Steady Two-dimensional Flow Research Articles

A semi-analytical passive strategy to examine a magnetized heterogeneous mixture having sodium alginate liquid with alumina and copper nanomaterials near a convectively heated surface of a stretching curved geometry

In this article, the authors have analyzed a steady and incompressible two-dimensional flow of sodium alginate (SA)-based viscous ternary nanofluid including copper and alumina nanoparticles near a stretchable curved surface. A uniform magnetic field is exerted on the nanofluid flow along the radial direction. Furthermore, an appropriate convective heating process and zero wall mass flux are adopted in this study as boundary conditions. The chemical reaction, variable internal heating, thermophoresis, Brownian motion, and Arrhenius activation energy impacts are assumed. A robust semi-analytical method abbreviated as HAM (i.e., homotopy analysis method) is chosen in this analysis to get accurate solutions for the modeled problem. Additionally, HAM results are compared extensively with an outstanding tabular/graphical agreement and consistency. The impressions of the embedded factors on the velocity profile, the temperature variation, the concentration distribution, the skin friction factor, and Nusselt's number of sodium alginate-based copper nanofluid, alumina nanofluid, and copper-alumina hybrid nanofluid are deliberated comprehensively. The results showed that the velocity distribution of SA-based nanofluid and hybrid nanofluid decreases as the nanoparticles' volume fraction and magnetic factor increase, whereas the temperature distribution of SA-based nanofluid and hybrid nanofluid improves as the nanoparticles' volume fraction escalates. The rising solid volume fraction and magnetic factor increase the strength of the surface drag force of SA-based copper nanofluid and alumina nanofluid. The increasing nanoparticles' volume fraction and internal heat source parameter upsurge the heat transfer rate of SA-based copper nanofluid and alumina nanofluid. It is also revealed that the hybrid nanofluid is highly affected by the involved physical factors as compared to the case of monotype nanofluids.

Entropy generation in Williamson hybrid nanofluid with inclined magnetic field, non-uniform heat flux, thermal radiation and slip effects

The present study provides the influence of entropy generation on steady two-dimensional laminar non-Newtonian Williamson hybrid nanofluid flow past a horizontal stretching sheet under the influence of the inclined magnetic field, radiation, non-uniform heat source/sink and slip effects. The governing partial differential equations are reduced to a system of ordinary differential equations using similarity transformations. The Runge–Kutta-4rth order method and the shooting technique are then adopted to solve the system. Two different kinds of fluids namely the engine oil based Molybdenum disulfide (MoS 2) nanofluid and Zinc Oxide (ZnO)-Molybdenum disulfide (MoS 2) engine oil hybrid nanofluids are considered to investigate the flow. The effect of important parameters on velocity, temperature, entropy generation and Bejan number are displayed in the form of figures and tables. Our results for some special cases are compared with previously published results to check the present study’s correctness and were found to be in good agreement. It is observed that the Williamson parameter increases the temperature but decreases the entropy generation whereas the angle of inclination of the magnetic field increases both the temperature and entropy generation. It is also observed entropy decreases with an increase in either velocity or thermal slips whereas it increases with radiation.

Thermal stable properties of solid hybrid nanoparticles for mixed convection flow with slip features

Following to improved thermal impact of hybrid nanomaterials, wide range applications of such materials is observed in the thermal engineering, extrusion systems, solar energy, power generation, heat transfer devices etc. The hybrid nanofluid is a modified form of nanofluid which is beneficial for improving energy transfer efficiency. In current analysis, the solid nanoparticles aluminium (phi_{{{text{Al}}_{2} {text{O}}_{3} }}) and copper (phi_{{{text{Cu}}}}) have been mixed with water to produce a new hybrid nanofluid. The investigation of a steady two-dimensional mixed convection boundary layer flow of the resultant hybrid nanofluid on a vertical exponential shrunk surface in the existence of porous, magnetic, thermal radiation, velocity, and thermal slip conditions is carried out. Exponential similarity variables are adopted to transform the nonlinear partial differential equation into a system of ordinary differential equations which has been then solved by employing the shooting method in Maple software. The obtained numerical results such as coefficient of skin friction f^{prime prime } left( 0 right), heat transfer rate - theta^{prime } left( 0 right), velocity f^{prime } left( eta right) and temperature left( {theta left( eta right)} right) distributions are presented in the form of different graphs. The results revealed that duality exists in solution when the suction parameter S ge S_{ci} in assisting flow case. Due to non-uniqueness of solutions, a temporal stability analysis needs to be performed and the result indicates that the upper branch is stable and realizable compared to the lower branch.

Forced convection of non-darcy flow of ethylene glycol conveying copper(II) oxide and titanium dioxide nanoparticles subject to lorentz force on wedges: Non-newtonian casson model.

The topic of two-dimensional steady laminar MHD boundary layer flow across a wedge with non-Newtonian hybrid nanoliquid (CuO-TiO2/C2H6O2) with viscous dissipation and radiation is taken into consideration. The controlling partial differential equations have been converted to non-linear higher-order ordinary differential equations using the appropriate similarity transformations. It is demonstrated that a number of thermo-physical characteristics govern the transmuted model. The issue is then mathematically resolved. When the method’s accuracy is compared to results that have already been published, an excellent agreement is found. While the thermal distribution increases with an increase in Eckert number, radiation and porosity parameters, the velocity distribution decreases as porosity increases.

Insight into the study of natural convection heat transfer mechanisms in a square cavity via finite volume method

A computer model of heat transmission in a square cavity was created in order to have a better understanding of the consequences. Temperature differences between the top and bottom walls are what cause convection, whereas the remaining left and right walls remain adiabatic and do not contribute to the process (unheated). In order to provide an accurate estimate of the two-dimensional steady flow inside a square cavity, a novel finite volume (FV) method that incorporates adaptive upwind convection is applied. Due to natural convection’s widespread use in the industrial sector, a significant amount of research has been conducted on the topic of how its usage affects the rate of heat transfer in enclosed areas. In a square cavity, the equations for the mass balance, momentum balance, and energy balance of the system are studied.

Heat transfer analysis of compressible laminar flow in a parallel-plates channel via integral transforms

The present work analyzes a coupled nonlinear mathematical model for heat transfer in compressible laminar flow within a parallel plates channel. The governing partial differential equations are obtained considering the conservation of mass, momentum and energy, based on a two-dimensional steady laminar flow of an ideal gas with constant physical properties and taking into account viscous dissipation. Two kinds of boundary conditions at the wall were considered, namely, prescribed arbitrary temperature or heat flux longitudinal distributions. The mathematical model was solved using the hybrid numerical-analytical method known as the Generalized Integral Transform Technique (GITT). A convergence analysis of the proposed eigenfunction expansions for velocity and temperature fields was undertaken, indicating that fairly low truncation orders are required for the accurate representation of the potentials. The proposed hybrid solution was also critically compared with the Mathematica NDSolve finite difference-based routine and additional theoretical and experimental results in the literature, with good agreement in all cases considered.

Hybrid Nanofluid Radiative Mixed Convection Stagnation Point Flow Past a Vertical Flat Plate with Dufour and Soret Effects

The widespread application of hybrid nanofluid in real applications has been accompanied by a large increase in computational and experimental research. Due to the unique characteristics of hybrid nanofluid, this study aspires to examine the steady two-dimensional mixed convection stagnation point flow of a hybrid nanofluid past a vertical plate with radiation, Dufour, and Soret effects, numerically. The formulations of the specific flow model are presented in this study. The model of fluid flow that is expressed in the form of partial differential equations is simplified into ordinary differential equations via the transformation of similarity, and then solved numerically by using the boundary value problem solver known as bvp4c in MATLAB, which implements the finite difference scheme with the Lobatto IIIa formula. Two possible numerical solutions can be executed, but only the first solution is stable and meaningful from a physical perspective when being evaluated via a stability analysis. According to the findings, it is sufficient to prevent the boundary layer separation by using 2% copper nanoparticles and considering the lesser amount of Dufour and Soret effects. The heat transfer rate was effectively upgraded by minimizing the volume fraction of copper and diminishing the Dufour effect. Stronger mixed convection would lead to maximum skin friction, mass transfer, and heat transfer rates. This important preliminary research will give engineers and scientists the insight to properly control the flow of fluids in optimizing the related complicated systems.

Numerical investigation of wind velocity effects on evaporation rate of passive single-slope solar stills in Khuzestan province in Iran

Khuzestan Province is located in Iran and has average annual evaporation of over 2000 ml. It also encounters water scarcity and water salinity issues. To make proper use of the high evaporation rate in Khuzestan and help overcome the water scarcity issue, this study simulates the effects of wind velocity on the performance of passive single-slope solar stills, identifying the optimal regions for the deployment of solar stills. The wind velocities of 2.5, 7.5, 10, 12.5, 15, 17.5, and 20 m/s were incorporated. To simulate the two-dimensional steady laminar flow within the solar still, the humid air model was employed. Furthermore, the turbulence k-ε model was utilized to simulate the external flow of the solar still. The accuracy of the numerical technique was evaluated by comparing the average Nusselt number results on the water surface to different models and by comparing the production rate results to experimental data. It was observed that the numerical approach was properly accurate. The results indicate that a rise in the wind velocity decreases the freshwater production rate, with the maximum production rate reduction was occurred at a wind velocity of 15 m/s. Ramhormoz, Dehdez, and Izeh were found to be optimal regions for deploying solar stills, based on the wind velocity.

A Primer on the Dynamical Systems Approach to Transport in Porous Media

Historically, the dominant conceptual paradigm of porous media flow, solute mixing and transport was based on steady two-dimensional flows in heterogeneous porous media. Although it is now well recognised that novel transport phenomena can arise in unsteady and/or three-dimensional flows at both the pore- or Darcy-scales, appropriate methods for analysis and understanding of these more complex flows have not been widely employed. In this primer we advocate for methods borrowed from dynamical systems (chaos) theory, which aim to uncover the \emph{Lagrangian kinematics} of these flows: namely how fluid particle trajectories (which form a dynamical system) are organized and interact and the associated impacts on solute transport and mixing. This dynamical systems approach to transport is inherently Lagrangian, and the Lagrangian kinematics form Lagrangian coherent structures (LCSs), special sets of trajectories that divide the Lagrangian frame into chaotic mixing regions, poorly mixing hold-up regions (and in some cases non-mixing ``islands'') and the transport barriers that organise these regions. Hence the dynamical systems approach provides insights into flows that may exhibit chaotic, regular (non-chaotic) or mixed Lagrangian kinematics, and also into how LCSs organize solute transport and mixing. Novel experimental methods are only recently permitting visualization of LCSs are in porous media flows. In this primer we review the dynamical systems approach to porous media flow and transport and connect the associated tools and techniques with the latest research findings from pore to Darcy scales. This primer provides an introduction to the methods and tools of dynamical systems theory. Once familiar with these approaches, porous media researchers will be better positioned to know when to expect complex Lagrangian kinematics, how to uncover and understand LCSs and their impacts ...

Analysis of forced convective nanofluid flow through a wavy channel with linearly varying amplitude at the entrance

PurposeThe purpose of this paper is to analyze the heat and momentum transfer for steady two-dimensional incompressible nanofluid flow through a wavy channel with linearly varying amplitude in the entrance region.Design/methodology/approachThe mass, momentum and energy conservation equations for laminar flow of Cu-water nanofluids are computationally solved using the finite element method. A parametric study is carried out by varying the dimensionless length of the channel section with varying amplitude (EL), Reynolds number (Re) and nanoparticle volume fraction (Φ) in the ranges 0 ≤ EL ≤ 25.5, 105 ≤ Re ≤ 900 and 0 ≤ Φ ≤ 0.04.FindingsA higher heat transfer rate is seen in the wavy channel compared to a plane channel beyond a critical value of Re (Recrit) whose value varies with EL; moreover, the overall heat transfer decreases with EL. The heat transfer rate increases with phi for all EL values investigated. The combined effects of the increase in the overall heat transfer and the associated pressure drop in the wavy channel compared to the parallel plate channel are presented as performance factor (PF) against EL. For the highest value of EL (= 25.5), PF monotonically decreases with Re. For smaller values of EL (= 5.5 and 11.5) and also for EL = 0, PF decreases with Re in the lower and the higher Re regimes, while it increases in the intermediate Re regime. In all cases, PF is higher for φ = 0.04 than for the base fluid. The sensitivity of the average Nusselt number to nanoparticle volume fraction follows a non-monotonic trend with the change in Re, φ and EL.Practical implicationsThis study finds relevance in several applications such as solar collectors, heat exchangers and heat sinks.Originality/valueTo the best of the authors’ knowledge, the analysis of forced convection flow of nanofluid through a wavy channel with linearly varying amplitude is reported for the first time in the literature.

Instabilities of thermocapillary flows in large Prandtl number liquid bridges between two coaxial disks with different radii

We explore the geometric effects on the thermocapillary flow instabilities in large Prandtl number (Pr = 1.4) liquid bridges between two coaxial disks with different radii under microgravity, focusing on the impacts of radius ratio Γr and aspect ratio Γ. The static deformation of the free surface is concerned by the solution of the Young–Laplace equation, and the linear stability analysis based on spectral element method is conducted for accurate identification of the instability characteristic. We observe that the flow stability is generally improved with the decrease in radius ratio Γr or aspect ratio Γ, especially for the liquid bridge heated from the upper disk. The critical oscillation frequency experiences an abrupt drop around Γr = 0.56 as Γr decreases for the liquid bridge with the bottom disk heated. Moreover, three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow are observed within the interval 0.87 < Γ ≤ 0.91 at Γr = 0.50 when the liquid bridge is heated from the upper disk. The energy analysis indicates that the instabilities for all cases are predominantly caused by the hydrothermal wave instability and the phenomenon of three transitions results from the variation of thermal energy transfer efficiency with the growth of the Marangoni number.

Variable thermal effects of viscosity and radiation of ferrofluid submerged in porous medium

Ferrofluid is a liquid that becomes magnetized in the presence of magnetic field. Applications involves in electronic devices, mechanical engineering, materials science research and loudspeakers. This study is achieved to explore the novel two-dimensional steady ferrofluid flow in a porous medium with the temperature dependent thermal conductivity and viscosity effect. ODE’s are obtained with the help of appropriate similarity transformation. Later the equations are work out by applying shooting scheme with RK-4 technique. To achieve the results of non-dimensional physical parameters the numerical computations are put into execution. The graphical consequences for fluids velocity and temperature for variable effects of viscosity and thermal conductivity are demonstrated. Velocity of fluid decays for viscosity parameter while the temperature uplifts in the presences of viscosity. Furthermore, comparison of the results with previous one shows that the applied method is efficient and useful for calculating the parameters of present problem and have acceptable accuracy.

Potential flow around polygonal shaped cylinders using hypotrochoidal mapping function

In this paper, some investigations on two-dimensional steady potential flow over polygonal shaped cylinders are presented. The polygonal shapes with finite corner radius are obtained using Hypotrochoidal mapping function. The complex potential function derived using Milne-Thompson circle theorem, along with Hypotrochoidal mapping is employed to get various flow parameters over different shaped cylinders. The uniform and non-uniform flow conditions are arrived at, by taking infinite and finite distance of vortex from the cylinder, respectively. The velocity and pressure distribution over various shaped cylinders are presented and some of them are compared with the results from commercial software package (ANSYS) and available literature. Formulas are developed to obtain velocity and pressure distribution around various shaped geometries. Also, the effect of various geometrical parameters on velocity and pressure distribution is studied.

Computation of heat transfer in magnetised Blasius flow of nano-fluids with suspended carbon nanotubes through a moving flat plate

This paper examines a two-dimensional steady, incompressible and laminar hydro-magnetic flow along with the transfer of heat above a plane plate that contains water and ethylene glycol-based nano-fluids with multi- and single-wall CNTs. The plate surface is subjected to variable wall temperatures. The transfer of heat has been contemplated in suspended CNTs above a plane plate. Navier–Stokes and the concept of the Prandtl boundary layer have been used to determine the governing equations of heat transfer and flow. Since the attained governing equations representing energy and flow are non-linear PDEs, they are altered into non-linear ODEs accompanied by analogous boundary conditions by applying several appropriate similarity transformations. Hence, the ‘bvp4c’ function is used to solve them numerically. Various graphs with physical interpretation demonstrate the consequence of determining terms on the characteristics of the flow. The plate velocity parameter and volume fraction have a positive effect. Temperatures are elevated markedly for most of the governing parameters. The rate of heat transfer and temperature exponent are enhanced by a magnetic field. SWCNTs give more substantial heat transfer than MWCNTs.

Momentum balance based model for predicting the scale of separation bubbles induced by incident shock wave/turbulent boundary layer interactions

The incident shock wave/turbulent boundary layer interactions (SWTBLIs) over a wide range of flow conditions are predicted by the Reynolds-averaged Navier–Stokes (RANS) numerical method to generate detailed two-dimensional steady flow field data. After examining the momentum balance terms over the control volume involving the separation bubble, it is concluded that the values of the pressure-force and the momentum-rate terms are significantly higher than the total stress-force term. Ignoring the effect of those small terms on the control surface, a model for the prediction of SWTBLI separation bubble scale is proposed based on the momentum balance over the two-dimensional control volume. For model prediction, essential correlations for key characteristic physical quantities are given. The predicted normal and streamwise scales of the SWTBLI separation bubble are in good agreement with the experimental results in the literatures.

Steady flow past elliptic cylinders with blockage effects

In the present work, steady two-dimensional flow past elliptic cylinders with different aspect ratios (Ar) have been investigated for Reynolds number (Re) up to 200. Main characteristics such as the bubble length, bubble width, separation Reynolds number, separation angle, drag coefficient, coefficients of the front and rear stagnation pressure, and the maximum vorticity on the cylinder surface have been obtained. Least squares fit equations for some of these quantities have also been presented. In the special case of a circular cylinder, results computed with the largest domain show that the bubble length, bubble width, maximum vorticity on the cylinder surface, coefficient of pressure drag, coefficient of total drag, and flow separation angle are linear functions of Re, Re0.5, Re0.35, Re−0.4, Re−0.5, and Re−0.1, respectively. As Ar changes, the trends in the growth, with respect to Ren (with the corresponding index), for the bubble length, bubble width, and the maximum surface vorticity deviate from their linear nature. The effect of blockage on the steady flow characteristics has been studied by changing the location of the side boundaries. In certain cases, the flow properties are found to vary in a non-monotonic fashion with the change in the blockage. An explanation based on the dual role of the side boundaries in promoting and suppressing the growth of the corresponding flow property is offered.

Particle and radiative heat transmission in the Sutterby nanoliquid over a curved stretched surface

The purpose of this paper is to investigate the steady two-dimensional flow of the incompressible Sutterby nanoliquid over a coiled stretched surface. Heat transfer is portrayed by the mechanisms of linear thermal radiation and viscous dissipation, whereas mass transfer is characterized by Brownian motion and thermophoresis. The curvilinear coordinates system is used to design the mathematical modeling. Using similarity transformation, the achieved equation set is reshaped into a system of nonlinear ordinary differential equations. The governed system is solved by shooting via the Runge Kutta Fehlberg (RKF) approach. The research seeks to evaluate physical quantities, such as flow velocity, temperature, and concentration distribution, surface resistance, heat, and mass fluxes for various pertinent parameters. The investigation states that the higher curvature, Sutterby fluid parameter, and thermal radiations enhance the temperature of a nanoliquid.

Mass-based hybrid nanofluid model for entropy generation analysis of flow upon a convectively-warmed moving wedge

In this research, the steady incompressible laminar two-dimensional hybrid nanofluid flow upon a convectively-warmed moving wedge with radiative transition has been studied numerically. The nanoparticles are the magnetite (Fe3O4) and the graphene oxide (GO), in two research parts of spherical and non-spherical (brick, cylinder, platelet, and disk) shapes, suspended in the pure water as base fluid. Three main geometries of the well-known Falkner-Skan problem including: (i) the flat plat (named Blasius flow), (ii) the wedge, and (iii) the vertical plate (named Hiemenz stagnation flow) have been considered to present a comprehensive development of this significant problem. The applied methodology is according to the single-phase Tiwari-Das hybrid nanofluid model considering the masses of nanoparticles and base fluid instead the volume concentration of first and second nanoparticles. For the first time, the mentioned mass-based method will be utilized in combination with the entropy generation analysis. The governing dimensional PDEs are varied to a system of non-dimensional ODEs with the use of similarity transformation technique which is then solved numerically through Runge–Kutta–Fehlberg method coupled with a conventional shooting procedure. The effect of the governing parameters on the hybrid nanofluid velocity, the temperature distribution, the skin friction coefficient, the Nusselt number, the entropy generation, and the Bejan number has been investigated and interpreted through the tabular and graphical results. A reliable treatment of the mass-based method for the hybrid nanofluid flow, the heat transfer and especially the entropy analysis is the substantial achievement of the present research; although, the detailed results have been presented and discussed in the article's body. Certainly, new modeling and approaches for the hybrid nanofluid can be dramatically beneficial in the various industries in which the cooling technologies are vital

Momentum and heat transfer characteristics for Newtonian fluid across a grooved cylinder

The present investigation set out to assess the influence of the surface roughness on the flow and thermal mean quantities, around the heated corrugated cylinder in the laminar steady flow. The current investigation has been devoted to a numerical analysis of a two-dimensional steady flow and forced convection heat transfer characteristics over a heated longitudinal sinusoidal shape grooved cylinder, immersed in an unconfined Newtonian fluid. The number of the grooved cavities was chosen to be 10, 20 and 30 grooves, equally distributed around the cylinder circumference with wavelength and wave amplitude of 1/50 and 1, respectively. Moreover, the thermal boundary condition effect has been analyzed by imposing a uniform heat flux and constant temperature on the cylinder periphery as a thermal boundary condition, over a Reynolds number range of ([Formula: see text]) and a fixed Prandtl number of 0.715. The numerical procedure is based on the finite volume method. The findings indicate that with increasing groove number, the total drag coefficient of the grooved cylinder reduces markedly compared to the smooth one. This trend is more pronounced as the Reynolds number increases. The effect of the groove number on the pressure coefficients is limited, where the profiles of the grooved cylinder coincide with that of the smooth one over the Reynolds number range. When the Reynolds number varies from 0.1 to 40, the average Nusselt number enhances noticeably by about 86% for the smooth and grooved cylinders. Moreover, the groove number affects significantly the average Nusselt number, where the increased groove number results in a gradual reduction in the average Nusselt number. This attenuation is more pronounced as the Reynolds number increases. To predict the average Nusselt number, a correlation has been proposed.

Numerical modeling of unsteady MHD flow of Casson fluid in a vertical surface with chemical reaction and Hall current

The non-Newtonian fluid flow plays an important role in industrial and manufacturing processes such as painting, printing, coating, and biomechanical. In the present paper, the steady two-dimensional MHD free convective flow of Casson fluid over a vertical surface is elucidated numerically with the impact of thermal radiation and chemical reaction are offered. The interaction of transverse magnetic field, viscous dissipation, and Hall current are taken into the account. A nonlinear flow system is developed to decompose the heat and mass transmission effects of this liquid, which is done by taking an appropriate extreme boundary condition. Non-dimensional nonlinear ordinary differential equations (ODEs) are diminished from governing partial differential equations (PDEs) via fitting transformations. The fundamental model of nonlinear constitutive flow laws is tackled numerically through the ND-solve technique in a Mathematica 11.0 environment. The computational upshot is also described explicitly to examine the consequences pertinent parameters. The attained sundry parameters are analyzed expediently, which include magnetic factor, radiation, chemical reaction, Prandtl number, heat source, modified Grashof number, and Schmidt number. The features of the governing relevant parameters on the flow frameworks are analyzed correctly via plots and tables. Additionally, the drag force, heat, and mass transference coefficients outlines are examined.