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Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated. [ABSTRACT FROM AUTHOR]

Abstract This work presents a novel approach to investigating the slip effect in nanofiber filter media. Electrospun nanofiber media with high efficiency and low pressure drop were produced at different concentrations and durations. The surface and cross-sectional morphology of nanofiber media were studied using FE-SEM. Fiber orientation and diameter distributions were also examined. The 3D virtual nanofiber media was modeled using this information along with the experimentally measured porosity and thickness of the media. The effect of the slip phenomenon in nanofiber media was studied numerically, and the results were compared to experimental data. Excellent agreements were found between the measured and simulation results. Additionally, filtration simulations considering aerosols injected with airflow through the nanofibrous filter media were conducted by considering the slip effect, and the effect of filter structure on filtration performance (removal efficiency and pressure drop) was investigated.

In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al2O3, for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/Dh), and volume fraction of Al2O3 nanoparticles (ϕ) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or ϕ would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/Dh ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and ϕ = 0.1 (Pr = 0.729). Finally, Nuavg, Nux, U/Um, and ReCf were corelated with Kn, Pr, Re, and x/Dh with proper coefficient of determination (R2) values. [ABSTRACT FROM AUTHOR]

This work presents a novel approach to investigating the slip effect in nanofiber filter media. Electrospun nanofiber media with high efficiency and low pressure drop were produced at different concentrations and durations. The surface and cross-sectional morphology of nanofiber media were studied using FE-SEM. Fiber orientation and diameter distributions were also examined. The 3D virtual nanofiber media was modeled using this information along with the experimentally measured porosity and thickness of the media. The effect of the slip phenomenon in nanofiber media was studied numerically, and the results were compared to experimental data. Excellent agreements were found between the measured and simulation results. Additionally, filtration simulations considering aerosols injected with airflow through the nanofibrous filter media were conducted by considering the slip effect, and the effect of filter structure on filtration performance (removal efficiency and pressure drop) was investigated. [ABSTRACT FROM AUTHOR]

Hybrid nanofluid flow analyses have obtained a lot of attention due to their usefulness as coolants in hybrid electric vehicles, health care, thermal exchange systems, cancer thermo-therapy, nuclear reactors, microfluidics, aerospace, acoustics, naval structures and power generation in power plants, This research investigated the impacts of slip and induced magnetic field effects on tangential hyperbolic hybrid nanofluid over a stretching wedge with non-uniform heat source. The nanoparticles used in this work are aluminum oxide (Al2O3) and copper (Cu) while water is the based fluid. The fluid flow are modelled as partial differential equations (PDEs). These are transformed to their corresponding ordinary forms (ODEs), which are solved by the homotopy analysis technique with the aid of similarity variables. The impact of prominent physical factors on fluid temperature, velocity, induced magnetic field, local Nusselt number and drag coefficient is explored. Tables and graphs are used to display the results which agreed with the existing ones in the literature. [ABSTRACT FROM AUTHOR]

Darcy-Forchheimer model has been used to consider the mathematical and statistical aspects of Prandtl nanofluid flow on a stretched curvy geometry, with homogenic-heterogenic reactions, nonlinear radiation, exponential heat, Joule heating, velocity slip, and convective heat conditions. An account of entropy significance has been given to boost the applicability of the study. The 4-5th ordered numerical tool, Runge-Kutta-Fehlberg, has been employed to establish the plots for the considered flow. ANOVA and Taguchi optimisation technique is used to obtain the optimal condition in enhancing the heat transfer rate for modelled mathematical problem. Here, the study reveals that the increasing homo-heterogenic strength parameters foster the concentration profile. The study also found that the thermal curves are positively affected by the radiation parameter and the temperature differential parameter. In addition to this, graphical portraits of isotherms and streamlines have been given to characterise the flow and heat pattern. Taguchi method reveal that first level of Prandtl number, magnetic parameter, Weissenberg number, heat source parameter and third level of curvature parameter, produce maximum Nusselt number. Heat source parameter has large contribution of about 49.45% among the other parameters and Prandtl number has the least contribution of about 1.4% for optimisation.

Microchannels are widely used across various industries, including pharmaceuticals and biochemistry, automotive and aerospace, energy production, and many others, although they were originally developed for the computing and electronics sectors. The performance of microchannels is strongly affected by factors such as rarefaction and viscous dissipation. In the present paper, a numerical analysis of the performance of microchannels featuring rectangular, trapezoidal and double-trapezoidal cross-sections in the slip flow regime is presented. The fully developed laminar forced convection of a Newtonian fluid with constant properties is considered. The non-dimensional forms of governing equations are solved by setting slip velocity and uniform heat flux as boundary conditions. Model accuracy was established using the available scientific literature. The numerical results indicated that viscous dissipation effects led to a decrease in the average Nusselt number across all the microchannels examined in this study. The degree of reduction is influenced by the cross-section, aspect ratio and Knudsen number. The highest reductions in the average Nusselt number values were observed under continuum flow conditions for all the microchannels investigated.

AbstractThe study of flow of blood through the blood vessels carries nanoparticles which opens new ways in the research. This study explores one such flow of trihybrid nanoparticles suspended in blood over a curved stretching surface which undergoes the Darcy-Forchheimer porosity model. The analysis employs Cattaneo-Christov heat flux model along with chemical reaction, linear heat source allowing the surface to slip with heat and mass convection. The trihybrid nanofluids consist of a mixture of titanium dioxide, iron oxide, and silica nanoparticles mixed with base fluid (blood) to generate TiO2-Fe3O4-SiO2/blood hybrid nanofluids. Runge-Kutta-Fehlberg 4th–5th order technique, a robust numerical technique, was employed to obtain mathematical solutions. Throughout the numerical process, all parameters, except those under examination, were kept at their default values. Additionally, various plots were generated based on numerical results to illustrate the obtained data. The findings indicate that an increase in the Forchheimer number and porosity results in a reduction in the velocity profile. Furthermore, an increase in the radiation parameter and thermal Biot number leads to an increase in the temperature profile, while the temperature profile decreases with an increase in the thermal relaxation parameter. Additionally, an increase in the chemical reaction parameter and concentration Biot number results in an increase in the concentration profile. Moreover, higher Brinkman and Prandtl numbers enhance the Nusselt number. [ABSTRACT FROM AUTHOR]

Non-Newtonian fluids have industrial and technical applications. Several liquids in nature do not have Newtonian viscosities. These fluids include applesauce, polymer mixtures, colloidal and fermented mixtures, clay glazes, paints, lubricants, cement, slush, shampoos, mud, foodstuffs, paper paste, aqueous froths, etc. This study considers stratified flow and variable heat transmission across a stretched surface. The magnetic hydrodynamics and slips' impacts are illustrated. On the basis of flow assumptions, the mathematical model was created using the Navier–Stokes equation. The boundary layer approximation approach is provided PDEs by working on the Navier–Stokes equation under flow assumptions. This system is converted into ODEs through similarity transformations. Dimensionless system is elucidated by means of RKF-45 technique. The concerning physical parameter effects are elaborated numerically as well as graphically. Based on the findings of the comparison, it was determined that Williamson fluid had superior performance in terms of fluid velocity compared to Maxwell fluid. Furthermore, the temperature of the fluid is greater for booming values of both e 1 and ε parameters. [ABSTRACT FROM AUTHOR]

This paper deals with a numerical study of heat and mass transfer in a vacuum membrane distillation unit used for desalination. The governing equations expressing the conservation of mass, momentum, energy, and species for the saline solution with coupled boundary conditions, as well as the mass and energy balances on the membrane sides, were solved numerically. The slip boundary condition due to the membrane's hydrophobicity was also taken into consideration. The numerical model was validated with available experimental data and found to be in good agreement. The effects of operational parameters on pure water production and temperature polarization were presented and discussed. A comparison between three flat-sheet membranes commonly used in vacuum membrane distillation was conducted under the same operating conditions. In addition, a comparison between the Nusselt and Sherwood numbers obtained in this study and correlations commonly used in the literature was conducted, which revealed remarkable deviations between models along the channel. The impact of the heat and mass transfer coefficients on the transmembrane permeate mass flux variation is found to be important. [ABSTRACT FROM AUTHOR]

MHD mixed convection heat transfer of an ionized gas in a vertical microchannel filled with a porous medium is simulated and discussed in this study. The considered flow is hydrodynamically and thermally developing with Local Thermal Non – Equilibrium (LTNE) between the gas and the solid matrix. The Darcy – Brinkman – Forchheimer model is utilized to describe the flow filed in the porous medium. Moreover, both velocity – slip and temperature – jump boundary conditions are applied to the gas at the walls. The governing equations are solved by the finite – volume method. Results are presented and discussed in terms of the developed profiles of velocity and temperature of the constituents as well as the variations of the Nusselt number through the microchannel, the numerical values of the hydrodynamic and thermal entry lengths, and the fully – developed Nusselt number for different conditions. It is found that direct relations exist between the fully – developed Nusselt number and the Richardson number, the Reynolds number, the Hartmann number, the Biot number, the thermal conductivity ratio, and the Forchheimer number. With rise in the Knudsen number or the Darcy number, however, the Nusselt number deteriorates. The results indicate that the Knudsen number, the Hartmann number, the Biot number, and the thermal conductivity ratio are the most influential parameters on the fully – developed Nusselt number. It is envisaged that a tenfold increase in the Hartmann number and a hundredfold elevation in the Knudsen number are accompanied by 14% rise and 42% reduction in the fully – developed Nusselt number, respectively. [ABSTRACT FROM AUTHOR]

In the era of sustainable development goals (SDGs), energy efficient heat transfer systems are a must. Convective heat transfer within circular pipes is an important field of research on a rarely addressed limitation of fluid flows. Vacuum solar tubes is one of many applications that could benefit from the existence of nanoparticles, Al2O3, for example, to enhance the heating of air or water steam. The current research investigates the impacts of the Reynolds number (Re), Prandtl number (Pr), Knudsen number (Kn), aspect ratio (x/Dh), and volume fraction of Al2O3 nanoparticles (ϕ) on the Nusselt number (Nu) under constant wall heat flux conditions. An axisymmetric computational fluid dynamics (CFD) analysis of the nanofluid flowing at the entrance region of a circular pipe was conducted under a slip flow at steady-state developing laminar conditions using the Ansys-Fluent 2018 software package. A mesh sensitivity analysis was conducted, and a proper number of mesh elements was selected. The results showed that an increasing Re and/or ϕ would result in an increasing Nu. The dependance of Nu on Kn was strong due to the high slip values and temperature jump. An increasing x/Dh ratio resulted in reduced Nu values. The major impact was due to Kn, which caused a reduction of up to 40% in the Nu value due to slip conditions. However, there was an enhancement of 2.5% in the heat transfer due to the addition of nanoparticles, which was found at Re = 250, Kn = 0.1, and ϕ = 0.1 (Pr = 0.729). Finally, Nuavg, Nux, U/Um, and ReCf were corelated with Kn, Pr, Re, and x/Dh with proper coefficient of determination (R2) values.

“The boundary layer flow past the stretching surface by the velocity slip and the temperature jumping boundary situations is the imperative type of the flow and temperature transports happening in a number of engineering and industrial applications. Keeping in this mind, the magnetohydrodynamic (MHD) flow and temperature transport of the Jeffreys nanoliquid past a stretching sheet by the non-uniform temperature source and/or sink is explored in the current investigation. The governing scheme of the partial differential equations represents the prescribed problem and is condensed into the non-linear ordinary differential equations with the help of similarity transformations. The revised non-dimensional equations are solved computationally making use of the Runge-Kutta-Fehlberg 45 order method and the shooting method. The results are comparing by the published work for some limiting cases and they are examined to the outstanding agreements. The impacts of all flow significant parameters are traced in terms of the tables and graphical profiles. This is established that, both initial and second order velocity slip parameters trim downs the thickness of momentum boundary layers and therefore decreases the velocity as a results of these one might found the increases in the thermal boundary layer.” The boundary layer thickness and the fluid velocity increases with increase in Deborah number.

Understanding heat transfer in slip flow scenarios involving a stretching or shrinking sheet has immediate applications in numerous fields, including materials processing, production, and temperature management systems. This information supports the development of novel heat transfer methods and systems. Therefore the present study focuses on stagnant point flow and discusses the dynamics and thermal characteristics of ternary hybrid nanofluids with the application of Tiwari and Das nanofluids. It is assumed that the ternary hybrid nanofluids are present on a stretching/shrinking sheet. The slipping effects and suction boundary conditions are implemented. The simulation will be performed using the finite element method with the software package COMSOL Multiphysics 6.0. The system of ordinary differential equations (ODEs) obtained through similarity transformation will be solved numerically to obtain simulation results. The average velocity, temperature profiles, and Nusselt number patterns using non-dimensional parameters are also analyzed. These non-dimensional parameters include the stretching/shrinking parameter, ranging from −1 to 0.5, and the suction parameter and slip flow parameter, both ranging from 0 to 2. The ternary hybrid nanofluids under investigation consist of a combination of TiO2, Silver-Ag, and ZnO particles in a base fluid (water). The volume fraction of these particles in the base fluid will be tested from 0.03 to 0.3. It was found that when there are no suction and no slipping effects, the Nusselt number decreases for the shrinking case and increases for the stretching case. It is also concluded that when there is no suction or slipping effect, the average temperature profile increases in the shrinking case and decreases in the stretching case.

Partially ionised fluids subject to an external magnetic field results in a completely different dynamical behaviour. Very few studies are conducted to explore the fascinating properties of Hall current and Ion slip in fluid flows. Flow over a Riga plate with MHD Ion and Hall currents, nonlinear thermal radiation is still rare. We aim to analyse the inclined stagnation point slip flow of Couple Stress fluid over a stretched horizontal Riga plate to close this gap. The flow problem is modelled using Navier stokes theory along with energy conservation and then principal partial differential equations are converted into ordinary differential equations. The governed system is solved mathematically by numerical technique RK Fehlberg method. The behaviour of fluid is described through graphs including fluid’s motion and energy. Local surface skin friction coefficients and local heat and mass flux at surface are the concerned physical magnitudes which are described through graphs and tables and are highly recommended in practical solicitations in numerous production plants and manufacturing workshops. Thermally radiative MHD flow with Ion Hall currents are broadly used in thermal controlling systems, spectro scopy, microchip technology, Magnetohydrodynamic energy conversion campaigns, exploration and expansion for high & low efficiency release, power-driven & power generation structures, MHD accelerations & thrusters, and drift regulator in hypersonic and automobiles.

- The main goal of this article is to outline the key elements of activation energy that govern the slip flow of Carreau fluid over a non-linear stretched surface with heat transfer. By using the Arrhenius relation, activation energy aspects are included. Brownian diffusion and thermophoretic effects are shown through the study of nanoparticle dispersion using the Buongiorno model. The governing issue was first formulated as PDEs with appropriate boundary conditions, which were then converted into non-linear ODEs by applying a comparable transformation. Then, using Runge-Kutta integration and shooting techniques, the solution to the obtained complex differential system is discovered. Graphs reveal the effect of flow on linked profiles with respect to parameters. A published study that compares the current result describes the accuracy and reliability of the work. Through graphs and tables, the amount of engineering interest for shear thinning and thickening aspects of Carreau fluid is assessed. This includes wall drag coefficient, heat, and mass flux at the surface in comparison. It is calculated that by increasing non-linearity index velocity field depreciates for n = 0.5 and n = 1.5. Additionally, opposite behavior in momentum distribution is found against power law index (n) by fixing (m). Temperature of fluid decreases against power law index for m = 1.0 and m = 0.5.

The heat generated during the startup process of dry gas seals, such as the friction heat of the asperities, viscous shear heat, and the expansion heat of the gas film, easily leads to seal failure and endangers the stable operation of turbomachinery. This study combines the statistically modified contact model and the average Reynolds equation by considering the adiabatic index and the microscale effects of dry gas seals to explore the heat generation characteristics of dry gas seals formed in series at multiple times. In particular, the change laws and influencing factors among the components, including the friction heat of asperities and the shear heat and expansion heat of the gas film and total heat, are investigated. A comparative analysis indicates that the slip flow effect increases the total heat during the startup process. The friction heat is much greater than expansion heat and shear heat. Despite constant acceleration, exponential acceleration, or Harrison acceleration, the heat changes are uneven during the startup process. In particular, the heat changes sharply in the early stage and slowly in the later stage. The Harrison acceleration mode is the most conducive to sealing stability. [ABSTRACT FROM AUTHOR]

In a rotational model, the Hall effect on two‐liquid magnetohydrodynamics plasma flows of ionized gases between two nonconducting horizontal channel plates in a slip regime is researched. The produced magnetic field is omitted under the presumption that the Reynolds magnetic number is low. The modeled governing equations are solved by using the existing analytical method so as to obtain solutions in closed form. We use the first order slip to obtain exact results for the velocity, temperature fields, and hence the rates of heat transfer coefficient. On the basis of different values for the Hartmann number, slip, Hall, and rotation parameters, also viscosity, density, height, and electrical conductivity ratios of the two fluids, a parametric investigation of the velocity, temperature fields is initiated. It was concluded that the velocity declined with the augmented values of Hartmann number and the fluid velocity and temperature profiles in both the zones oscillate with the effect of the Hall parameter. In addition to that, the stimulations are present in the heat transfer coefficient rate with various values of the slip and rotational parameters. [ABSTRACT FROM AUTHOR]

In this paper, we examine the effect of thermal radiation on rotating magnetohydrodynamic two liquid flows of ionized gasses past horizontal channel under slip and Hall conditions. The fluids in the two zones are considered to be immiscible, incompressible, and electrically conducting with various viscosities, thermal and electrical conductivities. We derive the exact solutions for the temperature profiles and coefficients of heat transfer rate at the plates in the two zones by solving governing equations in the presence of slip‐regime analytically. The temperature fields have been figured for various sets of values of the involved governing characteristics to analyze the behavior of heat transport. It has been noted that there is an enhancement in the temperature profile as the slip parameter rises for fixed values of the remaining parameters. Also, stimulations occur in the temperature field, with an increment in Taylor's number. This study may have some significant implementations in biomedical science such as destroying cancer cells during the drug delivery treatment, polishing damaged internal cavities, heart valves, and so forth. [ABSTRACT FROM AUTHOR]

Herein, nonequilibrium molecular dynamics simulations are conducted to study the hydraulic permeation and vehicle transport of protons in proton exchange membranes (PEMs) with different structures. The results indicate that water molecules and hydronium ions are transported in porous PEMs in the form of clusters. Water molecules are more concentrated in the bulk areas of pores, whereas hydronium ions had a high‐density profile near the pore surface areas since sulfonate ions of the side chain exhibit a stronger adsorption effect on hydronium ions. Due to the confined pore size, the slip flow of water molecules and hydronium ions occurs near the pore surfaces and it becomes more significant as side chain separation or pore size increases. As pore size decreases, the reduction of movement region and the deep attractive potential near the pore wall lower the specific enthalpy due to enhanced molecule‐wall collisions. In addition, the transport diffusivity coefficients of positively charged hydronium ions are smaller than that of water molecules due to the stronger Coulomb interactions and hydrogen bonding with negatively charged side chains. Transport diffusivity coefficients of water molecules and hydronium ions increase as pore size and side chain separation increase. [ABSTRACT FROM AUTHOR]

The present work delves into the Walter B fluid flow across the channel with the elongating enclosures when enthralled by linear radiation. The magnetic field is contemplated throughout the examination. The fluid suction and injection is permitted through the lower permeable wall. The slip regime is confined at the boundaries of the channel. Heat transfer in the channel is brought to light under two heating processes, namely prescribed surface temperature and prescribed surface heat flux case. The modeled equations are non-dimensionalized and then solved by the Runge-Kutta Fehlberg method in association with shooting scheme. Results deduce that the Reynolds number magnifies the velocity in the channel. Under two different heat boundary conditions, it is recorded that temperature is more pronounced for prescribed surface temperature case than prescribed heat flux. Flow profile for the varying viscoelastic parameter deciphers that at the lower end of the channel, the velocity is augmented and reverse response is recorded at the upper half of channel. Entropy profile magnifies with the augmentation of the magnetic parameter and shows depleting nature for higher Reynolds number. Examining the Walter B fluid flow in the channel enclosed with stretchable walls deliberates the flow of blood in the arterial wall under the exertion of strong magnetic field. [ABSTRACT FROM AUTHOR]

The problem of a slow Stokes flow past a sphere with modified slip condition on its surface is solved. The new boundary condition on the surface of a sphere establishes the linear relationship between the tangential velocity component and the vorticity of the flow. An analytical solution of the boundary value problem for the flow stream function is obtained. The expressions for drag force of the sphere and the tangential velocity are found as a function of the Knudsen number. The resulting expression for the drag force is consistent with the linear Cunningham correction factor. The developed model is compared against the results obtained within the molecular kinetic theory and the continuum mechanics model with the Basset–Maxwell slip condition. The proposed model shows the best agreement with the experimental data for the dependence of the aerodynamic drag force on Knudsen number. It is shown that in the limiting case of an infinite Knudsen number, the proposed model leads to a model of potential flow. [ABSTRACT FROM AUTHOR]

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Objective: The objective of current study is to discuss the effects of the Soret and Dufour with radiation absorption, applied heat source and viscous dissipation on an unsteady MHD mixed convective flow with velocity slip condition across a semi-infinite vertical permeable plate in porous medium. Method: A similarity transformation is used to turn the governing partial differential equations with proper boundary conditions into coupled, non-linear ordinary differential equations with variable coefficients. The inbuilt MATLAB solver bvp4c is used to generate numerical solutions. Findings: The effects on momentum, thermal and solutal boundary layers for various parametric values are graphically depicted. Skin friction, Nusselt number and Sherwood number are all tabulated and discussed in detail. An improvement in radiation absorption corresponds to enhancement of the heat transfer rate up to 59% while leading to a decline in mass transfer rate around 20%. The momentum, thermal and solutal boundary layers are all found to be boosted when the Soret effect is higher. For higher estimation of slip effect, the skin friction is found to decay around 23%. Also, as more time goes by the thermal and concentration boundary layers are enhanced. Novelty: Results obtained in this studied has also been compared and verified with available scientific literature and is found to be in good agreement, which establishes assurance in the numerical results reported in the study.

The objective of current communication is to study heat transfer phenomenon for slip flow of viscous fluid due to wavy channel with general cosine function boundaries and fixed amplitude. The walls along with slip boundary constraints are kept at different temperatures. The flow is incompressible and Newtonian with AIS as a predicting material being used to check the fluids and thermal properties. The Navier–Stokes expressions with 2D flow regime subject to heat transfer due to convection are used to develop the simulations. A parametric theoretical assumptions analysis is performed for specified range of Reynolds number (100–1000) with upper and lower surface vibration periods of 1 to 6. The results are displayed with graphs, surface and contours plots and first, ever a novel work was done to represent the percentage change in velocity magnitude and local Nusselt number as surface plots and contours, respectively. The results are authentic due to mesh independent study and verification with the experimental correlation. A periodic flow at the lower wall was deducted. The maximum and average rotation rates attain a linear relationship with Reynolds number and their correlation was found. The simulations show the strict relationship of Reynolds number and the geometry of the channel with shear rate. The pressure gradient in y -direction was found minimum in trough and maximum in the crest region. It has been observed that the boundary friction is reduced due to periodic variation of walls surface. [ABSTRACT FROM AUTHOR]

The flow of Casson fluid streaming through a porous zone in a permeable channel with homogeneously distributed dust particles is studied. The flow is oscillatory and exposed to thermal radiation. With non-uniform temperature and velocity slip at the wall, the channel is put under transverse magnetic flux control. The variable separation approach is used to obtain the exact analytic solution for the flow fields of fluid and dust particles. Physical insights of collective effects of suction/injection, magnetic field, thermal radiation, and buoyance force on the fluid velocity, temperature, rate of heat transport and friction at the wall surface are examined and analysed graphically. Results reveal that surface friction increases on both channel plates as an injection on the hot plate rises. [ABSTRACT FROM AUTHOR]

Two-dimensional developing flow in the entrance of a microchannel has been studied numerically. Due to its nature, a microchannel can be used in tight space applications and the length of channel can get very small values. Furthermore, if the hydrodynamic development length of flow in microchannel has comparably the same value with the channel length, the channel entrance parameters play critical role on the flow performance of a microscale channel. Lattice Boltzmann Method (LBM) was considered for studying and simulating the developing slip flows through a rectangular microchannel. A unique computational code for this study was developed by using LBM. The slip velocity boundary condition along with Knudsen number values in the slip flow regime was used for this model. The bounce-back boundary condition was considered at the top and bottom walls of the microchannel. The effects of the Reynolds numbers (1-100) and Knudsen numbers (0.001, 0.01, 0.1) on the hydrodynamic entrance length has been examined. The numerical results have been compared with the previous studies in the literature and the similarities have been found satisfactory. The entrance length is found to be increasing with the increase of Reynolds and Knudsen numbers. A correlation for hydrodynamic development length as a function of Knudsen and Reynolds numbers was obtained by using the data extracted from LBM simulations performed in this study. [ABSTRACT FROM AUTHOR]

Understanding and characterizing the transport of shale gas (methane) through the nanopores of kerogens are critical for the accurate prediction of shale gas recovery. However, the key factors that regulate shale gas transport through highly roughened nanopores of shale kerogens are not fully understood. In this work, methane transport in organic nanopores with a high relative roughness is characterized using equilibrium and non-equilibrium molecular dynamics methods. According to our results, the CH4 mass flux has a linear relationship with the pressure gradient, consistent with previous studies, while the calculated slip lengths and gas fluxes varied with different roughness geometries in the order of sigmoidal ≥ triangular > rectangular. Surface slip flow can be a major contributor to the overall gas flux, but surprisingly, the relative contribution of surface slip flow is independent of the pressure gradient. In contrast, the contributions of both slip flow and the average gas fluxes vary strongly with pore diameters. Typical contributions of the adsorbed layer to the overall gas flux are in the range 20–40% but vary from as high as 74% in a 4-nm pore to as low as 6% in a 16-nm pore. Compared to smooth nanopores, we find that, in nanopores with realistically high degrees of relative roughness, methane confinement in cavities decouples slip flow from the flow in the pore interior, significantly reducing the overall flux.

Understanding and characterizing the transport of shale gas (methane) through the nanopores of kerogens are critical for the accurate prediction of shale gas recovery. However, the key factors that regulate shale gas transport through highly roughened nanopores of shale kerogens are not fully understood. In this work, methane transport in organic nanopores with a high relative roughness is characterized using equilibrium and non-equilibrium molecular dynamics methods. According to our results, the CH4 mass flux has a linear relationship with the pressure gradient, consistent with previous studies, while the calculated slip lengths and gas fluxes varied with different roughness geometries in the order of sigmoidal ≥ triangular > rectangular. Surface slip flow can be a major contributor to the overall gas flux, but surprisingly, the relative contribution of surface slip flow is independent of the pressure gradient. In contrast, the contributions of both slip flow and the average gas fluxes vary strongly with pore diameters. Typical contributions of the adsorbed layer to the overall gas flux are in the range 20–40% but vary from as high as 74% in a 4-nm pore to as low as 6% in a 16-nm pore. Compared to smooth nanopores, we find that, in nanopores with realistically high degrees of relative roughness, methane confinement in cavities decouples slip flow from the flow in the pore interior, significantly reducing the overall flux.

This study explores the second-order slip effect on the flow of MHD chemically reacting fluid through an inclined micro-annular channel. As knowledge in flow and heat transfer is showcased in macro/micro-channel areas, consistent advancement is essential to familiar with fundamental phenomena associated. The free convection study encompasses the temperature-dependent viscosity and uniform magnetic field effect. The dimensionless equations governing the flow are modeled and solved semi-analytically via Akbari-Ganji’s Method (AGM). The velocity, energy, concentration and physical characteristics of the flow results are obtained and discussed with the aid of tables and graphs. It is found that a higher value of the slip parameter diminishes the velocity distribution at the annular gap and surfaces, while, the temperature-dependent exponential variability model enhances the fluid velocity.

Fluid-conveying nanotubes play key roles in nano electromechanical systems (NEMSs). The contact dynamic response and stress field of the fluid-conveying graphene reinforced composite (GRC) nanotube transporting high-speed nanoflow under lateral low-velocity impact are studied. The size-dependent models incorporating slip flow, nonlocal stress and strain gradient effect are established. The governing equations of flow-inducing post-buckling and contact vibration are derived based on a refined beam theory, in which the post-buckling equilibrium provides the initial configuration for the impact vibration analysis. A computation mode of two-step perturbation-higher-order Galerkin truncation-Runge-Kutta (R-K) method is employed to study the contact dynamic responses. Through the convergence analysis, the truncation terms required to ensure the accuracy are obtained. The contact force curves and the midspan displacement time history curves and the stress field are acquired to guide the strength design. Also, the dynamic snap-through instability behaviors of the nanotube under the flow-inducing post-buckling state are revealed. Results reveal the dual influences of nonlocal stress and strain gradient on the contact dynamic response and stress field and provide the flow velocity range sensitive to the size effect. [ABSTRACT FROM AUTHOR]

The purpose of this work is to offer a unique theoretical ternary nanofluid (graphene/tungsten oxide/zirconium oxide) framework for better heat transfer. This model describes how to create better heat conduction than a hybrid nanofluid. Three different nanostructures with different chemical and physical bonds are suspended in water to create the ternary nanofluid (graphene/tungsten oxide/zirconium oxide). Toxic substances are broken down, the air is purified, and other devices are cooled thanks to the synergy of these nanoparticles. The properties of ternary nanofluids are discussed in this article, including their thermal conductivity, specific heat capacitance, viscosity, and density. In addition, heat transport phenomena are explained by the Cattaneo–Christov (CC) heat flow theory. In the modeling of the physical phenomena under investigation, the impacts of thermal nonlinear radiation and velocity slip are considered. By using the right transformations, flow-generating PDEs are converted into nonlinear ordinary differential equations. The parameters' impacts on the velocity and temperature fields are analyzed in detail. The modeled problem is graphically handled in MATLAB using a numerical technique (BVP4c). Graphical representations of the important factors affecting temperature and velocity fields are illustrated through graphs. The findings disclose that the performance of ternary nanofluid phase heat transfer is improved compared to dusty phase performance. Furthermore, the magnetic parameter and the velocity slip parameter both experience a slowing-down effect of their respective velocities. [ABSTRACT FROM AUTHOR]

The impacts of single- (SPM) and two-phase models (TPMs), including Euler-Lagrange (ELM) and Eulerian-Eulerian models (EEM), on a laminar forced convection heat transfer and fluid flow of the Al 2 O 3 / water nanofluid are evaluated in a rotating U-shape microchannel with a square cross-section and constant wall temperature. The effects of Reynolds numbers, rotational speed, volume fraction, Brownian motion, and implementation of no-slip and slip conditions are investigated. The slip velocity and heat transfer increase by increasing the volume fraction and rotational speed. The EEM and ELM provide a higher total Nusselt number than the SPM. The maximum heat transfer augmentations of 53.3%, 45.7%, and 41% are achieved for the EEM, ELM, and SPM by increasing the rotational speed from zero to 600 at ϕ = 5%. The predictions of pressure drop by TPMs are essentially the same but considerably lower than SPM. Unlike the ELM, the nanoparticle concentrations of EEM and SPM are uniform. [ABSTRACT FROM AUTHOR]

This paper presents an exact analytical solution to the extended Graetz problem in microchannels and microtubes, including axial heat conduction, viscous dissipation, and rarefaction effects for an imposed constant wall temperature. The flow in the microchannel or microtube is assumed to be hydrodynamically fully developed. At the same time, the first-order slip-velocity and temperature jump models represent the wall boundary conditions. The energy equation is solved analytically, and the solution is obtained in terms of Kummer functions with expansion constants directly determined from explicit expressions. The local and fully developed Nusselt numbers are calculated in terms of the Péclet number, Brinkman number, Knudsen number, and thermal properties of the fluid. The constant pressure drop along the streamwise direction per unit length is imposed at a constant value and independent of the flow parameters, unlike the usual practice of fixing the average velocity. This solution can be used as the reference solution for optimization problems to enhance heat transfer using a fixed pressure drop. It is found that for no viscous dissipation and negligible axial heat conduction, the local Nusselt number is larger for imposed pressure drop compared to imposed average velocity. The thermal entrance length increases as the Knudsen number or the degree of temperature jump increases for imposed pressure drop, while it is approximately unchangeable for imposed average velocity. The quantitative differences between the cases of imposed pressure drop and imposed average velocity in the average Nusselt number over the largest thermal entrance length are reduced with the increase of axial heat conduction or viscous dissipation effects. The fully developed Nusselt number is the same for imposed pressure drop and imposed average velocity. [ABSTRACT FROM AUTHOR]

The heat generated during the startup process of dry gas seals, such as the friction heat of the asperities, viscous shear heat, and the expansion heat of the gas film, easily leads to seal failure and endangers the stable operation of turbomachinery. This study combines the statistically modified contact model and the average Reynolds equation by considering the adiabatic index and the microscale effects of dry gas seals to explore the heat generation characteristics of dry gas seals formed in series at multiple times. In particular, the change laws and influencing factors among the components, including the friction heat of asperities and the shear heat and expansion heat of the gas film and total heat, are investigated. A comparative analysis indicates that the slip flow effect increases the total heat during the startup process. The friction heat is much greater than expansion heat and shear heat. Despite constant acceleration, exponential acceleration, or Harrison acceleration, the heat changes are uneven during the startup process. In particular, the heat changes sharply in the early stage and slowly in the later stage. The Harrison acceleration mode is the most conducive to sealing stability.

The pressure for supporting the bearing load is induced by the generation of discontinuity of the shear flow rate in each region only by arranging areas in the slip direction with different slipperiness of fluid. In this report, the generated pressure and friction characteristics, which were important for clarifying the characteristics of disc type partial slip thrust bearing were investigated using three-dimensional modified Reynolds equation considering the slip on the solid surface. It was suggested that the relationship between the shear rate and the slip length which is determined with the film thickness estimated from the friction force measured in this bearing by assuming a pure shear condition can be treated as a two-term slip model. Finite width analysis was performed assuming critical shear rate and constant slip length, and the Stribeck curve and pressure distribution were obtained. The low shear rate region less than critical shear rate is increased in the center side of the disk type bearing for the lighter load and the thicker film cases. Then, the friction for supporting the same load shows the value higher than the friction where slip occurs on the entire surface of the assumed slip area of the bearing. On the other hand, since the entire slip area of the bearing surface approaches a slip state, the film thickness and friction when supporting the same load are the same as those when the entire assumed slip area is on slipping. The influence of such critical shear rate also appears in the results of the radial pressure distribution in disc type bearing, and the calculated pressure on the inner circumference side rapidly decreases due to the presence of the non-slip region on the inner circumference side with low shear rate. And then, this tendency agrees with that of the measured radial pressure distribution.

This paper describes the combination of experimental measurements with mathematical–physical analysis during the investigation of flow in an aperture at low pressures in a prepared experimental chamber. In the first step, experimental measurements of the pressure in the specimen chamber and at its outlet were taken during the pumping of the chamber. This process converted the atmospheric pressure into the operating pressure typical for the current AQUASEM II environmental electron microscope at the ISI of the CAS in Brno. Based on these results, a mathematical–physical model was tuned in the Ansys Fluent system and subsequently used for mathematical–physical analysis in a slip flow regime on a nozzle wall at low pressure. These analyses will be used to fine-tune the experimental chamber. Once the chamber is operational, it will be possible to compare the results obtained from the experimental measurements of the nozzle wall pressure, static pressure, total pressure and temperature from the nozzle axis region in supersonic flow with the results obtained from the mathematical–physical analyses. Based on the above comparative analyses, we will be able to determine the realistic slip flow at the nozzle wall under different conditions at the continuum mechanics boundary. [ABSTRACT FROM AUTHOR]

Analytical studies are performed on the problem of a thermally developing laminar gaseous slip flow through a parallel-plate microchannel with constant wall temperatures subject to the influences of axial conduction, pressure work, and viscous dissipation. The temperature profiles and local Nusselt numbers are obtained assuming that the flow is hydrodynamically fully developed in a heating zone of semi-infinite length. The obtained solution is based on the use of the self-adjoint formalism involviпg the rearrangement of the energy equation into a system of the first-order partial differential equations. For simplified limiting cases, the analytical results are compared with the available analytical and numerical ones, and a good agreement is found, which supports the validity of this solution. The effects of axial heat conduction, rarefaction, pressure work, and viscous dissipation on the heat transfer characteristics are studied and discussed in detail. [ABSTRACT FROM AUTHOR]

The micro-scale equipment has many advantages, including high thermal performance, high surface-to-volume ratio in heat transfer, small size, low weight, low required fluid and high design flexibility. In this study, fluid flow inside a microchannel is modeled under the assumption of laminar, incompressible, and two-dimensional flow under symmetric boundary conditions. The slip boundary condition is applied to the walls and the flow in the channel output is assumed to be fully developed. The effect of sinusoidal wall with the domain of 0.1 on the hydrodynamic and thermal behavior of the fluid is investigated and the results are compared with the results of smooth wall. The results show that for a constant Reynolds number, the maximum velocity decreases in the microchannel center by increasing the slip coefficient. Also, the comparison between the results of the wavy-wall microchannel and the microchannel with a smooth wall indicates that the heat transfer in the smooth microchannel is less than that in wavy-wall one. Considering the boundary conditions, the thermal behavior of the fluid is approximately the same for two cases in which both walls are sinusoidal and the only upper wall is sinusoidal.

In this study, two-dimensional, steady, laminar, and compressible gaseous flow of Newtonian fluid in a rectangular porous microchannel affected by an electromagnetic field, and under local thermal equilibrium condition was analytically investigated in the slip flow region (0.001< Kn

A flow that is subject to the influence of both thermal buoyancy and pressure gradient is called mixed convection. This kind of flow can be found in a wide variety of scientific and infrastructural functionalities, such as sunlight transceivers that are open to the airflow, digital devices that are kept cool by fans, nuclear reactors that are cooled during emergency shutdowns, and heat exchangers that are placed in low-velocity environments. This paper present MHD coupled convection flow of chemical reaction of an exothermic and chemical kinetic fluid with Newtonian heating in a vertical channel. chemical reaction (λ), magnetohydrodynamics (Ha), Navier slip (Γ), and Newtonian heating (Br) are all taken into consideration, in addition to the chemical kinetic exponent (m). Homotopy perturbation techniques and implicit finite difference scheme are used to find the steady-state solution and transient state solution for the set of dimensionless coupled governing equations. The rate of heat transfer and sheer stress were derived by differentiating the analytical solution obtained. Various pertinent parameters controlling the flow such as chemical reaction parameter (λ), MHD (Ha), Newtonian heating parameter (Br), chemical kinetic exponent (m) and Navier slip parameter (Γ) are illustrated graphically. Velocity and temperature fields are also demonstrated. The studies showed that a little rise in the Hartman number induces the Lorentz force, which streamlines the velocity boundary layer, decelerating the flow. A minor increase in the mixed convection parameter, on the other hand, resulted in significantly enhanced flow profiles, resulting in a greater flow rate during biomolecular kinds of chemical processes. Also during course of computation, the energy and velocity profiles improve with increase in (λ), (Br), (m),(γ) and (Gre). However, a graphical comparison of the transient solution and the steady state solution was also displayed, with an outstanding agreement.

In this work, we consider the flow of magnetohydrodynamic (MHD) fluid over a permeable surface due to continuous stretching. The stretching surface is subject to a constant magnetic field along normal direction and velocity-slip conditions. This flow is governed by nonlinear partial differential equations (PDEs) subject to associated boundary conditions. The similarity transformation technique was applied to obtain their non-dimensional form, coupled with nonlinear ordinary differential equations (ODEs). MATLAB-based program "bvp5c" was then used to obtain their numerical solution. Two artificial neural network models were also presented for predicting the coefficients of skin friction - f ″ 0 and heat transfer rate - θ ′ 0 . The present study revealed that heat transfer rate is decreased due to increases in first- and second-order slip parameters. Results also showed that neural network models can predict thermal conductivity with high accuracy. High R squared values of 0.99 were achieved for predicting coefficients of skin friction - f ″ 0 and heat transfer rate - θ ′ 0 . This shows the effectiveness of neural network models for predicting those characteristics and thus reducing the time required for numerical models for predicting MHD slip flow over a permeable stretching surface. Moreover, in comparison with the other numerical methods, the present ANN model can be applied to more complex mathematical models because it reduces the time and processing capacity required for solving the problem. [ABSTRACT FROM AUTHOR]

The numerical simulations are performed to investigate the electro-osmotic peristaltic flow of Prandtl fluid in the presence of tiny particles in a planner channel. The analysis is performed in the presence of slip effects, magnetic force and Joule heating. The governing nonlinear boundary value problem along with nonlinear boundary conditions is solved numerically using Keller Box method as well as numerical shooting technique by using the MATLAB tool. The solution validity is also ensured by computing the solution with BVP4C solver. The results claimed from analysis convey that concentration profile declined with concentration slip while an increasing trend for concentration has been noted for Soret number. The presence of slip factor reduces the magnitude of skin friction coefficient. With increasing the Grashof number and in the presence of electric forces, the temperature profile reduces. The Nusselt number increases with electro-osmotic parameter while reverse observations are predicted for Sherwood number. [ABSTRACT FROM AUTHOR]

Fast fluid transport on graphene has attracted a growing body of research due to a wide range of potential applications including thermal management, water desalination, energy harvesting, and lab-on-a-chip. Here, we critically review the theoretical, simulational, and experimental progress regarding the fluid slippage on graphene. Based on the summary of the past studies, we give perspectives on future research directions towards complete understanding and practical applications of slip flow on graphene. [ABSTRACT FROM AUTHOR]