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In this investigation, the laminar heat transfer of kerosene nanofluid/multi-walled carbon nanotubes in the microchannel heat sink is studied. The considered microchannel is two layers in which the length of bottom layer is truncated and is equal to the half of the length of bottom layer. The length of microchannel bottom layer is L = 3 mm, and the length of top layer is L1 = 1.5 mm. The microchannel is made of silicon, and each layer of microchannel has the thickness of t = 12.5 µm. Along the external bottom wall, the sinusoidal oscillating heat flux is applied. The top external and lateral walls are insulated, and they do not have heat transfer with the environment. The results of this research revealed that in different Reynolds numbers, applying oscillating heat flux significantly influences the profile figure of Nusselt number and this impressionability is obvious in Reynolds numbers of 10 and 100. Also, by increasing the slip velocity coefficient on the solid surfaces, the amount of minimum temperature reduces significantly which behavior remarkably entails the heat transfer enhancement.

In this research, the laminar flow and heat transfer of kerosene/MWCNT nanofluid in a novel design of a double-layer microchannel under the influence of oscillating heat flux and slip boundary condition have been studied. This research has been investigated in the dimensionless lengths of (λ1) 1/3, 2/3 and 3/3 and dimensionless slip velocity coefficients ranging from 0.001 to 0.1. The suspension of nanoparticles in kerosene as the base fluid has been studied in Reynolds numbers of 1–100 and volume fractions of 0–8%. The results indicate that, by using novel design of double-layer microchannel in λ1 = 1/3, the maximum rate of performance evaluation criterion is obtained and by increasing the slip velocity coefficient, the amount of PEC becomes significant. Among the studied cases, in all Reynolds numbers and volume fractions, the dimensionless length of 1/3 has the maximum amount of friction coefficient. Also, by enhancing the volume fraction of nanoparticles, slip velocity coefficient, Reynolds number and significant reduction in thermal resistance of solid wall, Nusselt number enhances.

The conversion of heat from the mechanical energy in a fluid basically depends upon the internal friction and the effect of viscosity. Joule dissipation along with Darcy frictional force that is used as a measure of the resistance to flow in a porous medium has an important role in various systems. Therefore, the present article aims to investigate the characteristic of velocity slip considering the flow of radiative hybrid nanofluid over an elongating and contracting surface. The flow file enriches for the inclusion of both the Joule, i.e., magnetic dissipation and the Darcy dissipation, in the energy equation. The complex system then transformed to ordinary as well as nondimensional form due to the adoption of particular similarity rules. Further, a traditional numerical technique equipped with shooting-based Runge–Kutta is used for the solution of the transformed designed model. The present model is validated with the earlier established system in the particular case of base fluid water with good agreement, and the parametric behavior is projected via several graphs and streamlines. However, the important outcomes of the study are presented as the concentration of solid nanoparticles that controls the velocity profiles, whereas the reverse trend is revealed in fluid temperature. Further, suction/injection provides greater control in decelerating the fluid velocity for the interaction of velocity slip.

This study is concerned with the three-dimensional (3D) stagnation-point for the mixed convection flow past a vertical surface considering the first-order and second-order velocity slips. To the authors’ knowledge, this is the first study presenting this very interesting analysis. Nonlinear partial differential equations for the flow problem are transformed into nonlinear ordinary differential equations (ODEs) by using appropriate similarity transformation. These ODEs with the corresponding boundary conditions are numerically solved by utilizing the bvp4c solver in MATLAB programming language. The effects of the governing parameters on the non-dimensional velocity profiles, temperature profiles, skin friction coefficients, and the local Nusselt number are presented in detail through a series of graphs and tables. Interestingly, it is reported that the reduced skin friction coefficient decreases for the assisting flow situation and increases for the opposing flow situation. The numerical computations of the present work are compared with those from other research available in specific situations, and an excellent consensus is observed. Another exciting feature for this work is the existence of dual solutions. An important remark is that the dual solutions exist for both assisting and opposing flows. A linear stability analysis is performed showing that one solution is stable and the other solution is not stable. We notice that the mixed convection and velocity slip parameters have strong effects on the flow characteristics. These effects are depicted in graphs and discussed in this paper. The obtained results show that the first-order and second-order slip parameters have a considerable effect on the flow, as well as on the heat transfer characteristics.

The following study investigates the effects of Rabinowitsch fluid on journal bearing lubrication under the influence of velocity slip and variable viscosity. The finite difference method is used to produce a numerical solution to the 2D Modified Reynolds equation. The findings verify the previous results, which indicate that the dilatant (shear-thickening) fluid pressure is higher than the Newtonian and pseudo-plastic (shear-thinning) fluids. The results show that in the presence of slip, the pressure distribution rises with the piezo- viscosity parameter (variable viscosity) by up to 75%. Compared to the Newtonian, and pseudo-plastic (shear thinning) fluid, the dilatant (shear-thickening) fluid produces the highest pressure. A higher eccentricity ratio, slip-velocity, piezo-viscosity parameter, and dilatant fluid enhances the load-carrying capacity. The reduction in the attitude angle plays an integral part in the load-carrying capacity of the journal bearing. The attitude angle decreases for all values of the bearing ratio; the dilatant fluid has the most significant reduction in attitude angle compared to the Newtonian and pseudo-plastic fluids. Slip effects reduce the attitude angle, and a further reduction occurs when the piezo-viscosity and slip factors are combined. The slip-velocity, lower values of the bearing’s length to diameter ratio, greater piezo-viscosity, higher values of the eccentricity ratio, and the dilatant fluid minimize friction. The Rabinowitsch fluid properties and the addition of both slip and variable viscosity increase bearing performance by increasing the pressure distribution, load-carrying capacity of the journal bearing and reduction of the frictional parameter, and should be considered when optimizing pressure, load, and friction for the creation of the ideal journal bearing.

This article aims to examine an unsteady 2-D laminar flow of magnetohydrodynamic fluid caused by an elastic surface immersed in a permeable medium under the influence of thermal radiation and extended heat flux. Thermal conductivity and viscosity both are supposed to vary with temperature. This flow model also includes velocity slip, heat source, and joule heating. The governing equations of the fluid, including momentum and energy equations, of the proposed problem are transfigured into a system of interconnected non-linear ordinary differential equations through similarity transformations. The resultant equations are solved efficiently by employing the shooting technique in combination with the fourth-order Runge-Kutta method. Numerical values and the effect of numerous governing factors on the flow field, temperature distribution, local skin friction coefficient, and Nusselt number are showcased via graphs and tables. The investigation reveals that velocity slip, heat source, and porosity parameters enhance the temperature field while diminishing the velocity field. Furthermore, the velocity slip parameter notably reduces both the coefficient of skin friction and the Nusselt number.

The slurry pump, which forms the core equipment of the deep-sea mining (DSM) system, provides lifting power for the ore from the seabed to the sea level, which is crucial for the safety of coarse ore particle transportation. Velocity slip plays a significant role in revealing the migration of the pump particles. Therefore, this study analyzes the velocity slip in a slurry pump using the computational fluid dynamics–discrete element method (CFD-DEM) for the first time. The relationship between the pump head and velocity slip was proposed and verified in this study based on the velocity triangle and Euler equation of the solid-liquid two-phase flow in the impeller. The effects of different particle sizes on the velocity slip are compared in detail. According to the computational results, the head depends on the larger velocity slip of the impeller outlet and lower velocity slip at the inlet. The peak value of the velocity slip was significantly reduced, and the peak position of the velocity slip and zero-point position moved backward for particle sizes ranging between 5-15 mm. This study provides a reference for the problems of particle migration and velocity slip in slurry pumps.

Archaeological structures built across active faults and ruptured by earthquakes have been used as markers to measure the amount of displacement caused by ground motion and thus to estimate the magnitude of ancient earthquakes. The example used in this study is the Crusader fortress at Tel Ateret (Vadum Iacob) in the Jordan Gorge, north of the Sea of Galilee, a site which has been ruptured repeatedly since the Iron Age. We use detailed laser scans and discrete element models of the fortification walls to deduce the slip velocity during the earthquake. Further, we test whether the in-situ observed deformation pattern of the walls allows quantification of the amount both sides of the fault moved and whether post-seismic creep contributed to total displacement. The dynamic simulation of the reaction of the fortification wall to a variety of earthquake scenarios supports the hypothesis that the wall was ruptured by two earthquakes in 1202 and 1759 CE. For the first time, we can estimate the slip velocity during the earthquakes to 3 and 1 m/s for the two events, attribute the main motion to the Arabian plate with a mostly locked Sinai plate, and exclude significant creep contribution to the observed displacements of 1.25 and 0.5 m, respectively. Considering a minimum long-term slip rate at the site of 2.6 mm/year, there is a deficit of at least 1.6 m slip corresponding to a potential future magnitude 7.5 earthquake; if we assume ~5 mm/year geodetic rate, the deficit is even larger.

Purpose The purpose of this study is to analyze the heat transfer and flow enhancement of an Al2O3-water nanofluid filling an inclined channel whose lower wall is embedded with periodically placed discrete hydrophobic heat sources. Formation of a thin depletion layer of low viscosity over each hydrophobic heated patch leads to the velocity slip and temperature jump condition at the interface of the hydrophobic patch. Design/methodology/approach The mixed convection of the nanofluid is analysed based on the two-phase non-homogeneous model. The governing equations are solved numerically through a control volume approach. A periodic boundary condition is adopted along the longitudinal direction of the modulated channel. A velocity slip and temperature jump condition are imposed along with the hydrophobic heated stripes. The paper has validated the present non-homogeneous model with existing experimental and numerical results for particular cases. The impact of temperature jump condition and slip velocity on the flow and thermal field of the nanofluid in mixed convection is analysed for a wide range of governing parameters, namely, Reynolds number (50 ≤ Re ≤ 150), Grashof number ( 103≤Gr≤5×104), nanoparticle bulk volume fraction ( 0.01≤φb≤0.05), nanoparticle diameter ( 30≤dp≤60) and the angle of inclination ( −60°≤σ≤60°). Findings The presence of the thin depletion layer above the heated stripes reduces the heat transfer and augments the volume flow rate. Consideration of the nanofluid as a coolant enhances the rate of heat transfer, as well as the entropy generation and friction factor compared to the clear fluid. However, the rate of increment in heat transfer suppresses by a significant margin of the loss due to enhanced entropy generation and friction factor. Heat transfer performance of the channel diminishes as the channel inclination angle with the horizontal is increased. The paper has also compared the non-homogeneous model with the corresponding homogeneous model. In the non-homogeneous formulation, the nanoparticle distribution is directly affected by the slip conditions by virtue of the no-normal flux of nanoparticles on the slip planes. For this, the slip stripes augment the impact of nanoparticle volume fraction compared to the no-slip case. Originality/value This paper finds that the periodically arranged hydrophobic heat sources on the lower wall of the channel create a significant augmentation in the volume flow rate, which may be crucial to augment the transport process in mini- or micro-channels. This type of configuration has not been addressed in the existing literature.

Flow field, heat transfer and entropy generation of forced convection of CuO-water nanofluid is investigated in a parallel plate microchannel in the presence of magnetic field. Two vertical micromixers are attached on the hot walls of the microchannel. To consider the effect of the Brownian motion of the nanoparticles, the KKL model is utilized to estimate thermal conductivity of the nanofluid. The governing equations, which are accompanied with the slip velocity and temperature jump boundary conditions, are solved by the finite volume method (FVM) and SIMPLER algorithm. The study is conducted for the Reynolds numbers in the range of 10 < Re < 100, Hartmann numbers in the range of 0 < Ha < 40, Knudsen numbers ranging of 0 < Kn < 0.1 and volume fraction of nanoparticles ranging of 0 < φ < 0.04. The results show that when the Hartmann or Reynolds numbers, or the volume fraction of nanoparticles increase, the average Nusselt number and the total entropy generation rate increase. Furthermore, when Knudsen number increases, the total entropy generation rate decreases.