OHAM simulation of 3D transverse magnetic field in rotating flow of Maxwell nanofluid over a stretching sheet with chemical reaction and heat source/sink

In this article, we investigate the heat transfer characteristics of a Maxwell nanofluid along a stretching sheet with transverse magnetic field, considering the presence of heat source/sink and chemical reaction. We consider appropriate similarity transformation for transforming the governing nonlinear equations into nondimensional highly nonlinear coupled ordinary differential equations. The optimal homotopy analysis method is utilized for solving the resultant-coupled equations. The impact of all sundry parameters, like, Deborah number, Prandtl number, magnetic parameter, thermophoresis, rotation parameter, chemical reaction, velocity slip, Schmidt number, Brownian motion parameter, heat sources per sink, Biot number, and Eckert number, on the temperature, velocity, and concentration fields is reported, analyzed, and described through graphs and tables. It is noticed that higher values of magnetic parameter and Deborah number reduce the horizontal velocity field. Furthermore, it is observed that the Biot number and heat source/sink parameter enhance the temperature distribution.     

Radiation and slip effects on MHD Maxwell nanofluid flow over an inclined surface with chemical reaction

The numerical solutions of the upper-convected Maxwell (UCM) nanofluid flow under the magnetic field effects over an inclined stretching sheet has been worked out. This model has the tendency to elaborate on the characteristics of “relaxation time” for the fluid flow. Special consideration has been given to the impact of nonlinear velocity slip, thermal radiation and heat generation. To study the heat transfer, the modified Fourier and Fick's laws are incorporated in the modeling process. The mass transfer phenomenon is investigated under the effects of chemical reaction, Brownian motion and thermophoresis. With the aid of the similarity transformations, the governing equations in the ordinary differential form are determined and then solved through the MATLAB's package “bvp4c” numerically. This study also brings into the spotlight such crucial physical parameters, which are inevitable for describing the flow and heat transfer behavior. This has been done through graphs and tables with as much precision and exactitude as is possible. The ascending values of the magnetic parameter, the Maxwell parameter and the angle of the inclined stretching sheet cause decay in the dimensionless velocity while an assisting behavior of the thermal and concentration buoyancy parameters is noticed.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Characteristics of Darcy–Forchheimer drag coefficients and velocity slip on the flow of micropolar nanofluid

The flow of magneto-micropolar nanofluid, that is, the composition of TiO₂ nanoparticles in an organic solvent, kerosene, and the normal water past a stretchable surface has been considered. With effectiveness idea on the application in several areas, the Darcy–Forchheimer inertial drag and the second-order velocity slip approach are vital for the current investigation. The influence of viscous, Joule and Darcy dissipations on the energy transfer cannot be neglected due to the interaction of the body forces characterized by magnetic and porosity of the medium. The dissipative heat energy with the heat generation/absorption is useful for the enhancement in the fluid temperature. Due to the complexity of the problem, a numerical solution is implemented using the in-built code bvp5c with the help of MATLAB software. The physical properties abide by the characterizing parameters that appeared in the flow profiles are presented via graphs and the computed results for the rate coefficients are also displayed through table both for water- and kerosene-based nanofluids. Finally, the main findings of the results are: the growth in the shear rate coefficient is marked due to the inclusion of second-order slip, and an attenuation in the fluid velocity is rendered with an increase in the volume fraction whereas impact is reversed in the case of nanofluid temperature.     

Numerical study of activation energy and thermal radiation effects on Oldroyd-B nanofluid flow using the Cattaneo–Christov double diffusion model over a convectively heated stretching sheet

This paper investigates a theoretical model of a mixed convective Oldroyd-B nanofluid with thermal radiation and activation energy effects. A thorough analysis is done by employing the nonhomogeneous Buongiorno model in the presence of velocity slip and suction. The surface is porous in nature, and nanoparticle mass flux is maintained passively at the surface. The thermal and concentration equations are modeled with the Cattaneo–Christov theory of heat and mass flux, respectively. Proper transformations are utilized for the conversion of transport equations and boundary conditions. The similarity solution is obtained through a numerical approach by utilizing the Runge–Kutta–Fehlberg method and shooting technique. The vital outcomes of this study and the influence of controlling parameters on the flow field, temperature, and concentration profiles are discussed graphically and in a tabular manner. Furthermore, a detailed discussion is provided to explain the results physically. The velocity of the nanofluid increases when the porosity parameter is increased, and temperature decreases with increasing thermal relaxation parameter. The outcomes elucidate that the suction parameter, thermal radiation parameter, and thermal relaxation parameter are positively correlated with the heat transfer coefficient. The result of passive control of nanoparticles at the surface is that the Brownian motion parameter has no influence on the temperature of the Oldroyd-B nanofluid flow and rate of heat transfer at the surface.     

A two-component modeling for free stream velocity in magnetohydrodynamic nanofluid flow with radiation and chemical reaction over a stretching cylinder

This analysis explores the influence of magnetohydrodynamic (MHD) nanofluid flow over a stretching cylinder with radiation effect in presence of chemically reactive species. The thermal radiation phenomenon is incorporated in the temperature equation. The mathematical modeling of the physical problem produces nonlinear set of partial differential equations corresponding to the momentum and energy equations that can be transformed into simultaneous system of ordinary differential equations with appropriate boundary conditions by applying similarity transformations. Shooting technique is used to solve the molded equations after adoption of Runge–Kutta–Fehlberg approach and ODE45 solver in MATLAB. A parametric analysis has been carried out to investigate the impacts of physical parameters that are considered in the current study. The attractive pattern studied the consequence of Brownian motion along with thermophoresis parameter. The outcomes of prominent fluid parameters, especially heat radiation, Lewis number, free stream velocity, chemical reaction, thermophoresis, and Brownian motion on the concentration, temperature, as well as velocity have been examined and are displayed through graphs and tables. The present study reveals that the temperature phenomenon enhances with an increase in radiation parameter, while nanoparticle concentration phenomenon reduces with an increase in chemical reaction parameter.     

Two-dimensional Darcy–Forchheimer flow of a dusty hybrid nanofluid over a stretching sheet with viscous dissipation

The main objective of the present examination is to design a stable mathematical model of a two-phase dusty hybrid nanofluid flow over a stretching sheet with heat transfer in a porous medium, and the Darcy–Forchheimer flow is taken into account with viscous dissipation and melting effect. The equations of motion are reduced to nonlinear ordinary differential equations by considering suitable similarity variables. These dimensionless expressions are solved by a well-known numerical technique known as Runge–Kutta–Fehlberg fourth–fifth order method. The behavioral study and analysis of the velocity and thermal profile in dual phases (fluid phase and dust phase) for diverse values of parameters are estimated using graphs and tables. The result outcome reveals that the velocity gradient declines in the fluid phase and increases in the dust phase for a rise in values of the velocity interaction parameter. Also, the velocity gradients of the both phases diminish for increasing values of the porosity parameter. Furthermore, it is determined that the increase in the value of melting parameter leads to a decline in the thermal gradient of both phases.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Numerical analysis on the heat and mass transfer MHD flow characteristics of nanofluid on an inclined spinning disk with heat absorption and chemical reaction

This work examines the heat transfer properties of magnetohydrodynamic nanofluid flow. Through a similarity conversion, the leading structure of partial differential equations is changed to that of ordinary differential equations. A rigorous mathematical bvp4c methodology is used to generate numerical results. The purpose of this study is to characterize the different temperature, concentration, and velocity limitations on a nanofluid with a magnetic effect that is spinning. The findings for rotating nanofluid flow and heat transfer characteristics of nanoparticles are shown using graphs and tables. The influence of physical factors such as heat transfer rates and skin friction coefficients is studied. When the magnetic parameter M is raised, the velocity of the nanoliquid decreases. A rise in thermal radiation (Rd) causes the temperature graphs to grow substantially, although the concentration profiles exhibit the opposite tendency. The effect of the convective heat transfer factor Bi on temperature is shown to increase as Bi increases, but the concentration distribution decreases as Biot increases.     

Nonlinear convection flow of dissipative Casson nanofluid through an inclined annular microchannel with a porous medium

The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro-annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev-based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence.     

Surveying the hybrid of radiation and magnetic parameters on Maxwell liquid with TiO2 nanotube influence of different blades

In this paper, the impacts of Maxwell nanoliquid transmission, rectangular with titanium oxide nanoparticles are explored over the triangular, chamfer blades. The innovation of this paper is the use of the number of chamfers, rectangular, and triangular blades at the top and bottom of a stretched plate to study physical nanofluid parameters such as temperature and the effects of magnetism. Also, by determining the appropriate height and length for the blades, we achieve the best optimization of temperature and velocity of nanofluid between the plate and the blades, which improves heat transfer and with a more and better effect of magnetic effects. The finite element method is utilized for the calculated differential equations. In this paper, by utilizing the reaction surface strategy, we optimized the titanium oxide nanofluid velocity and temperature, and magnetic parameter passing from the extending sheet. On average, the titanium oxide nanoparticle velocity around the two rectangular blades at the beginning of the sheet is 73.09% higher than triangular blades and 66.98% higher than chamfer blades. Based on the outcomes got from the titanium oxide nanofluid speed charts and the warm exchange cantors and magnetic impacts within the Design-Expert computer program, the most excellent optimization occurred for TiO₂ nanofluid speed and TiO₂ nanofluid temperature and TiO₂ magnetic parameter with u = 0.523, T = 3.25, and H = 2.671.     

Thermo-electrokinetic rotating non-Newtonian hybrid nanofluid flow from an accelerating vertical surface

This paper explores the combined effects of Coriolis force and electric force on the rotating boundary layer flow and heat transfer in a viscoplastic hybrid nanofluid from a vertical exponentially accelerated plate. The hybrid nanofluid comprises two different types of metallic nanoparticles, namely silver (Ag) and magnesium oxide (MgO) suspended in an aqueous base fluid. The Casson model is deployed for non-Newtonian effects. An empirical model is implemented to determine the thermal conductivity of the hybrid nanofluid. Rosseland's radiative diffusion flux model is also utilized. An axial electrical field is considered and the Poisson–Boltzmann equation is linearized via the Debye–Hückel approach. The resulting coupled differential equations subject to prescribed boundary conditions are solved with Laplace transforms. Numerical evaluation of solutions is achieved via MATLAB symbolic software. A parametric study of the impact of key parameters on axial velocity, transverse velocity, nanoparticle temperature and Nusselt number is conducted for both the hybrid (Ag–MgO)–water nanofluid and also unitary (Ag)–water nanofluid. With increasing volume fraction of silver nanoparticles, there is a reduction in both axial velocity and temperatures, whereas there is a distinct elevation in transverse velocity for both unitary and hybrid nanofluids. Elevation in the heat absorption parameter strongly decreases axial velocity, whereas it enhances transverse velocity. Increasing the radiation parameter strongly boosts temperatures. Increasing the heat absorption parameter significantly accelerates the transverse flow. Negative values of Helmholtz–Smoluchowski velocity decelerate the axial flow whereas positive values accelerate it; the opposite behavior is observed for transverse velocity. Increasing Taylor number significantly damps both the axial (primary) and transversal (secondary) flow. Increasing thermal Grashof number strongly enhances the axial flow but damps the transverse flow. The unitary nanofluid achieves higher Nusselt numbers than the hybrid nanofluid but these are decreased with greater radiative effect (due to greater heat transport away from the plate surface), Prandtl number and heat absorption. Nusselt number is significantly reduced with greater time progression and values are consistently higher for the unitary nanofluid compared with hybrid nanofluid. The computations provide insight into more complex electrokinetic rheological nanoscale flows of relevance to biomedical rotary electro-osmotic separation devices.     

Magnetohydrodynamic flow of a nanofluid due to a non‐linearly curved stretching surface with high order slip flow

This article numerically scrutinizes magnetohydrodynamic flow of a nanofluid due to a nonlinearly curved stretching surface with third order slip flow conditions. The third order slip flow condition has not yet been discussed in fluid dynamics research. The mathematical modeling of the flow problem is given in partial differential equation form. The governing partial differential equations are transformed to high order ordinary differential equations using the similarity transformation and then solved numerically using a boundary value problem solver, bvp4c from Matlab software. The effect of the governing parameters on the flow of the velocity profile, concentration, and heat transfer characteristics are studied. Also graphs of the skin friction coefficient, local Nusselt number, and Sherwood number are drawn and their numerical values are tabulated. The numerical results of the study are compared with previously published articles in the limiting condition. The velocity of the flow field is reduced as the third order slip parameter and the first order slip parameter rises, but the velocity grows as the values of the second order slip flow parameter are elevated. The findings also indicate that the local Nusselt number is depreciated but local Sherwood numbers are elevated when the Soret and Dufour numbers are larger.     

Statistical analysis on three-dimensional MHD convective Carreau nanofluid flow due to bilateral nonlinear stretching sheet with heat source and zero mass flux condition

This study focuses on analyzing the response of a magnetohydrodynamic convective Carreau nanofluid flow over a bilateral nonlinear stretching sheet in the presence of a heat source and zero mass flux condition. The problem has been solved numerically using the MATLAB built-in function bvp5c. The findings of velocity, temperature, and concentration profiles based on the various parameters are illustrated using graphs. The impact of various parameters on the heat transfer rate is scrutinized using statistical techniques, like, correlation coefficient, probable error, and regression. The effect of various parameters on skin friction coefficients is studied via tables and slope of linear regression. It is observed that the statistical results coincide with the numerical results. It is also noticed that the stretching ratio parameter increases the Y-directional velocity profile. Accuracy of the numerical procedure has been validated through a restrictive comparison of the present work with previous published results and is found to be in good agreement.     

Passive control nanoparticles in double‐diffusive free convection nanofluid flow over an inclined permeable plate

The present study has been conducted to acquire the solutions for the flow problem of an incompressible nanofluid past a permeable inclined plate implanted in a porous medium. In this study, double‐diffusivity, Brownian motion, and thermophoresis as well as passive control nanoparticles have been studied. We employ Lie group transformation on the ruling equations to extract nonlinear ordinary differential equations and solve them numerically using the fourth‐order Runge‐Kutta method and shooting approach. The supremacy of affined parameters on temperature and velocity distributions has been exposed by means of tables and graphs. This investigation suggests that both fluid velocity and nanoparticle concentration are enhanced by the modified Dufour parameter and the thermophoresis parameter. The assistance of the Lewis number intensifies the heat transport for suction.     

Terrific effect of H2 on 3D free convection MHD flow of C2H6O2H2O hybrid base fluid to dissolve Cu nanoparticles in a porous space considering the thermal radiation and nanoparticle shapes effects

In this article, the physical aspects of natural convection magnetohydrodynamic flow of Cu/Ethylene glycol-water nanofluid past a porosity vertical stretching sheet under impact of thermal radiation, shape and slip factor and suction/injection process has been analyzed using Runge- Kutta Fehlberg fifth order (RKF 5) numerical method. The influence of variable, different parameters such as nanoparticles shape factor, named hexahedron and Lamina on temperature and velocity profiles are exemplified quantitatively through graphs. Outputs demonstrate thermal radiation impact causes to produce heat and increase the temperature profile by increasing nanofluid molecules energy. Lamina shape nanoparticle has a greater effect on increasing Nusselt number (Nu) compared to hexahedron.     

Second order velocity slip and thermal jump of Cu–water nanofluid over a cone in the presence of nonlinear radiation and nonuniform heat source/sink using homotopy analysis method

The purpose of the present paper is to explore the second order slip effects on nanofluid flow over a vertical cone. The effects of nonlinear thermal radiation and nonuniform heat source/sink are also taken into account. Water with copper nanoparticles is used as nanofluid in this investigation. The governing partial differential equations for the flow are converted into ordinary differential equations by using transformations and then are solved using homotopy analysis method. The influence of various important parameters on velocity, temperature, skin‐friction, and Nusselt number are presented through graphs. Results indicate that the velocity and magnitude of skin friction decrease with a rise in first and second order velocity slips. A raise in either first or second order temperature jump causes a fall in temperature. Nonlinear radiation increases the more rapidly when compared to the linear radiation case.     

Comparative analysis of a Sisko nanofluid over a stretching cylinder through a porous medium

The present article examines the Sisko nanofluid flow and heat transfer through a porous medium due to a stretching cylinder using Buongiorno's model for nanofluids. Suitable similarity transformations are used to transform the governing boundary layer equations of fluid flow into nonlinear ordinary differential equations. The finite difference method is used to solve coupled nonlinear differential equations with MATLAB software. The impact of different parameters viz., the Sisko material parameter, porosity parameter, curvature parameter, thermophoresis parameter, and Brownian diffusion parameter on the velocity and temperature distribution are presented graphically. Moreover, the effect of the involved parameters on the heat transfer rate is also studied and presented through table values. It is noticed from the numerical values that the porosity parameter reduces the velocity while enhancing the temperature. The curvature parameter enhances the velocity throughout the fluid regime and reduces the temperature near the surface while enhancing the temperature far away from the surface. The study reveals that the thermophoresis and Brownian diffusion parameters that characterize the nanofluid flow reduce the wall heat transfer rate, while the curvature parameter enhances it. This investigation of wall heating/cooling has essential applications in solar porous water absorber systems, chemical engineering, metallurgy, material processing, and so forth.     

Arrhenius energy effect on the rotating flow of Casson nanofluid with convective conditions and velocity slip effects: Semi-numerical calculations

The present paper focuses on the effects of Arrhenius activation energy on the hydromagnetic rotating flow of Casson nanofluid. Entropy production, viscous dissipation Brownian dispersion, porous medium, velocity slip, magnetic field, convective heat, and mass conditions are taken into consideration. Transformation schemes are used to extract a nonlinear system of the differential equation. The generalized differential transform method (GDTM) is used to compute/obtain the solutions of the present system. Results for the distributions of velocities, nano concentration, and temperature are scrutinized graphically. The accuracy of GDTM is proved via a comparison of numerical and graphical results with the nearest published results by Hayat et al. and found to be excellent. Graphical results are extracted for different values of pertinent parameters versus velocities, nano concentration, and temperature profiles. The results show that more heat is produced due to the process of thermal radiation for which entropy is knowingly improved.     

Cattaneo–Christov double-diffusion model with Stefan blowing effect on copper–water nanofluid flow over a stretching surface

We often encounter many processes where the cooling rate is a key factor in deciding the features of a desired product. Due to increasing demands of controlled cooling systems, an effort is made to theoretically study the effect of volume fraction on mixed convective Cu–water nanofluid flow over a stretching surface with activation energy and thermal radiation. The nonlinear dynamical system is simplified using apt similarity variables and the obtained ordinary differential equations are dealt numerically using Runge–Kutta–Fehlberg method and shooting scheme. The thermal and solutal equations are modeled considering Cattaneo–Christov double-diffusion model. The flow problem is studied considering velocity slip and zero mass flux state at the surface. As a novelty, the present case considers the blowing effect at the surface to study massive species transport during nanofluid flow with Cattaneo–Christov double-diffusion model. The results show that an increase in strength of thermal radiation increases temperature and buoyancy ratio parameter, thereby escalating the skin friction coefficient. When thermal relaxation parameter changes from 0.001 to 0.005, heat transfer coefficient improves by 24.36%. Furthermore, with the change in value of the blowing parameter from 0.1 to 0.1015, the maximum value concentration of nanoparticles that is attained during the flow is increased by 7.15%.