Velocity Slip Boundary Condition Research Articles

On heat transfer in Carreau fluid flow with thermal slip: An artificial intelligence (AI) based decisions integrated with Lie symmetry

It is well accepted that non-Newtonian fluid flow narrating differential systems with thermal slip conditions at the surface plays an important role in instabilities subject to polymer extrusion like stick–slip and gross-melt-fracture instabilities. Therefore, the present article contains the artificial neural networking evaluation of the friction at magnetized porous surface having thermal and velocity slip boundary conditions. The Carrea fluid flow is mathematically formulated at a porous surface. The novelty is enhanced by considering velocity slip boundary condition, thermal slip boundary condition, chemical reaction, magnetic field, and heat generation effects. The flow differential equations are reduced by using Lie symmetry analysis. The reduced equations are solved by using the shooting method. The neural networking model is constructed by engaging 132 values of SFC. 92 (70%) is marked for training, and 20 (15%) each is marked for validation and testing. 10 number of neurons are chosen in the hidden layer. Levenberg-Marquardt algorithm is carried out to train the network. The performance of the constructed neural networking model is evaluated by MSE and R. The developed ANN is the best to predict the friction values at the magnetized porous plate. Owning to predicted values of ANN, SFC shows inciting values towards the magnetic field parameter.

Thermal radiative and Hall current effects on magneto-natural convective flow of dusty fluid: Numerical Runge–Kutta–Fehlberg technique

This research article intends to examine the consequences of Hall impact on the natural convection of magnetohydrodynamic (MHD) fluid flowing and the thermal characteristics of the fluid flow which containing dusty particles via a vertical stretchable sheet. Slip velocity and convective boundary conditions are taken into consideration in this research article. The flow is mathematically described by partial differential equations. The governing equations are renovated into a group of nonlinear differential equations with the use of similarity conversations, which are then resolved numerically by applying Runge–Kutta–Fehlberg. The behavior of these physical factors on the rapidity and temperature profiles of the dust and fluid phases are exposed graphically in this article. Furthermore, frictional force and heat transfer are also examined and discussed. According to the investigation, the existence of suspended particles in the fluid lead to increment in momentum and thermal boundary layer thickness. The temperature of the fluid seems can be controlled by the significant parameter, such as it seem to be increase due to the magnetic, radiation, and Hall parameters, while it is seen to have decreased due to the slip thermal parameter. While the radiation accelerates up the fluid velocity, the magnetic parameter is excellent at slowing it down. The fluid phase’s temperature and velocity profiles are almost usually higher than those of the dust phase. The outcomes contribute to a better understanding of the two-phase theory’s fluid flow phenomenon.

Thermal prediction of rotatory multiwall carbon nanotubes subject to convective boundary conditions and slip effects: Implicit finite difference simulations

This article presents the modeling and simulations 3D magneto-hydrodynamic rotating nanofluid flow through a stretched surface. Water is employed as the base liquid, and multiwall carbon nanotubes (MWCNTs) are used as nanosized materials. The unique structure of MWCNTs makes them stand out among the crowd. The principal concern is to enhance the thermal transport efficiency, chemical durability, and important optical and electronics properties. The classical Navier Stoke’s problem based upon the law of conservation of mass, momentum and energy with the Xue model’s implementation is transformed into an ordinary differential equation by applying similarity approach. Velocity slip and convective boundary conditions are also considered under the Lorentz force. The final form of nondimensional ODEs are, then, solved numerically using finite difference method with the assistance of MATLAB's powerful software. The impression of pertinent convergence flow constraints on fluid velocity, temperature, heat transfer rate, and friction factor are exposed through tables and graphs. A numerical comparison is used to evaluate the code efficiency, and the results show excellent agreement. The effect of the Biot number appears to be raising the temperature. Conversely, increasing the rotation and slip parameter parametric values results in a declining trend in the velocity profile.

SUTTERBY NANOFLUID FLOW WITH MICROORGANISMS AROUND A CURVED EXPANDING SURFACE THROUGH A POROUS MEDIUM: THERMAL DIFFUSION AND DIFFUSION THERMO IMPACTS

This study anticipates examining a slip bioconvective movement of a non-Newtonian Sutterby nanofluid (SF) layer with motile microorganisms, where the fluid layer flows over a curved stretching surface. The movement is taken across a permeable medium under the influence of thermal diffusion, diffusion thermo, an unchanged vertical magnetic field (MF), joule heating, thermal radiation, and chemical reactions. The mathematical construction comprises momentum, energy, nanoparticles volume fraction, and microorganism concentration equations along with linear slip velocity and applicable boundary conditions (BCs). The motivation of the problem concerns recent progress in curved electronics and microchip technology, which made a growing development of the remarkable weaknesses of traditional planar electronics, which concerns the importance of the current work. Furthermore, the implication of this work emerges from the participation of microorganisms in the flow over a curved surface and shares with the temperature, velocity, and nanoparticle system of equations. This prototype is widely applicable in some manufacturing and engineering mechanisms like conduits, sports balls, combustion, inflated broadcast, and flow-structure contact between hydrodynamics and aerodynamics. The configuration of nonlinear partial differential equations (PDEs) is converted into ordinary differential equations (ODEs) by consuming suitable similarity transformations. The resulting equations are numerically analyzed via the fourth-order Runge-Kutta (RK-4) in concurrence with the shooting technique. The graphical construction of the targeted distributions is analyzed to recognize the effects of the relevant material coefficients. As key outcomes, it is noted that the greater the curvature of the surface, the greater the temperature, velocity, microorganisms, and nanoparticle distributions. Correspondingly, the Soret and Dufour impacts are found to be the improvement coefficients of the heat and dampness of both nanoparticle and microorganism condensation. Additionally, heat transmission develops with almost all relevant parameters, which is a noteworthy finding that can benefit potential applications.

Numerical investigation of the natural transition in boundary layers on underwater axisymmetric bodies with superhydrophobic surfaces

The natural transition in boundary layers on axisymmetric bodies with superhydrophobic surfaces is studied using numerical methods. By boundary layer, we mean the boundary layer around the forebody and around the parallel body of an underwater vehicle. A method of calculating basic laminar flows on axisymmetric bodies with superhydrophobic curved surfaces is proposed, and a method of linear stability analysis for the boundary layers that considers the slip-velocity boundary condition for small disturbances is established. The eN method is used to predict the transition locations of the boundary layers. On a superhydrophobic surface, the slip velocity on the wall increases and then decreases along the streamwise direction, resulting in a maximum value at the forebody. The boundary layer thickness on a superhydrophobic surface becomes smaller than that on an ordinary surface. The superhydrophobic surface stabilizes the boundary layer and thus delays the natural transition. As the slip length on the superhydrophobic surface increases, the unstable zone shrinks, and the transition location moves further downstream, indicating that the delay effect of the superhydrophobic surfaces becomes stronger. As the oncoming flow velocity increases, the transition location on the superhydrophobic surface moves upstream and then downstream, leading to a “dangerous” velocity, at which the transition location is closest to the leading edge. The underlying mechanism of the dangerous velocity phenomenon is discussed: An increasing velocity has both stabilizing effect and destabilizing effect on the boundary layer.

Numerical investigation of the flow characteristics involving dissipation and slip effects in a convectively nanofluid within a porous medium

Abstract The aim of the present research is to discuss the numerical aspects of heat-mass transfer in power-law nanofluids on an stretched surface. In addition, the novelty in this research lies in its thorough exploration and incorporation of parameters such as viscous dissipation, slip velocity, and convective boundary conditions into the analysis. This distinguishes the study from previous work and underscores its originality. For non-Newtonian fluids, a power-law model is employed, while the nanofluid system associate the influences of thermophoresis and the Brownian motion. The fluid’s thermal conductivity is considered to change based on temperature, while the concentration of nanoparticles at the surface is maintained at a constant level. A heated fluid situated beneath the lower surface can act as a heat convection mechanism source. A process of similarity transformation is employed to simplify the equations related to the mass, momentum, thermal energy, and nanoparticle concentration into nonlinear ordinary differential equations. These equations are then treated numerically with the help of the shifted Chebyshev polynomials of the sixth order and the spectral collocation method. The proposed technique reduces the existing problem into a system of algebraic equations formulated as a constrained optimization challenge. Subsequently, the optimization technique is applied to determine the unknown coefficients of the series solution. Graphical representations depict the impacts of nanofluid parameters. A quantitative assessment is presented in a tabular format to illustrate a comparison with previously published results for specific scenarios, revealing a notable level of agreement.

Investigation of dissipation phenomenon of non-Newtonian nanofluid due to a horizontal stretching rough sheet through a Darcy porous medium

Recent advancements in thermal engineering have led to the development of stable thermal properties and practical applications for nanofluid flow. Consequently, this study aims to explore the heat and mass transfer characteristics of a non-Newtonian Maxwell nanofluid when it comes into contact with a stretched surface containing porous features that allow for fluid suction velocity. Additionally, the research takes into account how the Soret and Dufour effects impact the processes of heat and mass transfer. A less-explored aspect of research in this field relates to the velocity slip boundary conditions when nanofluids with changing viscosity are involved. Additionally, the model employed in this study illustrates the influence of both viscous dissipation and variable thermal conductivity on the processes of heat and mass transfer. The mathematical flow model is described by nonlinear partial differential equations, which are subsequently transformed into non-dimensional ordinary differential equations. The resulting system is then solved numerically using the shooting method. This study visually examines the impact of physical variables on temperature, flow characteristics, and concentration patterns. Furthermore, it provides graphical representations of estimated values for the skin friction coefficient, Sherwood numbers, and local Nusselt numbers, which are also organized in tables for analysis. In conclusion, by comparing our data with previous results, we confirm the accuracy and reliability of the proposed method. A significant discovery is that the nanofluid velocity decreases as the Maxwell, porous, and slip velocity parameters are increased. Furthermore, the nanofluid concentration rises when the thermophoresis and viscosity parameters increase.

Numerical investigation on flow, heat and mass transfer performance of fractional Oldroyd-B hybrid nanofluid as a coolant for power battery

This paper introduced for the first time a viscoelastic hybrid nanofluid as the coolant for direct contact cooling power battery. The governing boundary layer equations were established by adopting fractional Oldroyd-B model and fractional Buongiorno’s model. Second-order velocity slip boundary conditions were also considered. Then the solutions were numerically acquired by finite difference coupled with L1 algorithm. Impact of main physical parameters on the flow, heat and mass transfer of the viscoelastic hybrid nanofluid on the cylindrical battery was graphically presented and detailly discussed. Outcomes show that the heat transfer is improved by both Brownian motion(Nb) and thermophoresis(Nt) to different degrees. When Nb grows from 0.05 to 0.1, the average Nusselt number increases by 2.2%, higher than 0.027% of Nt. The slip behavior only affects the velocity distribution near the individual cell and slightly enhances heat and mass transfer. The velocity relaxation fractional derivative contributes to convection, heat and mass transfer on the cell wall, while velocity retardation fractional derivative behaves just the opposite. The proposed viscoelastic hybrid nanofluid with appropriate volume fractions of nanoparticles enhances heat transfer on the cell wall and is strongly recommended as a candidate for power battery coolant.

Electroosmotically induced peristaltic flow of a hybrid nanofluid in asymmetric channel: Revolutionizing nanofluid engineering

The exploration of electroosmotic peristaltic flow in asymmetric channels using hybrid non-Newtonian nanofluids holds significant promise across multiple domains. From microfluidics and electronics cooling to energy systems and biomedical applications, its implications are vast. By leveraging the distinctive attributes of nanofluids and the precision offered by electroosmotic and peristaltic flow, this research has the potential to drive the development of more efficient and innovative designs in these diverse fields. The current investigation reveals an analysis of heat transfer concerning hybrid nano liquid based on water. This nano liquid is influenced by both electroosmosis and peristalsis, operating simultaneously. Within this water-based hybrid nanofluid, there are nanoparticles composed of copper and iron oxide (Fe2O3−Cu/H2O). The study investigates into characteristics of flow and heat transport processes, considering key factors such as the applied electric and magnetic fields, thermal conductivity, mixed convection, shape of nanoparticles, variable viscosity, and assumptions related to Ohmic heating. Thermal and velocity slip boundary conditions are considered. To handle the analysis, the Poisson-Boltzmann equation is approximated using the Debye-Hückel approximation. The governing equations are then simplified using lubrication approximation. To solve the resulting system of dimensionless differential equations, NDSolve build in command of computational package Mathematica is employed. The outcomes of study affirm that inclusion of nanomaterials plays a vital role in enhancing heat transfer processes. Specifically, an increase in Joule heating and electromagnetic parameters contributes to a higher heat transfer rate at the boundary. Additionally, the incorporation of nanomaterials leads to a decrease in the flow rate of the nanofluid due to an increase in Helmholtz-Smoluchowski velocity. Furthermore, the heat transfer rate at wall diminishes as the Hartman number and Helmholtz-Smoluchowski velocity are increased. Showcasing the potential to enhance heat transfer, microfluidic devices, and various systems by harnessing the distinctive characteristics of hybrid nanofluids and regulating flow through peristaltic and electroosmotic methods. Providing insights into potential applications and industries that could profit from these findings, including microfluidics, electronics cooling, biomedical devices, and energy systems.

Inclined magnetic force impact on cross nanoliquid flowing with widening shallow and heat generating by using artificial neural network (ANN)

Artificial neural networks (ANNs) have a wide range of applications in science and technology. Artificial neural networks (ANNs) widely utilized in image and speech recognition, neural language processing, drug discovery, genomics and bioinformatics, Robotics and control systems, material science and energy and power system. Due to the above applications, the main focus of this article is to scrutinize the impact of inclined magnetic field on a cross nanofluid flow with slip velocity and convective boundary conditions over a variable porosity. Gold (Au) nanoparticles are suspended in base liquid blood. Thermal stratification and heat generation with joule heating impact is taken in the energy equation in order to see the heat transfer. To transform the non-linear partial differential equations (PDE's) into non-linear ordinary differential equations (ODE's) utilized the von-Karman similarity transformation parameters. For the solutions of the non-linear ODE's, the 4th- order Runge-Kutta numerical method is employed. A dataset for the employed neural network back propagated Levenberg-Marquard scheme (NN-BLMS) is generated for various estimations of the embedded parameters like Weissenberg number, magnetic parameter, angle of inclination, porosity and permeability parameters, thermal stratification parameter by utilizing the 4th-order Runge-Kutta numerical scheme. The testing, validation and training methods of NN-BLMS are utilized to scrutinize the approximate solution of cross nanofluid with slip velocity and convective boundary conditions. The performance of the proposed NN-BLMS to successfully solved the cross nanofluid model is endorsed via mean squared error, error histogram and regression analysis. Streamlines and heatlines are plotted for different parameters including in velocity and temperature equations.

A numerical study of electro-osmosis Williamson nanofluid flow in a permeable tapered channel

This paper aims to analyze the mathematical and theoretical scrutiny of non-Newtonian Williamson liquid on an asymmetry tapered channel with thermal and mass transportation. No slip boundary conditions for velocity, heat and concentration are kept on channel walls. Buongiorno model for thermal transport of nano-fluid is also incorporated. Flow in permeable surface is categorized via modified Darcy law. Current problem is formulated by incorporating distinct effects such as modified Darcy law, electro osmosis, heat generation and chemical reaction. RK-4 based shooting method has been utilized to evaluate the nonlinear equations. Graphical results are formulated to visualize the prominence of distinct parameters.

Effects of chemical reaction, Soret and Dufour parameters on MHD dissipative Williamson nanofluid flow over a slippery stretching sheet through a porous medium

ABSTRACT The goal of this study is to determine the effects of Soret, Dufour, and chemical reaction parameters on 2-D MHD Williamson nanofluid flow over a slippery-stretching sheet immersed in a porous medium. Under the influence of both magnetic field and thermal radiation, the significance of viscous dissipation and velocity slip boundary condition with heat generation have been explored. Similarity components were used to turn the nonlinear Partial Differential Equations (PDEs) into nonlinear Ordinary Differential Equations (ODEs), and they were solved using the fourth-order approach of the Runge–Kutta (R–K) method along with the shooting technique. The numerical computations were subsequently illustrated visually to demonstrate the influence of various physical factors on the plots of temperature, velocity, and concentration of the nanofluid. With the use of comparison with previously published data in a restricted sense, the veracity of computation results is evaluated. The tabular values illuminate that the local skin friction coefficient upsurge as the values of the magnetic parameter, porosity parameter, and Brownian motion parameter intensifies, whereas the opposite trend exists for other parameters. The local Nusselt number grows as the Schmidt number rises whereas the reverse trend was experienced for the freed-up parameters.

Velocity-slip boundary conditions and shape factor effects on MHD hybrid nanofluid flow via converging/diverging channels

The most important objective of this research-work is to investigate the impacts of velocity-slip boundary conditions and shape factor of solid nanoparticles on the hydrodynamic behavior of the nonlinear problem of MHD Jeffery–Hamel hybrid nanofluid flow where the mixture H2O-C2H6O2 (50%-50%) was utilized as a base fluid. Using appropriate velocity transformations, the basic partial differential equations arising from mathematical modeling are transformed into non-linear ordinary differential equations. Afterwards, the determined nonlinear equation was numerically solved utilizing Runge-Kutta-Fehlberg 4th–5th order approach featuring shooting technique and analytically with the help of Duan–Rach Approach (DRA). The impact of active factors like Reynolds number, channel half-angle, Hartman number, base fluids nature, hybrid nanoparticles, velocity-slip boundary conditions, shape and Geometry of solid nanoparticles on hybrid nanofluid velocity and skin friction coefficient are visualized and investigated. The minimal local skin friction is found to be obtainable with the nanoparticles of Platelet form and second-order slip model where a reduction of 70% is gained compared to the local skin friction coefficient with spherical nanoparticles when the Hartmann number is higher. Results obtained also reveal that a higher reduction of 69% in local skin friction coefficient intensity is observed for both hybrid phase Al2O3-Cu and mixture base fluid H2O-C2H6O2 with second-order slip boundary condition model when Knudsen number Kn = 0,08. A comparison was made between the results obtained from this investigation in particular cases and the results obtained via the HAM-based Mathematica package for validation. Also, the obtained analytical DRA data are compared with numerical RKF45 data and the ones represented in the literature. The comparison revealed that the results match perfectly which justifies applicability, validity, and the higher exactness of the adopted Duan-Rach approach.

Thermal convection and entropy generation analysis of hybrid nanofluid slip flow over a horizontal poignant thin needle with an inclined magnetic field: A numerical study

Hybrid nanofluids have emerged as a promising field of research in recent years, finding applications in various industries and sectors. The entropy generation and impact of an inclined magnetic field on a water-Ethylene Glycol (50:50) mixture-based nanofluid over a poignant thin needle has been investigated under slip conditions. The flow is swotted using thermal and velocity slip boundary conditions. The numerical effects of an inclined magnetic field on the flow of ferrous and aluminum oxide nanoparticles in a hybrid nanoliquid with as base fluids have been examined. The non-dimensional ODEs along with boundary conditions are solved by numerical technique based on the Runge–Kutta fourth-order method. Velocity profile has been analyzed for the magnetic parameter, inclined angle and volume fractions. The Bejan number provides insights into the balance between heat transfer and entropy generation in a system. From the numerical values of skin friction coefficient and Nusselt number, it is analyzed that [Formula: see text]O3 possesses 1.01% and 1.06% of high heat transfer rate and high surface drag force than [Formula: see text]O4. Heat transfer profile has been analyzed for entropy generation and the Bejan number. The applications of hybrid nanofluids are vast, and one specific area where they can be utilized is in horizontal needle systems.

A new thin layer model for viscous flow between two nearby non‐static surfaces

AbstractWe propose a two‐dimensional flow model of a viscous fluid between two close moving surfaces. We show, using a formal asymptotic expansion of the solution, that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier‐Stokes equations.The leading term of the formal asymptotic expansions of the solutions to the new model and Navier‐Stokes equations are solution of the same limit problem, and the type of the limit problem depends on the boundary conditions. If slip velocity boundary conditions are imposed on the upper and lower bound surfaces, the limit is a solution of a lubrication model, but if the tractions and friction forces are known on both bound surfaces, the limit is a solution of a thin fluid layer model.The model proposed has been obtained to be a valuable tool for computing viscous fluid flow between two nearby moving surfaces, without the need to decide a priori whether the flow is typical of a lubrication or a thin fluid layer problem, and without the enormous computational effort that would be required to solve the Navier‐Stokes equations in such a thin domain.

Mathematical analysis of MHD hybrid nanofluid flow with variable viscosity and slip conditions over a stretching surface

There are number of real-world uses for hybrid nanofluids. Studies have shown that hybrid nanofluid is better at transferring heat than nanofluid with only one type of nanoparticle. It can be used in new ways, like in microfluidics, dynamic sealing, heat dissipation, and so on. The use of hybrid nanofluids in MHD flow over a stretching surface with varying viscosity can enhance heat transfer rates. This has various applications in industries such as, cooling systems in electronics, thermal management in aerospace, and energy system. But the properties of boundary layer flow and rate of heat transfer for hybrid nanofluids could be studied more in a space with more dimensions and with other physical assumptions around the flow of fluids. The current study's major purpose is to investigate the flow of a three-dimensional hybrid nanofluid over a stretched sheet as its viscosity changes. Furthermore, the effects of the Smoluchowski temperature and Maxwell velocity slip boundary conditions are considered. Hybrid nanofluid was created by dispersing copper (Cu) and alumina (Al2O3) nanoparticles in a base fluid (H2O). Similarity variables are employed to transform a set of nonlinear partial differential equations (PDEs) that govern fluid flow and heat transfer into a system of higher-order ordinary differential equations (ODEs). The RKF method in Mathematica solves the higher-order nonlinear ODEs. Graphical analyses and in-depth discussions examine how leading variables affect velocity and temperature profiles. The expressions for skin friction and local Nusselt number are explicitly formulated, and graphs illustrate the variations of these two quantities across different parameter values. When velocity slip parameter goes up, velocity profile f′ηgoes down, and the temperature profile θ(η) also goes down when the temperature slip parameter goes up. As the velocity slip parameter goes up, skin friction goes down, while the Nusselt number goes up as the temperature slip parameter goes up. When results of this study are compared to some of results that have already been published, they are found to be very interesting as heat transfer increases due to the impacts of physical parameters.

Effect of hydrodynamic slip on thermoelectric response in negatively-charged nanofluidic channels

Nanofluidic thermoelectrics has attracted significant interest recently due to its potential for low-grade heat recovery. However, the impact of hydrodynamic slippage on power generation performance in nanofluidic channels has generally been ignored in previous studies, although slip velocity boundary conditions are relevant at the nanoscale. To fill this research gap, this study conducted two-dimensional (2D) numerical simulations based on non-isothermal Poisson, Nernst–Planck, Navier–Stokes, and energy equations to investigate the thermoelectric response, including Seebeck coefficient, thermoelectric current, power factor, and normalized maximum power density, within a nanochannel with slippage at the channel walls. The simulations considered three thermal-driven ion transport mechanisms: temperature-dependent ion electrophoretic mobility (TDIEM), Soret-type ion thermodiffusion, and thermoosmosis. The results showed that TDIEM and thermoosmosis primarily dominate the thermoelectric response of electrolyte confined in slip nanochannels in the presence of the overlapping electrical double layer. The study also found that the impact of access resistance on the thermoelectric response must be considered. The slip-enhancement of the Seebeck coefficient, i.e., the thermoelectric voltage at open-circuit condition, is not significant due to the increase in surface conductivity caused by slip-amplified electroosmosis, especially at low electrolyte concentrations. However, slip-amplified thermoosmosis greatly enhances the thermoelectric current at short-circuit condition, in the absence of the access resistance effect, leading to a significant improvement in the performance of ionic thermoelectricity in nanochannels with hydrodynamic slippage. At a moderate slip length ranging from 10 to 50 nm, it was found that the normalized maximum power density in a 2 nm nanochannel exceeded 10 mW K−2 m−2, even under a small temperature difference of 10 K, which is one order of magnitude higher than the typical thermionic capacitors and thermocells. Overall, this study provides valuable insights into developing efficient nanofluidic-based thermoelectric generators for low-grade heat energy harvesting by highlighting the importance of considering the effect of hydrodynamic slippage.

Mixed convective-quadratic radiative MoS 2–SiO 2/H 2 O hybrid nanofluid flow over an exponentially shrinking permeable Riga surface with slip velocity and convective boundary conditions: Entropy and stability analysis

In this work, the flow of a hybrid /water nanofluid across a porous exponentially diminishing Riga surface with the effects of quadratic heat radiation is taken into account. We also considered the effects of mixed convection, slip velocity, and convective thermal boundary conditions. Before numerically solving the governing partial differential equations, the MATLAB function bvp4c was used to get a comprehensive description of all relevant flow characteristics. The ramifications of physical characteristics concerning fluid flow and thermal profile are investigated using graphs and tables. The primary objective of this study is to investigate the Nusselt number, skin friction coefficient, and entropy production. Using the second law of thermodynamics, the irreversibility factor is computed. For a given value of the mass suction parameter, the findings also indicate the occurrence of dual-nature solutions in the shrinking sheet area, with a stable upper solution branch and unstable bottom solution branch. In addition, the first solution produces a positive minimum eigenvalue, whereas the second solution produces a negative eigenvalue, showing the stability of the first solution. For heat transfer enhancement, the existence of quadratic thermal radiative parameter impacts is more advantageous. With a larger value for the modified Hartman number, the velocity field has expanded. Also, recent research demonstrates that raising the thermal Biot number enhances the thermal gradient. Increases in nanoparticle volume fraction and thermal radiation parameters lead to a commensurate rise in entropy production. Because of these findings, we can better regulate the temperature of various environments by controlling the flow of heat.

Analysis of the slip flow in the hydrodynamic entrance region of a 2D microchannel

Two-dimensional developing flow in the entrance of a microchannel has been studied numer-ically. 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 Reyn-olds 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 stud-ies 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.

Entropy generation in magnetohydrodynamic radiative non-Darcy slip flow of a Casson nanofluid with Hall effects and activation energy

The present research work examines the entropy generation in the magnetohydrodynamic second-order slip flow of Casson nanofluid surpassing a horizontal stretching sheet inside a non-Darcy porous medium under the dominance of Hall current and nonlinear thermal radiation. The present model is made more realistic by taking second-order velocity slip flow. The energy field is pursued by incorporating the consequences of distinctive viscous dissipation and Joule heating. The chemical reaction incited by activation energy is comprised in the current exploration. A substantive mathematical problem is modeled by assigning nonlinear partial differential equations together with second-order velocity slip and convective boundary conditions. A compatible similarity transformation comprised is exerted to produce a set of nonlinear ordinary differential equations with competent boundary conditions. The resulting mathematical model is numerically solved via the spectral quasi-linearization method. The present article deals with an in-depth exploration of the characteristics of diagnostic flow parameters against the-flow field and other efficient physical quantities with the help of distinctive graphs and tables. As per the regression analysis, the maximum relative error for the reduced Nusselt number ranging from .000090231% to .00015936% is less than that of the other physical quantities. Magnetic force, thermophoresis, and Brownian motion assist in lessening the heat transport rate, but it gets enriched under the Hall current effects. For the increasing Casson parameter, fluid movement tends to rise near the sheet’s surface and gets decelerated afterwards. The intense Hall current accelerates the Casson fluid’s motion. But the velocity components in xandz-directions become abated across the flow region due to increasing the first-order velocity slip parameter. Besides, the enhancement in the magnitude of the second-order velocity slip parameter undermines the velocity components in xandz-directions.