On the convective heat and zero nanoparticle mass flux conditions in the flow of 3D MHD Couple Stress nanofluid over an exponentially stretched surface

On hybrid nanofluid Yamada-Ota and Xue flow models in a rotating channel with modified Fourier law

The present study analyzes the comparison of the Xue and Yamada-Ota models for a hybrid nanoliquid flow in porous media occurring amidst a rotating channel with surface catalyzed reaction. Here, the hybrid nanofluid flow is studied under the effect of Cattaneo Christov (C-C) heat flux and homogenous heterogeneous (Homo-Hetero) chemical reaction with entropy generation minimization analysis. The assumptions of the viscosity of hybrid nanomaterial fluid and variable thermal conductivity are added characteristics to the inimitability of the flow model. Two kinds of nanoparticles, namely single-wall carbon nanotubes and multi-wall carbon nanotubes with ethylene glycol (EG) as the base fluid are considered. Carbon nanotubes possess diverse applications in daily life including energy storage, drug delivery, cancer treatment, tissue generation, platelet activation, magnetic force microscopy, and microwave absorption, etc. Similarity transformations are utilized to translate the modeled problem into the coupled ordinary differential equations. This system of ordinary differential equations is addressed numerically. The graphical outcomes are scrutinized by utilizing the MATLAB software bvp4c function. The results revealed that the velocity profile decreases for the higher rotation parameter while increases for the escalated slip parameter. Furthermore, the fluid concentration and temperature are on the decline for higher surface catalyzed reaction and thermal relaxation parameters respectively.

Bioconvection in Magneto Hydrodynamics Casson Nanoliquid (Fe3O4-Sodium Alginate) With Gyrotactic Microorganisms Over an Exponential Stretching Sheet

The present investigation focuses on the influence of motile gyrotactic microorganisms and thermal heat flux on three-dimensional convective flow of a Casson nanoliquid over an elongated surface. The flow equations are modelled by using Tiwari-Das nanofluid model. Sodium alginate (SA) is considered as the base fluid together with Ferromagnetic oxide (Fe3O4) nanoparticles. The governing flow equations are changed into a system of ODEs with the aid of similarity variables and are then addressed computationally. Influence of various pertinent parameters on different physical quantities is examined graphically. The outcomes of present investigation is validated through comparison study and is found to be in good arrangement. It is noticed that the coefficient of heat transfer rises with growing radiation and Biot numbers. Also the mass transfer coefficient surges for higher values of Schmidt number and generative chemical reaction parameter.

Gravity-driven hydromagnetic flow of couple stress hybrid nanofluid with homogenous-heterogeneous reactions

This investigation describes the hydromagnetic flow of gravity-driven couple stress hybrid nanofluid past a heated plate. The carbon nanotubes (CNTs) are used to characterize the hybrid nanofluid. The heated plate is placed vertically with an application of homogenous-heterogeneous reactions to the assumed flow system. The homogeneous reaction governs by isothermal cubic autocatalytic kinetics while the heterogeneous reaction governs by the first order kinetics. For current study the couple stress hybrid nanofluid is presumed to be conducted electrically with impact of non-uniform magnetic effects. An appropriate set of dimensionless quantities has employed to governing equations and then has solved by homotopy analysis method. The influence of emerging parameters encountered in this work has discussed in detail with the help of graphs. In this study it has examined that, flow of fluid reduces with upsurge in magnetic parameter and volumetric concentrations, whereas thermal and concentration characteristics augment with increase in volumetric concentrations. Moreover, growth in Prandtl number leads to a reduction in thermal characteristics and growth in Schmidt number result a reduction in concentration profile. The impact of various emerging parameters has also studied numerically upon physical quantities. It has established that, with augmentation in values of buoyancy parameter there is a growth in the values of skin friction. A comparison has also carried out between current and established results with a fine agreement in both results.

Hybrid nanofluid flow through a spinning Darcy-Forchheimer porous space with thermal radiation

This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{\prime}\left( \xi \right),g\left( \xi \right)$$\end{document}f′ξ,gξ are decayed for high values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi_{1} ,\phi_{2} ,\,Fr$$\end{document}ϕ1,ϕ2,Fr and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{1}$$\end{document}k1 factors.

Features of entropy optimization on MHD couple stress nanofluid slip flow with melting heat transfer and nonlinear thermal radiation

Numerical analysis is performed for magnetohydrodynamics (MHD) couple stress nanofluid flow over a stretching sheet with melting and nonlinear radiation. The second law of thermodynamics is also incorporated with first-order slip. Nanofluid characteristics for thermophoresis and Brownian moments are encountered. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved numerically through the Runge-Kutta-Fehlberg fourth-fifth (RKF-45) order technique. The physical parameters, which emerges from the derived system are discussed in graphical format. The significant outcomes of the current investigation are that the velocity field decays for a higher magnetic parameter. Another, important outcome of the study is both temperature and concentration are increasing functions of the first-order slip. Nusselt and Sherwood numbers are decreasing with an increase in magnetic strength. Further, Bejan number augment due to enhancement in the first-order slip and couple stress fluid parameters whereas a differing tendency is shown for magnetic and radiation parameters.

Nanofluid flow with autocatalytic chemical reaction over a curved surface with nonlinear thermal radiation and slip condition

The study of nanofluids is the most debated subject for the last two decades. Researchers have shown great interest owing to the amazing features of nanofluids including heat transfer and thermal conductivity enhancement capabilities. Having such remarkable features of nanofluids in mind we have envisioned a mathematical model that discusses the flow of nanofluid comprising Nickel-Zinc Ferrite-Ethylene glycol (Ni-ZnFe₂O₄–C₂H₆O₂) amalgamation past an elongated curved surface with autocatalytic chemical reaction. The additional impacts added to the flow model are the heat generation/absorption with nonlinear thermal radiation. At the boundary, the slip and the convective conditions are added. Pertinent transformations are affianced to get the system of ordinary differential equations from the governing system in curvilinear coordinates. A numerical solution is found by applying MATLAB build-in function bvp4c. Graphical illustrations and the numerically computed estimates are discussed and analyzed properly. It is comprehended that velocity and temperature distributions have varied trends near and away from the curve when the curvature parameter is enhanced. Further, it is comprehended that the concentration field declines for both homogeneous and heterogeneous reaction parameters.

Entropy generation in bioconvection nanofluid flow between two stretchable rotating disks

Buongiorno's nanofluid model is followed to study the bioconvection in two stretchable rotating disks with entropy generation. Similarity transformations are used to handle the problem equations for non-dimensionality. For the simulation of the modeled equations, Homotopy Analysis Method is applied. The biothermal system is explored for all the embedded parameters whose effects are shown through different graphs. There exists interesting results due to the effects of different parameters on different profiles. Radial velocity decreases with increasing stretching and magnetic field parameters. Temperature increases with Brownian motion and thermophoresis parameters. Nanoparticles concentration decreases on increasing Lewis number and thermophoresis parameter while motile gyrotactic microorganisms profile increases with increasing Lewis and Peclet numbers. Convergence of the solution is found and good agreement is obtained when the results are compared with published work.

Numerical Simulation of 3D Condensation Nanofluid Film Flow with Carbon Nanotubes on an Inclined Rotating Disk

Here, we discuss three-dimensional dusty nanofluid thin film flow with nonlinear thermal radiation, where carbon nanotubes flow past an inclined rotating disk with a constant angular velocity of Ω. This novel mathematical model is unique and is discussed here for the first time. Downward draining flow and lateral flow arise due to inclination. The demonstrated geometry is characterized in terms of time-independent continuity, momentum, and energy balance. Similarity transformations convert the partial differential equation into a system of ordinary differential equations. The obtained equations are analyzed numerically using the bvp4c MATLAB function. The thermal field of the dust phase was smaller than that of the nanofluid phase, and this difference was exacerbated by increasing the thermal radiation. To validate the model presented here, it is compared to a previous model; the models showed high concordance.

Impact of Second-Order Slip and Double Stratification Coatings on 3D MHD Williamson Nanofluid Flow with Cattaneo–Christov Heat Flux

The present research examines the impact of second-order slip with thermal and solutal stratification coatings on three-dimensional (3D) Williamson nanofluid flow past a bidirectional stretched surface and envisages it analytically. The novelty of the analysis is strengthened by Cattaneo–Christov (CC) heat flux accompanying varying thermal conductivity. The appropriate set of transformations is implemented to get a differential equation system with high nonlinearity. The structure is addressed via the homotopy analysis technique. The authenticity of the presented model is verified by creating a comparison with the limited published results and finding harmony between the two. The impacts of miscellaneous arising parameters are deliberated through graphical structures. Some useful tabulated values of arising parameters versus physical quantities are also discussed here. It is observed that velocity components exhibit an opposite trend with respect to the stretching ratio parameter. Moreover, the Brownian motion parameter shows the opposite behavior versus temperature and concentration distributions.

Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions

In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in x- and y-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the y-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables.

Magnetohydrodynamic nanofluid radiative thermal behavior by means of Darcy law inside a porous media

Radiative nanomaterial thermal behavior within a permeable closed zone with elliptic hot source is simulated. Darcy law is selected for simulating permeable media in existence of magnetic forces. Contour plots for various buoyancy, Hartmann numbers and radiation parameter were illustrated. Carrier fluid is Al2O3-water with different shapes. Outputs prove that conduction mode augments with enhance of Ha. Nu augments with considering radiation source term.

Magnetized suspended carbon nanotubes based nanofluid flow with bio-convection and entropy generation past a vertical cone

The captivating attributes of carbon nanotubes (CNT) comprising chemical and mechanical steadiness, outstanding electrical and thermal conductivities, featherweight, and physiochemical consistency make them coveted materials in the manufacturing of electrochemical devices. Keeping in view such exciting features of carbon nanotubes, our objective in the present study is to examine the flow of aqueous based nanofluid comprising single and multi-wall carbon nanotubes (CNTs) past a vertical cone encapsulated in a permeable medium with convective heat and solutal stratification. The impacts of heat generation/absorption, gyrotactic-microorganism, thermal radiation, and Joule heating with chemical reaction are added features towards the novelty of the erected model. The coupled differential equations are attained from the partial differential equations by exercising the local similarity transformation technique. The set of conservation equations supported by the associated boundary conditions are worked out numerically by employing bvp4c MATLAB function. The sway of numerous appearing parameters in the analysis on the allied distributions is scrutinized and the fallouts are portrayed graphically. The physical quantities of interest including Skin friction coefficient, the rate of heat and mass transfers are assessed versus essential parameters and their outcomes are demonstrated in tabulated form. It is witnessed that the velocity of the fluid decreases for boosting values of the magnetic and suction parameters in case of both nanotubes. Moreover, the density of motile microorganism is decreased versus larger estimates of bio-convection constant. A notable highlight of the presented model is the endorsement of the results by matching them to an already published material in the literature. A venerable harmony in this regard is achieved.

Entropy Generation Optimization in Squeezing Magnetohydrodynamics Flow of Casson Nanofluid with Viscous Dissipation and Joule Heating Effect

In this research article, the investigation of the three-dimensional Casson nanofluid flow in two rotating parallel plates has been presented. The nanofluid has been considered in steady state. The rotating plates have been considered porous. The heat equation is considered to study the magnetic field, joule heating, and viscous dissipation impacts. The nonlinear ordinary system of equations has been solved analytically and numerically. For skin friction and Nusslt number, numerical results are tabulated. It is found that velocity declines for higher values of magnetic and porosity parameter while it is heightened through squeezing parameter. Temperature is an enhancing function for Eckert number and nanoparticles volume fraction. Entropy generation is augmented with radiation parameter, Prandtl, and Eckert numbers. The Casson, porosity, magnetic field, and rotation parameters were reduced while the squeezing and suction parameters increased the velocity profile along x-direction. The porosity parameter increased the Bejan number while the Eckert and Prandtl numbers decreased the Bejan number. Skin friction was enhanced with increasing the Casson, porosity, and magnetic parameters while it decreased with enhancing rotation and squeezing parameters. All these impacts have been shown via graphs. The influences by fluid flow parameters over skin friction and Nusselt number are accessible through tables.

Influence of MHD on Thermal Behavior of Darcy-Forchheimer Nanofluid Thin Film Flow over a Nonlinear Stretching Disc

The aim of this research work is to increase our understanding of the exhaustion of energy in engineering and industrial fields. The study of nanofluids provides extraordinary thermal conductivity and an increased heat transmission coefficient compared to conventional fluids. These specific sorts of nanofluids are important for the succeeding generation of flow and heat transfer fluids. Therefore, the investigation of revolutionary new nanofluids has been taken up by researchers and engineers all over the world. In this article, the study of the thin layer flow of Darcy-Forchheimer nanofluid over a nonlinear radially extending disc is presented. The disc is considered as porous. The impacts of thermal radiation, magnetic field, and heat source/sink are especially focused on. The magnetic field, positive integer, porosity parameter, coefficient of inertia, and fluid layer thickness reduce the velocity profile. The Prandtl number and fluid layer thickness reduce the temperature profile. The heat source/sink, Eckert number, and thermal radiation increase the temperature profile. The suggested model is solved analytically by the homotopy analysis method (HAM). The analytical and numerical techniques are compared through graphs and tables, and have shown good agreement. The influences of embedded parameters on the flow problem are revealed through graphs and tables.

Entropy Analysis of Carbon Nanotubes Based Nanofluid Flow Past a Vertical Cone with Thermal Radiation

Our objective in the present study is to scrutinize the flow of aqueous based nanofluid comprising single and multi-walled carbon nanotubes (CNTs) past a vertical cone encapsulated in a permeable medium with solutal stratification. Moreover, the novelty of the problem is raised by the inclusion of the gyrotactic microorganisms effect combined with entropy generation, chemical reaction, and thermal radiation. The coupled differential equations are attained from the partial differential equations with the help of the similarity transformation technique. The set of conservation equations supported by the associated boundary conditions are solved numerically with the bvp4c MATLAB function. The influence of numerous parameters on the allied distributions is scrutinized, and the fallouts are portrayed graphically in the analysis. The physical quantities of interest including the skin friction coefficient and the rate of heat and mass transfers are evaluated versus essential parameters, and their outcomes are demonstrated in tabulated form. For both types of CNTs, it is witnessed that the velocity of the fluid is decreased for larger values of the magnetic and suction parameters. Moreover, the value of the skin friction coefficient drops versus the augmented bioconvection Rayleigh number. To corroborate the authenticity of the presented model, the obtained results (under some constraints) are compared with an already published paper, and excellent harmony is achieved in this regard.

A Numerical Simulation of Silver–Water Nanofluid Flow with Impacts of Newtonian Heating and Homogeneous–Heterogeneous Reactions Past a Nonlinear Stretched Cylinder

The aim of the present study is to address the impacts of Newtonian heating and homogeneous–heterogeneous (h-h) reactions on the flow of Ag–H2O nanofluid over a cylinder which is stretched in a nonlinear way. The additional effects of magnetohydrodynamics (MHD) and nonlinear thermal radiation are also added features of the problem under consideration. The Shooting technique is betrothed to obtain the numerical solution of the problem which is comprised of highly nonlinear system ordinary differential equations. The sketches of different parameters versus the involved distributions are given with requisite deliberations. The obtained numerical results are matched with an earlier published work and an excellent agreement exists between both. From our obtained results, it is gathered that the temperature profile is enriched with augmented values radiation and curvature parameters. Additionally, the concentration field is a declining function of the strength of h-h reactions.