Lid-Driven Chamber with 3D Elliptical Obstacle under the Impacts of the Nano-Properties of the Fluid, Lorentz Force, Thermal Buoyancy, and Space Porosity.

In this work, we have performed an investigation to increase our understanding of the motion of a hybrid nanofluid trapped inside a three-dimensional container. The room also includes a three-dimensional heated obstacle of an elliptic cross-section. The top wall of space is horizontally movable and adiabatic, while the lower part is zigzagged and thermally insulated as well. The lateral walls are cold. The container's space is completely replete with Al2O3-Cu/water; the concentration of nanoparticles is 4%. The space is also characterized by the permeability, which is given by the value of the Darcy number (limited between 10-5 and 10-2). This studied system is immersed in a magnetic field with an intensity is defined in terms of Hartmann number (limited between 0 and 100). The thermal buoyancy has a constant impact (Gr = 1000). This study investigates the influences of these parameters and the inclination angle of the obstacle on the heat transfer coefficient and entropy generation. The Galerkin finite element method (GFEM) was the principal technique for obtaining the solution of the main partial equations. Findings from our work may be exploited to depict the conditions for which the system is effective in thermal cooling and the case in which the system is effective in thermal insulation.

Modelling Entropy in Magnetized Flow of Eyring-Powell Nanofluid through Nonlinear Stretching Surface with Chemical Reaction: A Finite Element Method Approach.

The present paper explores the two-dimensional (2D) incompressible mixed-convection flow of magneto-hydrodynamic Eyring-Powell nanofluid through a nonlinear stretching surface in the occurrence of a chemical reaction, entropy generation, and Bejan number effects. The main focus is on the quantity of energy that is lost during any irreversible process of entropy generation. The system of entropy generation was examined with energy efficiency. The set of higher-order non-linear partial differential equations are transformed by utilizing non-dimensional parameters into a set of dimensionless ordinary differential equations. The set of ordinary differential equations are solved numerically with the help of the finite element method (FEM). The illustrative set of computational results of Eyring-Powell (E-P) flow on entropy generation, Bejan number, velocity, temperature, and concentration distributions, as well as physical quantities are influenced by several dimensionless physical parameters that are also presented graphically and in table-form and discussed in detail. It is shown that the Schemit number increases alongside an increase in temperature, but the opposite trend occurs in the Prandtl number. Bejan number and entropy generation decline with the effect of the concentration diffusion parameter, and the results are shown in graphs.

Finite element analysis for ternary hybrid nanoparticles on thermal enhancement in pseudo-plastic liquid through porous stretching sheet.

Thermal performance can be enhanced due to the mixing of nanoparticles in base fluid. This research discusses the involvement of ternary hybrid nanoparticles in the mixture of pseudo-plastic fluid model past over a two dimensional porous stretching sheet. Modelling of energy equation is carried out in the presence of external heat source or sink and viscous dissipation. The flow presenting equations and derived in Cartesian coordinate system under usual boundary layer theory in the form of complex coupled partial differential equations (PDEs). The derived PDEs have been converted into corresponding ordinary differential equations (ODEs) with the engagement of suitable transformation. The engineers, scientists and mathematicians have great interest in the solution of differential equations because to understand the real physics of the problem. Here, finite element scheme has been used to approximate the solution of the converted problem. The contribution of several emerging parameters on solution have been displayed through graphs and discussed. It is recommended that the finite element method can be engaged to approximate the solution of nonlinear problems arising in modelling the problem in mathematical physics.

Hydrothermal and Entropy Investigation of Nanofluid Mixed Convection in Triangular Cavity with Wavy Boundary Heated from below and Rotating Cylinders.

Nanofluids have become important working fluids for many engineering applications as they have better thermal properties than traditional liquids. Thus, this paper addresses heat transfer rates and entropy generation for a Fe3O4/MWCNT-water hybrid nanoliquid inside a three-dimensional triangular porous cavity with a rotating cylinder. The studied cavity is heated by a hot wavy wall at the bottom and subjected to a magnetic field. This problem is solved numerically using the Galerkin finite element method (GFEM). The influential parameters considered are the rotating cylinder speed, Hartmann number (Ha), Darcy number (Da), and undulation number of the wavy wall. The results showed that higher Da and lower Ha values improved the heat transfer rates in the cavity, which was demonstrated by a higher Nusselt number and flow fluidity. The entropy generation due to heat losses was also minimized for the enhanced heat transfer rates. The decrease in Ha from 100 and 0 improved the heat transfer by about 8%, whereas a high rotational speed and high Da values yield optimal results. For example, for Ω = 1000 rad/s and Da = 10-2, the enhancement in the average Nusselt number is about 38% and the drop in the Bejan number is 65% compared to the case of Ω = 0 rad/s and Da = 10-5. Based on the applied conditions, it is recommended to have a high Da, low Ha, one undulation for the wavy wall, and high rotational speed for the cylinder in the flow direction.

Significance of Dust Particles, Nanoparticles Radius, Coriolis and Lorentz Forces: The Case of Maxwell Dusty Fluid.

This study aimed to analyze the momentum and thermal transport of a rotating dusty Maxwell nanofluid flow on a magnetohydrodynamic Darcy-Forchheimer porous medium with conducting dust particles. Nanouids are the most important source of effective heat source, having many applications in scientific and technological processes. The dust nanoparticles with superior thermal characteristics offer a wide range of uses in chemical and mechanical engineering eras and modern technology. In addition, nanofluid Cu-water is used as the heat-carrying fluid. The governing equations for the two phases model are partial differential equations later transmuted into ordinary ones via similarity transforms. An efficient code for the Runge-Kutta technique with a shooting tool is constructed in MATLAB script to obtain numeric results. The study is compared to previously published work and determined to be perfect. It is observed that the rising strength of the rotating and magnetic parameters cause to recede the x- and y-axis velocities in the two phase fluid, but the temperature function exhibits an opposite trend. By improving the diameter of nanoparticles Dm, the axial velocity improves while transverse velocity and temperature show the opposite behaviors. Furthermore, it is reported that the inclusion of dust particles or nanoparticles both cause to decline the primary and secondary velocities of fluid, and also dust particles decrease the temperature.

Applications of bioconvection for tiny particles due to two concentric cylinders when role of Lorentz force is significant.

The bioconvection flow of tiny fluid conveying the nanoparticles has been investigated between two concentric cylinders. The contribution of Lorenz force is also focused to inspect the bioconvection thermal transport of tiny particles. The tiny particles are assumed to flow between two concentric cylinders of different radii. The first cylinder remains at rest while flow is induced due to second cylinder which rotates with uniform velocity. Furthermore, the movement of tiny particles follows the principle of thermophoresis and Brownian motion as a part of thermal and mass gradient. Similarly, the gyro-tactic microorganisms swim in the nanofluid as a response to the density gradient and constitute bio-convection. The problem is modeled by using the certain laws. The numerical outcomes are computed by using RKF -45 method. The graphical simulations are performed for flow parameters with specific range like 1≤Re≤5, 1≤Ha≤5, 0.5≤Nt≤2.5, 1≤Nb≤3, 0.2≤Sc≤1.8, 0.2≤Pe≤1.0 and 0.2≤Ω≤1.0. It is observed that the flow velocity decreases with the increase in the Hartmann number that signifies the magnetic field. This outcome indicates that the flow velocity can be controlled externally through the magnetic field. Also, the increase in the Schmidt numbers increases the nanoparticle concentration and the motile density.

Steady Squeezing Flow of Magnetohydrodynamics Hybrid Nanofluid Flow Comprising Carbon Nanotube-Ferrous Oxide/Water with Suction/Injection Effect.

The main purpose of the current article is to scrutinize the flow of hybrid nanoliquid (ferrous oxide water and carbon nanotubes) (CNTs + Fe3O4/H2O) in two parallel plates under variable magnetic fields with wall suction/injection. The flow is assumed to be laminar and steady. Under a changeable magnetic field, the flow of a hybrid nanofluid containing nanoparticles Fe3O4 and carbon nanotubes are investigated for mass and heat transmission enhancements. The governing equations of the proposed hybrid nanoliquid model are formulated through highly nonlinear partial differential equations (PDEs) including momentum equation, energy equation, and the magnetic field equation. The proposed model was further reduced to nonlinear ordinary differential equations (ODEs) through similarity transformation. A rigorous numerical scheme in MATLAB known as the parametric continuation method (PCM) has been used for the solution of the reduced form of the proposed method. The numerical outcomes obtained from the solution of the model such as velocity profile, temperature profile, and variable magnetic field are displayed quantitatively by various graphs and tables. In addition, the impact of various emerging parameters of the hybrid nanofluid flow is analyzed regarding flow properties such as variable magnetic field, velocity profile, temperature profile, and nanomaterials volume fraction. The influence of skin friction and Nusselt number are also observed for the flow properties. These types of hybrid nanofluids (CNTs + Fe3O4/H2O) are frequently used in various medical applications. For the validity of the numerical scheme, the proposed model has been solved by another numerical scheme (BVP4C) in MATLAB.

Electro-osmotic flow of biological fluid in divergent channel: drug therapy in compressed capillaries.

The multi-phase flow of non-Newtonian through a divergent channel is studied in this article. Jeffrey fluid is considered as the base liquid and tiny gold particles for the two-phase suspension. Application of external electric field parallel to complicated capillary with net surface charge density causes the bulk motion of the bi-phase fluid. In addition to, electro-osmotic flow with heat transfer, the simultaneous effects of viscous dissipation and nonlinear thermal radiation have also been incorporated. Finally, cumbersome mathematical manipulation yields a closed-form solution to the nonlinear differential equations. Parametric study reveals that more thermal energy is contributed in response to Brinkman number which significantly assists gold particles to more heat attain high temperature, as the remedy for compressed or swollen capillaries/arteries.

Exploration of bioconvection flow of MHD thixotropic nanofluid past a vertical surface coexisting with both nanoparticles and gyrotactic microorganisms.

This communication presents analysis of gravity-driven flow of a thixotropic fluid containing both nanoparticles and gyrotactic microorganisms along a vertical surface. To further describe the transport phenomenon, special cases of active and passive controls of nanoparticles are investigated. The governing partial differential equations of momentum, energy, nanoparticles concentration, and density of gyrotactic microorganisms equations are converted and parameterized into system of ordinary differential equations and the series solutions are obtained through Optimal Homotopy Analysis Method (OHAM). The related important parameters are tested and shown on the velocity, temperature, concentration and density of motile microorganisms profiles. It is observed that for both cases of active and passive control of nanoparticles, incremental values of thermophoretic parameters corresponds to decrease in the velocity distributions and augment the temperature distributions.

Bioconvective Reiner-Rivlin nanofluid flow over a rotating disk with Cattaneo-Christov flow heat flux and entropy generation analysis.

The non-Newtonian fluids possess captivating heat transfer applications in comparison to the Newtonian fluids. Here, a new type of non-Newtonian fluid named Reiner-Rivlin nanofluid flow over a rough rotating disk with Cattaneo-Christov (C-C) heat flux is studied in a permeable media. The stability of the nanoparticles is augmented by adding the gyrotactic microorganisms in the nanofluid. The concept of the envisaged model is improved by considering the influences of Arrhenius activation energy, chemical reaction, slip, and convective conditions at the boundary of the surface. The entropy generation is evaluated by employing the second law of thermodynamics. The succor of the Shooting scheme combined with the bvp4c MATLAB software is adapted for the solution of extremely nonlinear system of equations. The noteworthy impacts of the evolving parameters versus engaged fields are inspected through graphical illustrations. The outcomes show that for a strong material parameter of Reiner-Rivlin, temperature, and concentration profiles are enhanced. The behavior of Skin friction coefficients, local Nusselt number, Sherwood number, and local density number of motile microorganisms against the different estimates of emerging parameters are represented in tabular form. The authenticity of the intended model is tested by comparing the presented results in limiting form to an already published paper. A proper correlation between the two results is attained.

Dual solution framework for mixed convection flow of Maxwell nanofluid instigated by exponentially shrinking surface with thermal radiation.

This paper presents the analysis of transfer of heat and mass characteristics in boundary layer flow of incompressible magnetohydrodynamic Maxwell nanofluid with thermal radiation effects confined by exponentially shrinking geometry. The effects of Brownian motion and thermophoresis are incorporated using Buongiorno model. The partial differential equations of the governing model are converted in non-dimensional track which are numerically inspected with proper appliances of Runge-Kutta fourth order scheme.The significant effects of heat and mass fluxes on the temperature and nanoparticles volume fractions are investigated. By the increases in Lewis number between [Formula: see text] to [Formula: see text], the decrease in nanoparticle volume fraction and temperature is noted. With the change in the Prandtl constant that varies between [Formula: see text] to [Formula: see text], the nanoparticles volume fraction and temperature are dwindled. Nanoparticles volume fraction and temperature distribution increase is noted with applications of radiation constant. With consequent variation of thermophoresis parameter between [Formula: see text] to [Formula: see text], nanoparticles volume fraction and temperature distribution increases. It is also noted that the increase in thermophoresis parameter and Brownian parameter from [Formula: see text] to [Formula: see text], nanoparticles volume fraction decreases while temperature distribution increases.

Numerical study of bio-convection flow of magneto-cross nanofluid containing gyrotactic microorganisms with activation energy.

In this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Appropriate similarity transformations are utilized to transform partial differential equations (PDE's) into ordinary ones and then numerically tackled by shooting method. The impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveal that, the escalation in magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.

Entropy optimized dissipative flow of hybrid nanofluid in the presence of non-linear thermal radiation and Joule heating.

Present article reads three dimensional flow analysis of incompressible viscous hybrid nanofluid in a rotating frame. Ethylene glycol is used as a base liquid while nanoparticles are of copper and silver. Fluid is bounded between two parallel surfaces in which the lower surface stretches linearly. Fluid is conducting hence uniform magnetic field is applied. Effects of non-linear thermal radiation, Joule heating and viscous dissipation are entertained. Interesting quantities namely surface drag force and Nusselt number are discussed. Rate of entropy generation is examined. Bvp4c numerical scheme is used for the solution of transformed O.D.Es. Results regarding various flow parameters are obtained via bvp4c technique in MATLAB Software version 2019, and displayed through different plots. Our obtained results presents that velocity field decreases with respect to higher values of magnetic parameter, Reynolds number and rotation parameter. It is also observed that the temperature field boots subject to radiation parameter. Results are compared with Ishak et al. (Nonlinear Anal R World Appl 10:2909-2913, 2009) and found very good agreement with them. This agreement shows that the results are 99.99% match with each other.

Multiple slips impact in the MHD hybrid nanofluid flow with Cattaneo-Christov heat flux and autocatalytic chemical reaction.

The present study deliberates the nanofluid flow containing multi and single-walled carbon nanotubes submerged into Ethylene glycol in a Darcy-Forchheimer permeable media over a stretching cylinder with multiple slips. The innovation of the envisaged mathematical model is enriched by considering the impacts of non-uniform source/sink and modified Fourier law in the energy equation and autocatalytic chemical reaction in the concentration equation. Entropy optimization analysis of the mathematical model is also performed in the present problem. Pertinent transformations procedure is implemented for the conversion of the non-linear system to the ordinary differential equations. The succor of the Shooting technique combined with the bvp4c MATLAB software is utilized for the solution of a highly nonlinear system of equations. The impacts of the leading parameters versus engaged fields are inspected through graphical sketches. The outcomes show that a strong magnetic field strengthens the temperature profile and decays the velocity profile. Also, the fluid velocity is lessened for growing estimates of the parameter of slip. Additionally, it is detected that entropy number augmented for higher thermal relaxation parameter and Reynolds number. To substantiate the existing mathematical model, a comparison table is also added. An excellent correlation is achieved here.

Analyzing the impact of induced magnetic flux and Fourier's and Fick's theories on the Carreau-Yasuda nanofluid flow.

The current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.

Irreversibility minimization analysis of ferromagnetic Oldroyd-B nanofluid flow under the influence of a magnetic dipole.

Studies highlighting nanoparticles suspensions and flow attributes in the context of their application are the subject of current research. In particular, the utilization of these materials in biomedical rheological models has gained great attention. Magneto nanoparticles have a decisive role in the ferrofluid flows to regulate their viscoelastic physiognomies. Having such substantial interest in the flow of ferrofluids our objective is to elaborate the melting heat transfer impact in a stretched Oldroyd-B flow owing to a magnetic dipole in the presence of entropy generation optimization. Buongiorno nanofluid model expounding thermophoretic and Brownian features are considered. Moreover, activation energy with chemical reaction is also considered. The Cattaneo-Christov heat flux model is affianced instead of conventional Fourier law. The renowned bvp4c function of MATLAB is utilized to handle the nonlinearity of the system. Impacts of miscellaneous parameters are portrayed through graphical fallouts and numeric statistics. Results divulge that the velocity and temperature profiles show the opposite trend for growing estimates of the ferromagnetic parameter. It is also noticed that the temperature ratio parameter diminishes the entropy profile. Moreover, it is seen that the concentration profile displays a dwindling trend for the Brownian motion parameter and the opposite trend is witnessed for the thermophoretic parameter.

Impact of Newtonian heating and Fourier and Fick's laws on a magnetohydrodynamic dusty Casson nanofluid flow with variable heat source/sink over a stretching cylinder.

The present investigation aims to deliberate the magnetohydrodynamic (MHD) dusty Casson nanofluid with variable heat source/sink and modified Fourier's and Fick's laws over a stretching cylinder. The novelty of the flow model is enhanced with additional effects of the Newtonian heating, activation energy, and an exothermic chemical reaction. In an exothermic chemical reaction, the energy of the reactants is higher than the end products. The solution to the formulated problem is attained numerically by employing the MATLAB software function bvp4c. The behavior of flow parameters versus involved profiles is discussed graphically at length. For large values of momentum dust particles, the velocity field for the fluid flow declines, whereas an opposite trend is perceived for the dust phase. An escalation is noticed for the Newtonian heating in the temperature profile for both the fluid and dust-particle phase. A comparison is also added with an already published work to check the validity of the envisioned problem.

Significance of nanoparticle's radius, heat flux due to concentration gradient, and mass flux due to temperature gradient: The case of Water conveying copper nanoparticles.

The performance of copper selenide and effectiveness of chemical catalytic reactors are dependent on an inclined magnetic field, the nature of the chemical reaction, introduction of space heat source, changes in both distributions of temperature and concentration of nanofluids. This report presents the significance of increasing radius of nanoparticles, energy flux due to the concentration gradient, and mass flux due to the temperature gradient in the dynamics of the fluid subject to inclined magnetic strength is presented. The non-dimensionalization and parameterization of the dimensional governing equation were obtained by introducing suitable similarity variables. Thereafter, the numerical solutions were obtained through shooting techniques together with 4th order Runge-Kutta Scheme and MATLAB in-built bvp4c package. It was concluded that at all the levels of energy flux due to concentration gradient, reduction in the viscosity of water-based nanofluid due to a higher radius of copper nanoparticles causes an enhancement of the velocity. The emergence of both energy flux and mass flux due to gradients in concentration and temperature affect the distribution of temperature and concentration at the free stream.