Incompressible Nanofluid Flow Research Articles

Intelligent neuro-computational modelling for MHD nanofluid flow through a curved stretching sheet with entropy optimization: Koo–Kleinstreuer–Li approach

Abstract The present study explores the dynamics of a two-dimensional, incompressible nanofluid flow through a stretching curved sheet within a highly porous medium. The mathematical model is formulated by including external forces such as viscous dissipation, thermal radiation, Ohmic heating, chemical reactions, and activation energy by utilizing a curvilinear coordinate system. The viscosity and thermal conductivity of the nanofluids are examined using the Koo–Kleinstreuer–Li model. The choice of $Al_{2}O_{3}$ and $CuO$ nanoparticles in this model stems from their distinct thermal properties and widespread industrial applicability. By non-dimensionalizing the governing partial differential equations, the physical model is simplified into ordinary differential equations. BVP-5C solver in MATLAB is utilized to numerically solve the obtained coupled non-linear ordinary differential equation. Graphical results are presented to investigate the velocity, temperature, and concentration profiles with entropy generation optimization under the influence of several flow parameters. The artificial neural network backpropagated with Levenberg–Marquardt method (ANN-BLMM) used to study the model. The performance is validated using regression analysis, mean square error and error histogram plots. The outcome illustrates that the velocity and temperature profiles increase with increasing the Forchhiemer parameter. Also, the velocity profile increases with increasing curvature parameter, while, reverse effect is observed for temperature profile. This research augments our comprehension of nanofluid dynamics over curved surfaces, which has implications for engineering applications. The insights gained have the potential to significantly contribute to the advancement of energy-efficient and environmentally sustainable cooling systems in industrial processes.

Peristaltic flow of incompressible nano fluid Al2O3/water under the effect of heat addition/absorption inside a vertical cylindrical tube

Peristaltic flow of incompressible nano fluid Al2O3/water under the effect of heat addition/absorption inside a vertical cylindrical tube

MHD NANOFLUID FLOW PAST AN INCLINED PLATE WITH SORET AND DUFOUR EFFECTS

A steady incompressible nanofluid flow past an inclined permeable plate is numerically studied, including radiation, viscous dissipation, and Soret and Dufour effects. A coupled non-linear simultaneous differential similarity equation is created by non-dimensionalizing the ruling partial differential equations. Then, nonlinear coupled equations with transformed boundary conditions are resolved by the shooting method based on the Runge-Kutta fourth-order method. The Prandtl number, Grashof number, Schmidt number, magnetic parameter, and Soret and Dufour effects are just a few of the controlling flow parameters for which computations are done. Graphs are used to illustrate how various flow factors affect momentum, energy, and concentration equations. The impacts of these variables on skin friction coefficients, Nusselt number, and Sherwood number are given in tabular form. The concentration profile increases with the Soret number and the reverse trend is observed with the Dufour number. It is further noted that heat-mass transfer rate reduces in the boundary layer due to an increase in the values of Soret or a decrease in the values of Dufour.

Influence of non-uniform magnetic field on the thermal efficiency hydrodynamic characteristics of nanofluid in double pipe heat exchanger

Enhancement of the heat transfer rate inside the double pipe heat exchangers is significant for industrial applications. In present work, the usage of non-uniform magnetic field on the heat transfer rate of the nanofluid flow streamed inside double pipe heat exchangers are comprehensively studied. Computational technique of CFD is used for the visualization of the nanofluid hydrodynamic in existence of the magnetic source. Influences of the magnetic intensity and nanofluid velocity on the heat transfer are also presented. Simple algorithm is used for the modeling of the incompressible nanofluid flow with addition of magnetic source. Presented results show that magnetic source intensifies the formation of the circulation in the gap of the inner tube and consequently, heat transfer is enhanced in our domain. Comparison of different geometries of tube reveals that the triangle tube is more efficient for improvement of the heat transfer of nanofluid flow. Our results indicate that heat transfer in the tube with triangular shape is more than other configurations and its performance is 15% more than smooth tube.

Impact of Artificial Compressibility on the Numerical Solution of Incompressible Nanofluid Flow

The numerical solution of compressible flows has become more prevalent than that of incompressible flows. With the help of the artificial compressibility approach, incompressible flows can be solved numerically using the same methods as compressible ones. The artificial compressibility scheme is thus widely used to numerically solve incompressible Navier-Stokes equations. Any numerical method highly depends on its accuracy and speed of convergence. Although the artificial compressibility approach is utilized in several numerical simulations, the effect of the compressibility factor on the accuracy of results and convergence speed has not been investigated for nanofluid flows in previous studies. Therefore, this paper assesses the effect of this factor on the convergence speed and accuracy of results for various types of thermo-flow. To improve the stability and convergence speed of time discretizations, the fifth-order Runge-Kutta method is applied. A computer program has been written in FORTRAN to solve the discretized equations in different Reynolds and Grashof numbers for various grids. The results demonstrate that the artificial compressibility factor has a noticeable effect on the accuracy and convergence rate of the simulation. The optimum artificial compressibility is found to be between 1 and 5. These findings can be utilized to enhance the performance of commercial numerical simulation tools, including ANSYS and COMSOL.

Effect of chemical reaction on double diffusive MHD squeezing copper water nanofluid flow between parallel plates

This article presents the investigation relating to the mass and heat transfer characteristics of MHD copper–water unsteady incompressible nanofluid flow squeezed within two parallel plates in the presence of applied magnetic field and chemical reaction by employing a systematic method called Differential Transformation Method (DTM) and numerically solved using Runge–Kutta–Fehlberg method. The distinct feature is the inclusion of chemical reaction term of order greater than or equal to one. The governing nonlinear two-dimensional PDEs are altered into ODEs using similarity transformations. The flow, heat and mass transfer results thus found are validated with previous investigations. Effects of squeezing parameter, Eckert and Hartmann numbers on velocity, thermal and mass transfer profiles are analysed and the behaviour of squeeze number on skin friction, Sherwood and Nusselt numbers are dissertated and concluded by means of diagrams. Through this study, it is found that the concentration field reduces for positive values of Cr and rises for negative values of Cr whereas Sherwood number decreases when Cr increases. Increment in order of chemical reaction parameter results in increasing solutal profile.

Entropy Optimization in MHD Nanofluid Flow over an Exponential Stretching Sheet

We numerically investigate mixed convective heat and mass transport in incompressible nanofluid flow through an exponentially stretching sheet with temperature-dependent viscosity. The fluid flow equations are transformed to a system of non-linear ordinary differential equations using appropriate similarity transformations and solved numerically by using the multi-domain bivariate spectral quasi-linearization technique. The fast convergence of the method is shown by demonstrating that the error is exponentially small for a finite number of iterations. The significance and impact of different fluid parameters are presented and explained. For engineering relevance, the entropy generation number has been calculated for different fluid parameter values.

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.

A Study of MHD Fluid with Second Order Slip and Thermal Flow Over a Nonlinear Stretching Sheet

An electrically conducted viscous incompressible nanofluid flow caused by the nonlinear stretching surface with stagnation flow has been investigated numerically. The effect of Brownian motion and thermophoresis on the nanofluid is also incorporated. The governing partial differential equations with nonlinear second order boundary conditions are solved by the fourth order Runge-Kutta technique using MATLAB programming. The effect of the radiation parameter (<i>Rd</i>), stretching parameter (n), Brownian motion parameter (<i>Nb</i>), thermophoresis parameter (<i>Nt</i>) on temperature, velocity and mass transfer are shown graphically. The influence of some of these parameters on the local Nusselt number (− <i>θ</i>′(0)) and local Sherwood number (−<i>ϕ</i>′(0)) are shown by the graphs.

Crank Nicholson scheme to examine the fractional-order unsteady nanofluid flow of free convection of viscous fluids.

Fractional fluid models are usually difficult to solve analytically due to complicated mathematical calculations. This difficulty in considering fractional model further increases when one considers nth order chemical reaction. Therefore, in this work an incompressible nanofluid flow as well as the benefits of free convection across an isothermal vertical sheet is examined numerically. An nth order chemical reaction is considered in the chemical species model. The specified velocity (wall's) is time-based, and its motion is translational into mathematical form. The fractional differential equations are used to express the governing flow equations (FDEs). The non-dimensional controlling system is given appropriate transformations. A Crank Nicholson method is used to find solutions for temperature, solute concentration, and velocity. Variation in concentration, velocity, and temperature profiles is produced as a result of changes in discussed parameters for both Ag-based and Cu-based nanofluid values. Water is taken as base fluid. The fractional-order time evaluation has opened the new gateways to study the problem into a new direction and it also increased the choices due to the extended version. It records the hidden figures of the problem between the defined domain of the time evaluation. The suggested technique has good accuracy, dependability, effectiveness and it also cover the better physics of the problem specially with concepts of fractional calculus.

Heat flow saturate of Ag/MgO-water hybrid nanofluid in heated trigonal enclosure with rotate cylindrical cavity by using Galerkin finite element

MHD Natural convection, which is one of the principal types of convective heat transfer in numerous research of heat exchangers and geothermal energy systems, as well as nanofluids and hybrid nanofluids. This work focuses on the investigation of Natural convective heat transfer evaluation inside a porous triangular cavity filled with silver-magnesium oxide/water hybrid nanofluid [H2O/Ag-MgO]hnf under a consistent magnetic field. The laminar and incompressible nanofluid flow is taken to account while Darcy–Forchheimer model takes account of the advection inertia effect in the porous sheet. Controlled equations of the work have been approached nondimensional and resolved by Galerkin finite element technique. The numerical analyses were carried out by varying the Darcy, Hartmann, and Rayleigh numbers, porosity, and characteristics of solid volume fraction and flow fields. Further, the findings are reported in streamlines, isotherms and Nusselt numbers. For this work, the parametric impact may be categorized into two groups. One of them has an effect on the structural factors such as triangular form and scale on the physical characteristics of the important outputs such as fluidity and thermal transfer rates. The significant findings are the parameters like Rayleigh and slightly supported by Hartmann along with Darcy number, minimally assists by solid-particle size and rotating factor as clockwise assists the cooler flow at the center and anticlockwise direction assists the warmer flow. Clear raise in heat transporting rate can be obtained for increasing solid-particle size.

Dynamics of Activation Energy and Nonlinear Mixed Convection in Darcy-Forchheimer Radiated Flow of Carreau Nanofluid Near Stagnation Point Region

Abstract In this research work, heat and mass transport and radiated, two-dimensional, steady, incompressible nanofluid flow of non-Newtonian material (Carreau fluid) over a stretchable moving surface of sheet is examined. The flow is saturated through Darcy-Forchheimer porous medium and generated by stretching phenomenon. Furthermore, magnetodydrodynamics (MHD), mixed convection, heat generation/absorption, nonlinear thermal radiation, thermophoresis diffusion, activation energy, Brownian motion, and chemical reaction effects are accounted to develop the governing expressions, i.e., momentum, energy, and concentration for the considered flow problem. The governing equations are first altered into nonlinear ordinary differential equations with the help of appropriate similarity variables and then computational results are computed by Built-in-Shooting technique via mathematica. The salient aspects of sundry variables are discussed graphically on the velocity field, skin friction coefficient, temperature profile, Nusselt number, concentration field, and Sherwood number. Outcomes illustrate that the velocity field and temperature profile have contrast behavior against higher values of magnetic parameter. Also, the engineering quantities are discussed numerically with the help of important flow variables and the results are demonstrated through tables.

Computational modelling of nanofluid flow over a curved stretching sheet using Koo–Kleinstreuer and Li (KKL) correlation and modified Fourier heat flux model

• Flow and heat transfer characteristics of nanoliquid by using Koo–Kleinstreuer and Li (KKL) correlation is studied. • Modified Fourier heat flux law is utilised to model the temperature equation. • Viscous dissipation, activation energy and chemical reaction effects are used to study heat and mass transfer characteristics. • Accurate numerical solutions are obtained using Runge-Kutta-Fehlberg fourth fifth order along with shooting technique. The objective of the current paper is to study the two-dimensional, incompressible nanofluid flow over a curved stretching sheet coiled in a circle. Further, the impact of dispersion of nanoparticle CuO in base liquid water on the performance of flow, thermal conductivity and mass transfer using KKL model in the presence of Cattaneo-Christov heat flux and activation energy is deliberated. A curvilinear coordinate system is used to develop the mathematical model describing the flow phenomena in the form of partial differential equations . Further, by means of apt similarity transformations the governing boundary value problems are reduced to ordinary differential equations. Mathematical computations are simplified using Runge-Kutta-Fehlberg-45(RKF-45) process by adopting shooting method. Graphical illustrations of velocity, temperature, concentration gradients for various pertinent parameters are presented. The result reveals that, the heightening of porosity parameter heightens the thermal gradient but converse trend is depicted in velocity gradient. The enhancing values of Schmidt number and chemical reaction rate parameter declines concentration gradient whereas converse trend is depicted for upsurge in activation energy parameter.

Thermal effects of the nonuniform magnetic force on nanofluid stream along the convergent tube: A computational study

In this research study, computational investigations are prepared to demonstrate the influence of the nonhomogeny magnetic source on the thermal efficiency of the convergent tube with the nanofluid flow. The major attention of our examination is to analyze the flow stream and temperature spreading on the average Nusselt number of the base fluid with Fe2O3 nanoparticles. The effects of inlet velocity and magnetic intensity on the thermal characteristics of nanofluid stream through the convergent tube are fully investigated. SIMPLEC algorithm is used for the imitation of the incompressible nanofluid flow inside the convergent tube. Our results indicate that growing Reynolds number from 50 to 100 surges heat rates up to 18% in the convergent tube because of the existence of the magnetic field in the vicinity of the tube.

Influence of Magnetic Field on Thermal Radiation and Particle Shapes of Copper-Water Nanofluid Considering Marangoni Boundary Layer

This problem aims to address hydrodynamic Marangoni boundary layer flow of incompressible nanofluid along different shapes of particle like sphere, tetrahedron, column and lamina with exponential temperature. Choosing appropriate transformations, the governing equations are reduced to non-linear ordinary differential equations and then solved by using a perturbation technique. Impacts in velocity and temperature profiles for the relevant considering parameters namely nanoparticle volume fraction, magnetic parameter, empirical shape factor and radiation parameter are evaluated and shown through graphs. Moreover, computational values for influences of physical parameters on local surface heat flux are presented in table.

The method of lines for solution of the carbon nanotubes engine oil nanofluid over an unsteady rotating disk

The main target of the present model is to find the idea of magneto-hydrodynamics incompressible nanofluid flow past over an infinite rotating disk. The effect of the magnetic field is existed to check the nanofluid flow. The single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) engine oil can be utilized despite carrier fluid for an unsteady rotating disk. Here, we transform the nonlinear system of differential equations to the dimensionless ordinary differential equation by using similarity transformation. Then, we use the numerical method of lines to solve the nonlinear ODE via the Runge–Kutta technique. The resultant of the velocity, Nusselt number and Skin friction is demonstrated under the effect of several factors. We note that when we increase the velocity of the rotating disk, fluid velocity and temperature are safely increased. Finally, we note that the outcomes obtained demonstrate that the SWCNTs nanofluids improved the heat transfer more than the MWCNTs.

Theoretical Investigation of Entropy Generation in Axisymmetric Stagnation Point Flow of Nanofluid Impinging on the Cylinder Axes with Constant Wall Heat Flux and Uniform Transpiration

Dimensionless temperature, Nusselt number and entropy generation in stagnation flow of incompressible nanofluid impinging on the infinite cylinder with uniform suction and blowing have been presented in this study. Initial stream rate of steady free stream is . Similarity solution of Navier-stokes and energy equations has been presented. These equations are simplified implementing appropriate transformations introduced in this research. The governing equations are solved where the heat flux at the cylinder’s wall is constant. All these solutions are acceptable for Reynolds numbers of 0.1-1000, various dimensionless surface diffusion and specific volume fractions of nanoparticles where a is the cylinder radius and is the kinematic viscosity of the base-fluid. The results show that for all Reynolds numbers, diffusion depth of radial and axial components of velocity field and wall shear stress increases as a result of decline in nano particles volume fraction and growth in surface diffusion. Moreover, increase in nanoparticles volume fraction and surface suction raises heat transfer coefficient and Nusselt number. Also the most entropy generated is calculated.

Magnetohydrodynamic and Heat Transfer Impacts on Ferrofluid Over a Rotating Disk: An Application to Hard Disk Drives

Abstract The motivation behind this article is to explore the impacts of heat transfer, magnetohydrodynamic, and hall current on two-dimensional incompressible nanofluid flow over a rotating disk. The nanofluid model utilized in the present investigation comprises the nanoparticle fraction model. Two sorts of nanoparticles to be specific Hematite (Fe2O3) is the principal source of iron and Cobalt alloy (Co64 Cr30 W6) is generally used metal alloy that is primarily Cobalt and Chromium with base fluid Motor Oil 10W30 is taken into consideration. The Prandtl number identifying with motor oil is (Pr = 1531.92). The governing equations are reduced to a system of ordinary differential equations by using Von-Karman transformation and then solved numerically utilizing matlab bvp4c. Impacts of the magnetic field, hall current, and nanoparticle volume fraction on tangential, radial velocities, and temperature profiles have been examined. Numerical outcomes have been acquired for various physical parameters through graphical representation. We have demonstrated that a remarkable reconciliation exists among the current outcomes and those in the literature for various values of magnetic parameter and velocity slip parameters, in the absence of other parameters. It is also found that radial and tangential velocities increase more in the case of Fe2O3 nanoparticles when compared with Co64 Cr30 W6 because of density variations. It is discovered that enhancement in a nanoparticle volume fraction reduces the heat transfer rate. It can moreover be clarified such a way that as the nanoparticle volume fraction raise, the density of nanoparticles increases, temperature also increases subsequently heat transfer rate decreases. This result keeps more cooling for the hard disk drives and might be intrigued for engineers.

Influences of electrical MHD and Hall current on squeezing nanofluid flow inside rotating porous plates with viscous and joule dissipation effects

Nanofluids have the ability to flow smoothly in micro-cavities in addition with scattering of the nanoparticles. Because of the good convection between nanoparticles and the base fluid, nanofluids can achieve a good thermal conductivity. The main advantages of adding nanosize particles with base fluid are to improve the ability of storing heat, effective surface area, heat transmission, collisions and interaction among the nanoparticles. The main aim of this research work is to examine the steady and incompressible nanofluid flow between parallel rotating plates. Viscose and joule dissipation effects are taken into account. To our knowledge, impact of electrical MHD and Hall effect with Cattaneo–Christov heat flux on the squeezing 3-D flow nanofluid between parallel rotating plates are not examined yet. Heat in the form of Cattaneo–Christov heat flux is applied. We used similarity transformations to transform the primary equations to a system of ordinary differential equations (ODEs). These ODEs are then solved through the standard procedure of homotopy analysis technique. The skin friction and Nusselt number are numerically tabulated under the influence of some focused parameters. The effects produced by different parameters on the velocity (components) and temperature profiles are graphically depicted and explained in a bit detail.

Impact of Nonlinear Chemical Reaction and Melting Heat Transfer on an MHD Nanofluid Flow over a Thin Needle in Porous Media

A novel mathematical model is envisioned discussing the magnetohydrodynamics (MHD) steady incompressible nanofluid flow with uniform free stream velocity over a thin needle in a permeable media. The flow analysis is performed in attendance of melting heat transfer with nonlinear chemical reaction. The novel model is examined at the surface with the slip boundary condition. The compatible transformations are affianced to attain the dimensionless equations system. Illustrations depicting the impact of distinct parameters versus all involved profiles are supported by requisite deliberations. It is perceived that the melting heat parameter has a declining effect on temperature profile while radial velocity enhances due to melting.