using both the three-stage Lobatto IIIa collocation scheme ( bvp4c in MATLAB) and the shooting method with a classical fourth-order Runge–Kutta algorithm. The findings reveal that higher Eckert number ( Ec ) values lead to a substantial reduction in the Nusselt number by 18.3%–53% due to intensified viscous dissipation, but cause a moderate increase in the Sherwood number by 0.5%–1.5%. From the thermodynamic perspective, entropy generation increases with increasing Eckert number and Joule heating parameter and rises with higher chemical reaction parameter and Biot number as well. These patterns offer helpful recommendations for reducing losses and improving thermal efficiency in procedures including biofluid transport and polymer extrusion.

A comprehensive investigation of squeeze film lubrication in porous elliptical plates: Analyzin the influences of magneto-hydrodynamics, couple stress and slip velocity

Influence of couple stresses, viscosity variation, and slip velocity on squeeze film lubrication characteristics of Rayleigh step slider bearing

Heat generation effect on 3D MHD flow of Casson fluid via stretching/shrinking surface with velocity slip Condition

Abstract A novel externally pressurized porous gas journal bearing with herringbone grooves is proposed to provide larger load-carrying capacity especially under high compressibility number conditions. The steady-state performance of the proposed bearing is investigated systematically. Considering the Beavers and Joseph velocity slip boundary conditions at the film-bushing interface, the steady-state model of the porous gas journal bearing with herringbone grooves is established by using the boundary-fitted coordinate system and finite volume method. The Newton-Raphson method and successive over-relaxation scheme are applied to solve the nonlinear equivalent modified Reynolds equation and three-dimensional porous flow equation, respectively. The numerical model is then validated by comparing with the previously published data regarding the conventional porous gas journal bearing and self-acting herringbone-groove gas journal bearing. The influence of slip effect, groove effect and groove parameters on the steady-state performance of the bearing is analyzed under different operating conditions. The calculated result shows that, when the compressibility number Λ>15 and feeding parameter Λp<2, the load capacity of the proposed bearing is much larger than of the conventional type; but when Λ<5, the conventional type might be more superior for all practical Λp. The groove effect could lead to a reduction in the direct moment but an increase in the cross-coupled moment. Taking the slip effect into account, the load capacity and attitude angle of the bearing reduce by less than 10% and 4.5 deg, respectively. The effect of slip on the load capacity could become the most significant at approximately Λp=2 corresponding to the maximum load capacity obtained without considering the slip effect. The optimum values of spiral angle and groove depth ratio corresponding to the maximum load capacity and minimum attitude angle are related to the feeding parameter.

This study illustrates the effects of radiation, convective heating, activating energy, and second order velocity slip condition on the magnetohydrodynamic (MHD) Carreau nanofluid and heat/mass transfer. Brownian motion and thermophoresis effects are used in mathematical models of the Carreau nanofluid. A system of nonlinear coupled differential equations is created from the governing equations. The altered equations' solutions are obtained. Furthermore, a graphic representation of the effects of temperature, dimensionless velocity, and nanoparticle concentration profile is provided.

CFD investigation of solid–liquid two-phase flow in sewer pipes: influence of inlet slip velocity on particle resuspension

This work examines the influence of Cattaneo–Christov heat flux on magneto hydrodynamic (MHD) flow of non-Newtonian fluids; Jeffrey, Maxwell and Oldroyd-Bover a stretching sheet, integrating activation energy and velocity slip effects. The governing partial differential equations are converted into similarity-based nonlinear ordinary differential equations and solved numerically utilizing MATLAB’s BVP5C solver. Results reveal that higher relaxation-to-retardation ratios, larger Deborah numbers and increased slip significantly reduce fluid velocity with Oldroyd-B fluid and Maxwell fluid exhibits the greatest decrease, while Jeffrey fluid is minimally affected. Thermal Deborah number enhances heat flux relaxation, leading to elevated temperature profiles and a thicker thermal boundary layer. Increased activation energy slows chemical reactions but raises nanoparticle concentration with Jeffrey fluid. Validation against previous studies confirms the accuracy and reliability of the solutions. Furthermore, skin friction decreases with magnetic parameters, relaxation ratio and slip, whereas the Nusselt number increases with heat flux relaxation and radiation but diminishes due to Brownian motion, thermophoresis and non-uniform heat. Sherwood number rises with Lewis number, reaction rate, Brownian motion and reaction strength but decreases with thermophoresis and activation energy. Maxwell fluid consistently exhibits the most favourable transport rates, Jeffrey fluid the least, with Oldroyd-B liquid intermediate due to rheological differences.

This study addresses the growing need for advanced thermal regulation by investigating the nonlinear flow behavior of a hybrid nanofluid within a porous medium under realistic physical conditions. The primary objective is to evaluate how slip effects, variable viscosity, and thermophoresis influence heat and mass transfer performance when multiple physical mechanisms act simultaneously. A comprehensive mathematical model is developed to describe the momentum, thermal, and concentration transport of a water-based hybrid nanofluid containing two distinct nanoparticle species, subjected to magnetic field effects, thermal radiation, and internal heat generation. The governing partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformations and solved numerically via a shooting technique under appropriate boundary conditions. The novelty of this work lies in the combined consideration of slip velocity, thermophoresis-driven nanoparticle migration, and variable viscosity within a magnetohydrodynamic porous framework. The present study is relevant to practical applications, including microelectronics cooling, advanced heat exchangers, and maritime thermal management. The results indicate that increasing thermophoretic effects and internal heat generation significantly influence transport behavior, as enhanced particle migration reduces concentration gradients while internal heating shifts the heat transfer mechanism toward convection-dominated regimes. Further, the findings reveal that hybrid nanofluids exhibit enhanced thermal control capabilities, with thermophoresis and slip mechanisms playing a key role in improving heat and mass transfer rates, highlighting their potential for high-performance cooling applications.

This numerical study highlights the sensitivity analysis of the ternary copper-alumina-titania/water hybrid nanofluid flow over a permeable cylinder under the influence of magnetic field (MHD), curvature parameter and velocity slip. The governing boundary layer and energy equations are simplified and numerically solved using the bvp4c solver available in Matlab. Meanwhile, the response surface methodology (RSM) and sensitivity analysis are employed using Minitab software to assess the contribution and significance of these physical factors on the selected responses, namely, heat transfer and skin friction coefficients. The findings indicate that velocity slip (factor C) has the most dominant influence on heat transfer enhancement, while curvature (factor B) is the primary determinant of the skin friction coefficient. Moreover, interaction effects, particularly BC (combination of curvature and velocity slip factors) and AC (combination of magnetic parameter and velocity slip factors), significantly impact the flow behaviour, emphasizing the importance of considering coupled parameter interactions for optimizing system performance. The results highlight the practical implications of these findings in heat exchangers, industrial cooling systems, and thermal management technologies, where precise control of flow and heat transfer is crucial.

Thermal transport performance of ternary hybrid nanofluids in Darcy-Forchheimer mixed convection with slip velocity and heat generation

This study looks into the magneto hydrodynamics (MHD) flow of a micropolar hybrid nanofluid in a stretching permeable arterial channel. It considers external magnetic and electric fields, along with velocity slip and thermal effects. Transforming the nonlinear momentum, micro rotation, energy, and concentration equations into a system of ordinary differential equations using similarity transformations, and solve this system with a collocation shooting method. Validation against Newtonian and non-micropolar limits shows deviations below 1.8%, confirming the model’s reliability. The results indicate that increasing the Hartmann number ( M = 0 − 4) reduces axial velocity by up to 27% and raises nanoparticle concentration by 15–20%. A higher thermophoresis parameter (Nt = 0.1 − 0.5) increases the wall Nusselt number by 12%. In contrast, Brownian motion (Nb = 0.2 − 0.8) lowers the Sherwood number by 9%. The micropolar coupling parameter greatly affects microrotation and reduces wall shear stress by 18% compared to Newtonian flow. These findings show that external fields can effectively control nanoparticle transport and suggest promising applications for better intravascular drug delivery.

Experimental study on the resetting of IRSL and IRPL signals induced by frictional heating in rocks at seismic slip velocities

This study applied decision-tree (DT) machine learning models to determine whether this approach is more accurate when classifying slip outcome during walking, and to refine the cutoff thresholds of each slip type. Kinematic data of the heel were collected from 50 adults (23.1 [3.6]y) during 516 walking trials. The first DT model (DT1) was trained with heel slip distance and heel slip velocity as predictor variables; the second model (DT2) added heel slip acceleration as the third predictor variable. Walking trials were first classified as a no-slip, slip-recovery, or slip-fall outcome based on visual observation, and these classifications were used as response labels to train the DT models. Results indicated that both DT models yielded different thresholds in classifying slip outcomes and were similar to thresholds suggested in previous studies. However, both DT models resulted in 4.1% to 7.6% greater overall prediction accuracy compared with previously suggested thresholds, with DT2 generally performing better than DT1. Although the improved performance was offset by a ∼7% lower sensitivity when classifying no-slip outcomes and greater model complexity, future studies examining slip responses during gait should incorporate the thresholds derived from the DT2 model to most accurately classify the type of slip outcome.

Artificial neural network algorithm for hybrid nanofluid in Jeffery-Hamel flow under Thompson and Troian velocity slip effects: Comparison of Xue and Yamada-Ota models

With the shift towards virtual verification in automotive development, virtual tire sampling is crucial. Existing finite-element (FE) methods, however, are computationally expensive and prone to convergence issues under complex combined loads involving camber and sideslip. This paper proposes a novel pure-condition-based prediction method to overcome these limitations, eliminating the need for direct full-camber-sideslip-condition FE simulation. Our major contributions include: Firstly, developing an ABAQUS subroutine to decouple the effects of contact pressure and slip velocity on friction based on the Savkoor model; secondly, conducting experimental friction tests on tire rubber to analyze camber and sideslip angle influences; and lastly Introducing an equivalent camber-to-sideslip transformation framework that incorporates carcass layout and lateral force effects. Validation confirms that pure-sideslip friction characteristics can be effectively extended to camber sideslip combined conditions by equivalencing camber with sideslip angle. This approach provides an accurate and computationally efficient solution for virtual tire sampling, balancing predictive performance with practical application needs in tire-vehicle matching.

Ferrofluids flowing over a hydrophobic surface are important in enhancing heat transfer properties for mechanical devices and reducing friction on the surface for efficient use in lubrication. This effort investigates the motion of water-based ferrofluid on a vertical hydrophobic stretching sheet exposed to a magnetic field. In this flow, natural convection and temperature flow in the system are demonstrated. A non-dimensional transformation is used to change the mathematical model into a set of nonlinear formulations of differential equations. Due to the hydrophobic surface, the slip effects are considered. Finally, the system of nonlinearly coupled equations is simulated using the finite element technique. All the aspects of the numerical solution are validated with the previously published literature. The significance of surface roughness, magnetostatic field, and Prandtl number on the velocity profiles, convective boundary layer, and temperature is explained. The hydrophobic surface, the velocity slip parameter enhances the convective boundary layer and roughness factor plays a crucial role in the heat transfer enhancement and self-cleaning purposes in biomedical applications.

Reliable measurement of multiphase flow is fundamental to production evaluation in complex oil and gas wells. However, conventional sensors often suffer from low integration, limited measurement capability, and potential environmental impact. To address these challenges, a photoelectric composite three-phase flow sensor is developed, integrating multiple electrode rings for water holdup and liquid-phase velocity measurement, with dual optical-fiber probes for gas holdup and gas-phase velocity detection. A slip model is further applied to quantify the dependence of slip velocity on liquid holdup based on measured phase rates. Experimental results demonstrate high sensitivity to bubble-flow structures, accurate extraction of gas holdup and phase velocities, and stable full-range water holdup calibration from 0% to 100% at 5 V and 15 V with effective temperature and salinity compensation. And compared with existing technologies, the sensor designed in this paper has the advantages of high integration, a simple structure, multiple measurement parameters, and higher water-holding capacity resolution in low-saturation areas, providing more advanced technical means for conventional profile three-phase flow logging.

The deterioration of friction on icy roads poses a significant threat to driving safety, particularly under meltwater film conditions where friction rapidly declines, becoming a critical issue in transportation engineering. In this study, a novel bionic tread structure is proposed, inspired by the anti-slip denticle features of Scylla serrata , which effectively grip hard objects in fluid environments, and the superior ice-gripping performance of reindeer hooves. Friction tests on wet ice were conducted to systematically evaluate the influence of denticle angles under varying water film thicknesses. In addition, the dynamic friction performance of conventional patterned tread blocks (CPT), bionic tread blocks (PT), and bionic structures embedded with rigid protrusions (BST) was compared under different water film thicknesses, normal loads, and slip velocities. The results indicate that the 64° denticle angle yields a higher dynamic coefficient of friction (DCOF), with an increase of 18%–27% compared to 38° and 90° configurations across all tested conditions. BST exhibited superior DCOF to both PT and CPT under various load and velocity conditions, and its friction performance on wet ice was better than that on dry ice. This study provides new insights and a potential design strategy for high-traction bionic winter tires.

The current study mainly explores unsteady, laminar and mixed convection boundary layer flow of Casson ternary hybrid nanofluid in Dary-Forchheimer porous medium about a rotating sphere with slip velocity condition. The study considers quadratic thermal radiation and Cattaneo-Christov heat flux model subjected to convective heating condition with entropy generation for efficient heat transfer and irreversible processes. The non-dimensional similarity variables are employed to convert the governing equations, nonlinear partial differential equations into nonlinear coupled ordinary differential equations. An implicit finite difference approach known, as Keller-box method numerically applied to solve the flow problem. The main findings for thermal and flow behavior of ternary hybrid nanofluid containing silver, titanium and alumina nanoparticles with blood as base fluid are presented through graphical and tabular forms. The outcomes depict that the magnetic field, inertia constant, unsteady and material parameter increases the velocity field, while angular velocity decreases. Moreover, the presence of thermal radiation and convective heat parameters highly optimize the thermal distributions of boundary layer, whereas the coefficient of heat transfer decreases. Conversely, thermal time relaxation and unsteadiness parameters lead to a decrease in temperature field and thermal boundary layer thickness for hybrid and ternary hybrid nanofluids. Entropy production reduces as magnetic parameter strengthen and increase with the Brinkmann number and convection parameter. The findings are confirmed a strong correlations with previous literature. Moreover, Response Surface Methodology and sensitivity analysis are established to quantify the effects of input parameters on thermal performance with values [Formula: see text] = 99.99%, and [Formula: see text]-adjusted = 99.98%, which confirm reliability of the result. The sensitivity analysis depicted that heat transfer rate is high sensitivity to heat generation, moderate sensitivity to nanoparticle volume fraction, and low sensitivity to radiation parameter with their maximum point 1.4178, 0.9898, and 0.4425, respectively. Further, ternary hybrid nanofluid reveals that greater heat transfer enhancement rate of [Formula: see text] than heat transfer enhancement of hybrid nanofluid [Formula: see text] at maximum value.