A numerical treatment of MHD radiative flow of Micropolar nanofluid with homogeneous-heterogeneous reactions past a nonlinear stretched surface

Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

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.

Peristaltic channel flow and heat transfer of Carreau magneto hybrid nanofluid in the presence of homogeneous/heterogeneous reactions

The purpose of present work is to explore the features of homogeneous–heterogeneous reactions in peristalsis flow of Carreau magneto hybrid nanofluid with copper and silver nanoparticles in a symmetric channel. The velocity slip condition and thermal radiation effect is also taken in the simplified model. Thermodynamic optimization aspect is discussed through the entropy generation analysis. The proposed mathematical systems are modified by using a lubrication approach and solved by a homotopy-based package-BVPh 2.0. The impacts of different involved parameters on flow characteristics, thermal characteristics, chemically reactive concentration and entropy generation are scrutinized through analytic results. It reveals that the fluid velocity decreases with the increasing values of the Weissenberg and the Hartman numbers. Characteristics of the Brinkman and the thermal radiation numbers are quite reverse for the heat transfer rate. In addition, entropy generation decreases with thermal radiation and Weissenberg number. The main outcome signifies that hybrid nanofluid is better thermal conductor as compared to the conventional nanofluid.

Multiple Fractional Solutions for Magnetic Bio-Nanofluid Using Oldroyd-B Model in a Porous Medium with Ramped Wall Heating and Variable Velocity

Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid. Based on three different definitions of fractional operators, three different models of the resulting nanofluid are developed. These three operators are based on the definitions of Caputo (C), Caputo–Fabrizio (CF), and Atnagana–Baleanu in the Caputo sense (ABC). Nanofluid is taken over an upright plate with ramped wall heating and time-dependent fluid velocity at the sidewall. The effects of magnetohydrodynamic (MHD) and porous medium are also considered. Triple fractional analysis is performed to solve the resulting three models, based on three different fractional operators. The Laplace transform is applied to each problem separately, and Zakian’s numerical algorithm is used for the Laplace inversion. The solutions are presented in various graphs with physical arguments. Results are computed and shown in various plots. The empirical results indicate that, for ramped temperature, the temperature field is highest for the ABC derivative, followed by the CF and Caputo fractional derivatives. In contrast, for isothermal temperature, the temperature field of C-derivative is higher than the CF and ABC derivatives, respectively. It was noticed that the velocity field for the ABC derivative is higher than the CF and Caputo fractional derivatives for ramped velocity. However, the velocity field for the Caputo fractional derivative is lower than the ABC and CF for isothermal velocity.

Effect of asymmetrical heat rise/fall on the film flow of magnetohydrodynamic hybrid ferrofluid

The movement of the ferrous nanoparticles is random in the base fluid, and it will be homogeneous under the enforced magnetic field. This phenomenon shows a significant impact on the energy transmission process. In view of this, we inspected the stream and energy transport in magnetohydrodynamic dissipative ferro and hybrid ferrofluids by considering an uneven heat rise/fall and radiation effects. We studied the Fe₃O₄ (magnetic oxide) and CoFe₂O₄ (cobalt iron oxide) ferrous particles embedded in H₂O-EG (ethylene glycol) (50–50%) mixture. The flow model is converted as ODEs with suitable similarities and resolved them using the 4th order Runge-Kutta scheme. The influence of related constraints on transport phenomena examined through graphical illustrations. Simultaneous solutions explored for both ferro and hybrid ferrofluid cases. It is found that the magnetic oxide and cobalt iron oxide suspended in H₂O-EG (ethylene glycol) (50–50%) mixture effectively reduces the heat transfer rate under specific conditions.

Micropolar gold blood nanofluid flow and radiative heat transfer between permeable channels

This article characterizes flow and heat transmission of blood that carries the micropolar nanofluid of gold in a permeable channel. The thermal radiations are also present in the channel while its walls are either moving or stationary. The base-fluid is considered as blood while micro polar nanofluid is taken as gold. By using similarity transformations along with dimensionless quantities the modeled equations of the problem are transmuted into a system of non-linear ODEs with a set of appropriate boundary conditions. The semi-analytical method, HAM is then applied to determine the solution of a set of resultant equations. The results obtained by HAM have also compared with numerical solutions. The influence of non-dimensional parameters like fractional parameter suction/injection β, Reynolds Number Re, Darcys Number Da, micropolar parameter  K, Prandtl number Pr and Radiation parameter Rd etc., which provides physical interpretations of temperature, microrotation n and velocity fields are discussed in detail with the help of graphical representations. Nusselt number is calculated and presented through table. This study determined that the temperature of micropolar nanofluid augmented along with augmentation in the volume fraction. Radiation Rd augmented the heat transfer rate at the upper wall and reduce it at the lower wall. The suction/injection parameter 'β' reduces the heat transfer rate in case of β < 0 at the upper wall, where it is augmented at lower wall.

Thermally Stratified Darcy Forchheimer Flow on a Moving Thin Needle with Homogeneous Heterogeneous Reactions and Non-Uniform Heat Source/Sink

This study discusses the flow of viscous fluid past a moving thin needle in a Darcy–Forchheimer permeable media. The novelty of the envisioned mathematical model is enhanced by adding the effects of a non-uniform source/sink amalgamated with homogeneous–heterogeneous (hh) reactions. The MATLAB bvp4c function is employed to solve the non-linear ordinary differential equations (ODEs), which are obtained via similarity transformations. The outcomes of numerous parameters are explicitly discussed graphically. The drag force coefficient and heat transfer rate are considered and discussed accordingly. It is comprehended that higher estimates of variable source/sink boost the temperature profile.

Simultaneous solutions for first order and second order slips on micropolar fluid flow across a convective surface in the presence of Lorentz force and variable heat source/sink

This report presents the flow and heat transfer characteristics of MHD micropolar fluid due to the stretching of a surface with second order velocity slip. The influence of nonlinear radiation and irregular heat source/sink are anticipated. Simultaneous solutions are presented for first and second-order velocity slips. The PDEs which govern the flow have been transformed as ODEs by the choice of suitable similarity transformations. The transformed nonlinear ODEs are converted into linear by shooting method then solved numerically by fourth-order Runge-Kutta method. Graphs are drowned to discern the effect of varied nondimensional parameters on the flow fields (velocity, microrotation, and temperature). Along with them the coefficients of Skin friction, couple stress, and local Nussel number are also anticipated and portrayed with the support of the table. The results unveil that the non-uniform heat source/sink and non-linear radiation parameters plays a key role in the heat transfer performance. Also, second-order slip velocity causes strengthen in the distribution of velocity but a reduction in the distribution of temperature is perceived.

MHD Boundary Layer Flow of Carreau Fluid over a Convectively Heated Bidirectional Sheet with Non-Fourier Heat Flux and Variable Thermal Conductivity

In the present exploration, instead of the more customary parabolic Fourier law, we have adopted the hyperbolic Cattaneo–Christov (C–C) heat flux model to jump over the major hurdle of “parabolic energy equation”. The more realistic three-dimensional Carreau fluid flow analysis is conducted in attendance of temperature-dependent thermal conductivity. The other salient impacts affecting the considered model are the homogeneous-heterogeneous (h-h) reactions and magnetohydrodynamic (MHD). The boundary conditions supporting the problem are convective heat and of h-h reactions. The considered boundary layer problem is addressed via similarity transformations to obtain the system of coupled differential equations. The numerical solutions are attained by undertaking the MATLAB built-in function bvp4c. To comprehend the consequences of assorted parameters on involved distributions, different graphs are plotted and are accompanied by requisite discussions in the light of their physical significance. To substantiate the presented results, a comparison to the already conducted problem is also given. It is envisaged that there is a close correlation between the two results. This shows that dependable results are being submitted. It is noticed that h-h reactions depict an opposite behavior versus concentration profile. Moreover, the temperature of the fluid augments for higher values of thermal conductivity parameters.

Entropy Analysis of 3D Non-Newtonian MHD Nanofluid Flow with Nonlinear Thermal Radiation Past over Exponential Stretched Surface

The present study characterizes the flow of three-dimensional viscoelastic magnetohydrodynamic (MHD) nanofluids flow with entropy generation analysis past an exponentially permeable stretched surface with simultaneous impacts of chemical reaction and heat generation/absorption. The analysis was conducted with additional effects nonlinear thermal radiation and convective heat and mass boundary conditions. Apposite transformations were considered to transform the presented mathematical model to a system of differential equations. Analytical solutions of the proposed model were developed via a well-known homotopy analysis scheme. The numerically calculated values of the dimensionless drag coefficient, local Nusselt number, and mass transfer Nusselt number are presented, with physical insights. The graphs depicting the consequences of numerous parameters on involved distributions with requisite deliberations were also a part of this model. It is seen that the Bejan number is an increasing function of the thermal radiation parameter.