Study of graphene Maxwell nanofluid flow past a linearly stretched sheet: A numerical and statistical approach

This study aims to unfold the significance of numerous physical parameters such as magnetic field, heat absorption, thermal radiation, viscous and Joule dissipations, etc. on the flow of graphene Maxwell nanofluid over a linearly stretched sheet with considerations of momentum and thermal slip conditions. The prevailing mathematical equations are reformed into extremely nonlinear coupled ordinary differential equations (ODE) utilizing similarity variables and then the equations are solved numerically by the scheme of Runge-Kutta Fehlberg method along with the shooting technique. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters are shown via numerous graphs whereas numerical values of skin friction coefficients and Nusselt numbers are illustrated and reported in different tables. In addition, statistical approach is followed for the multiple regression estimation analysis on the numerical findings of wall velocity gradient and local Nusselt number and are reported in tabular form to demonstrate the relationship among the heat transfer rate and physical parameters. Our results reveal that the graphene Maxwell nanofluid velocity gets reduced owing to enhancement in magnetic field, angle of inclination of magnetic field, porosity and unsteadiness parameters whereas behavior of nanofluid velocity is reversed due to Maxwell parameter. Further, it is noticed that the heat transfer rate of nanofluid is augmented owing to heat absorption, radiation and thermal slip parameters while it is reduced due to increase in viscous dissipation and unsteadiness parameters. The numerical results of the paper are validated by making comparisons with the earlier published paper under the restricted conditions and we found an excellent agreement with those results. A careful review of research papers reported in literature reveals that none of the authors has attempted this problem earlier although the thoughts and methodology explained in this paper can be anticipated to lead to enormously prolific connections across disciplines.     

Thermal radiation effects on Williamson fluid flow due to an expanding/contracting cylinder with nanomaterials: Dual solutions

The phenomena of heat and mass transfer during the flow of non-Newtonian transfer are amongst the core subjects in mechanical sciences. Recently, the nanomaterials are among the eminent tools for improving the low thermal conductivity of working fluids. Therefore, in view of the existing contributions, this article presents a two-dimensional numerical simulation for the transient flow of a non-Newtonian nanofluid generated by an expanding/contracting circular cylinder. This critical review further explores the impacts of variable magnetic field, thermal radiation, velocity slip and convective boundary conditions. The basic governing equations for Williamson fluid flow are formulated with the assistance of boundary layer approximations. The non-dimensional form of partially coupled ordinary differential equations has been tackled numerically by utilizing versatile Runge–Kutta integration scheme. The momentum, thermal and concentration characteristics are investigated with respect to several critical parameters, like, Weissenberg number, unsteadiness parameter, viscosity ratio parameter, slip parameter, suction parameter, magnetic parameter, thermophoresis parameter, Brownian motion parameter, Prandtl number, Lewis number and Biot number. The outcomes of the systematic reviews of these parameters and forest plots are illustrated. The study reveals that multiple solutions for the considered problem occurs for diverse values of involved physical parameters. The computed results indicate that the friction and heat transfer coefficients are significantly raised by the magnetic parameter for upper branch solutions.     

Boundary layer flow and heat transfer of a nanofluid over a permeable unsteady stretching sheet with viscous dissipation

A numerical study of the boundary layer flow past unsteady stretching surface in nanofluid under the effects of suction and viscous dissipation is investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. A similarity solution is presented, which depends on the unsteadiness parameter A, Eckert number Ec, ζ suction or injection parameter, Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt. The governing partial differential equations were converted to nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with the previously published work, and the results are found to be in excellent agreement. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal and nanoparticle volume fraction boundary layers. The thermal boundary layer thickens with a rise in the local temperature as the Brownianmotion, thermophoresis, and convective heating each intensify.     

Entropy generation analysis for peristaltically driven flow of hybrid nanofluid

Present study investigates entropy generation analysis for peristaltic motion of hybrid nanofluid. Hybrid nanofluid is composed of iron-oxide and copper nanoparticles suspended in water. Effects of Hall current, Ohmic heating and mixed convection are taken into account. Governing equations are simplified by utilizing lubrication approach. The numerical solutions for resulting system of differential equations are obtained with the aid of Shooting method. Attention has been given to the analysis of hybrid nanoparticles, Hall parameter and Grashoff number on entropy generation, heat transfer rate, velocity profile and pressure gradient. Outcomes reveal that insertion of nanoparticles decreases the temperature of hybrid nanofluid. It is found that increase in Hall parameter reduces the heat transfer rate at wall. Increment in Hall parameter reduces the entropy generation. Velocity and pressure gradient increases by enhancing Grashoff number. It is believed that the present flow model can prove useful in improving the efficiency of similar thermodynamical systems.     

Models base study of inclined MHD of hybrid nanofluid flow over nonlinear stretching cylinder

Focus of the present analysis is on the stagnation point flow of hybrid nanofluid with inclined magnetic field over a moving cylinder. The extended version of two models (e.g. Xue model and Yamada-Ota model for hybrid nanofluids) are considered in this study). A mathematical model of hybrid nanofluid flow is developed under certain flow assumptions. Boundary layer approximations are also utilized to model a system of partial differential equations. The systems of partial differential equations are further converted to dimensionless systems of ordinary differential equations by means of suitable similarity transformations. A numerical solution is obtained by applying bv4c technique. Effects of variation in physical parameters involved are depicted through graphs. Skin friction coefficient and Nusselt number are highlighted through tables. Our main objective is to investigate the heat transfer rate on the surface of the nonlinear stretching cylinder. The results of Xue model and Yamada-Ota model for the hybrid nanofluid due to nonlinear stretching cylinder are computed for comparison. In both cases, velocity and temperature profiles are best compared to the decay results.     

Heat generation/absorption effect on MHD flow of hybrid nanofluid over bidirectional exponential stretching/shrinking sheet

The idea of hybrid nanofluid has triggered many researchers because of its credential in improving the thermal characteristics. Hence, this study performed a mathematical analysis to evaluate the heat generation/absorption effect on magnetohydrodynamics (MHD) flow towards bidirectional exponential stretching/shrinking sheet of hybrid nanofluid. A system of ordinary differential equations was attained through a simplification of governing partial differential equations by employing appropriate similarity transformation and numerically determined via the bvp4c function in MATLAB programming system. The results revealed that the volume fraction of nanoparticle and magnetic parameter applied to the hybrid nanofluid improved the skin friction coefficient in the current work. The rate of heat transfer was strengthened by the intensity of the suction parameter, whereas the appearance of heat generation reduced the heat transfer rate performance. The results are proven to have dual solutions and lead to stability analysis implementation, hence confirming the first solution's achievability.     

Variable viscosity effects on the flow of MHD hybrid nanofluid containing dust particles over a needle with Hall current—a Xue model exploration

This study scrutinizes the flow of engine oil-based suspended carbon nanotubes magneto-hydrodynamics (MHD) hybrid nanofluid with dust particles over a thin moving needle following the Xue model. The analysis also incorporates the effects of variable viscosity with Hall current. For heat transfer analysis, the effects of the Cattaneo-Christov theory and heat generation/absorption with thermal slip are integrated into the temperature equation. The Tiwari-Das nanofluid model is used to develop the envisioned mathematical model. Using similarity transformation, the governing equations for the flow are translated into ordinary differential equations. The bvp4c method based on Runge-Kutta is used, along with a shooting approach. Graphs are used to examine and depict the consequences of significant parameters on involved profiles. The results revealed that the temperature of the fluid and boundary layer thickness is diminished as the solid volume fraction is raised. Also, with an enhancement in the variable viscosity parameter, the velocity distribution becomes more pronounced. The results are substantiated by assessing them with an available study.     

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter,heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter,volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.     

Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.     

Unsteady radiative nanofluid flow near a vertical heated wavy surface with temperature-dependent viscosity

In the present contribution, a numerical treatment is provided to describe unsteady nanofluid flow near a vertical heated wavy surface. A memorable feature of the present work is the investigation of nanofluid flow associated with thermal radiation that acts as a catalyst for heat transfer rates. Likewise, the effectiveness of variable viscosity is examined as it controls fluid flow as well as heat transfer. It is necessary to study heat and mass transfer for complex geometries because predicting heat and mass transfer for irregular surfaces is a topic of fundamental importance, and irregular surfaces frequently appear in many applications, such as flat-plate solar collectors and flat-plate condensers in refrigerators. A simple coordinate transformation from the wavy surface into a flat one is employed. The non-dimensional boundary layer equations that governing both heat transfer and nanofluid flow phenomena along the wavy surface are solved via a powerful numerical approach called the implicit Chebyshev pseudospectral (ICPS) method with Mathematica code. A comparison graph of the current numerical computation and the published data shows a perfect match. Figures depict the effect of various physical parameters on nanofluid velocities, temperature, salt concentration, nanoparticle concentration, skin friction, Sherwood, nanoparticle Sherwood, and Nusselt numbers. According to the numerical results, increasing the variable viscosity parameter value causes a drop in the local skin friction coefficient value and an increase in the steady-state axial nanofluid velocity profile near the wavy surface. Furthermore, as heat radiation is increased, the local Nusselt number decreases but the nanoparticle Sherwood number increases.     

Flow and heat transfer of a hybrid nanofluid past a permeable moving surface

A steady flow and heat transfer of a hybrid nanofluid past a permeable moving surface is investigated. In this study, 0.1 solid volume fraction of alumina (Al₂O₃) is fixed, then consequently, various solid volume fractions of copper (Cu) are added into the mixture with water as the base fluid to form Cu-Al₂O₃/water hybrid nanofluid. The similarity equations are obtained by converting the governing equations of the hybrid nanofluid using the technique of similarity transformation. The bvp4c function available in Matlab software is used to solve the similarity equations numerically. The numerical results are obtained for selected parameters and discussed in detail. It is found that hybrid nanofluid enhances the heat transfer rate compared to the regular nanofluid. The results show that two solutions exist up to a certain value of the moving parameter and suction strengths. The critical value in which the solution is in existence decreases as nanoparticle volume fractions increase. The temporal stability analysis is conducted in determining the stability of the dual solutions, and it is revealed that only one of them is stable and physically reliable.     

Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis

This research presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in the presence of distinct thermal features. The novel aspects of various features, such as Joule heating, porous medium, dissipation features, and radiative mechanism are addressed. In order to improve thermal transportation systems based on nanomaterials, convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in terms of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using the homotopy analysis method (HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that the presence of a permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number. Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.     

Induced magnetic field stagnation point flow of nanofluid past convectively heated stretching sheet with Buoyancy effects

This paper presents the buoyancy effects on the magneto-hydrodynamics stagnation point flow of an incompressible,viscous,and electrically conducting nanofluid over a vertically stretching sheet.The impacts of an induced magnetic field and viscous dissipation are taken into account.Both assisting and opposing flows are considered.The overseeing nonlinear partial differential equations with the associated boundary conditions are reduced to an arrangement of coupled nonlinear ordinary differential equations utilizing similarity transformations and are then illuminated analytically by using the optimal homotopy investigation strategy(OHAM).Graphs are introduced and examined for different parameters of the velocity,temperature,and concentration profile.Additionally,numerical estimations of the skin friction,local Nusselt number,and local Sherwood number are explored using numerical values.     

Effects of Thermal Radiation and Slip Mechanism on Mixed Convection Flow of Williamson Nanofluid Over an Inclined Stretching Cylinder

The current investigation highlights the mixed convection slip flow and radiative heat transport of uniformly electrically conducting Williamson nanofluid yield by an inclined circular cylinder in the presence of Brownian motion and thermophoresis parameter.A Lorentzian magnetic body force model is employed and magnetic induction effects are neglected.The governing equations are reduced to a system of nonlinear ordinary differential equations with associated boundary conditions by applying scaling group transformations.The reduced nonlinear ordinary differential equations are then solved numerically by Runge-Kutta-Fehlberg fifth-order method with shooting technique.The effects of magnetic field,Prandtl number,mixed convection parameter,buoyancy ratio parameter,Brownian motion parameter,thermophoresis parameter,heat generation/absorption parameter,mass transfer parameter,radiation parameter and Schmidt number on the skin friction coefficient and local Nusselt are analyzed and discussed.It is found that the velocity of the fluid decreases with decrease in curvature parameter,whereas it increases with mixed convection parameter.Further,the local Nusselt number decreases with an increase in the radiation parameter.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Magnetohydrodynamics (MHD) axisymmetric flow and heat transfer of a hybrid nanofluid past a radially permeable stretching/shrinking sheet with Joule heating

The main interest of the present work is to fundamentally investigate the flow characteristics and heat transfer of a hybrid Cu-Al₂O₃/water nanofluid due to a radially stretching/shrinking surface with the mutual effects of MHD, suction and Joule heating. The surface is permeable to physically allow the wall mass fluid suction. Tiwari and Das model of nanofluid is used with the new thermophysical properties of hybrid nanofluid to represent the problem. A similarity transformation is adopted to convert the governing model (PDEs) into a nonlinear set of ordinary differential equations (ODEs). A bvp4c solver in MATLAB software is employed to numerically compute the transformed system. The numerical results are discussed and graphically manifested in velocity and temperature profiles, as well as the skin friction coefficient and heat transfer rate with the pertinent values of the dimensionless parameters namely magnetic, Cu volume fraction, suction and Eckert number. The Eckert number has no impact on the boundary layer separation while the higher value of the suction parameter may affect the heat transfer performance. The presence of dual solutions (first and second) is seen on all the profiles within a limited range of the physical parameters. The stability analysis is executed, and it is validated that the first solution is the real solution.     

Thermo-physical characteristics during the flow and heat transfer analysis of GO-nanoparticles adjacent to a continuously moving thin needle

Nanofluids have shown significant promise in thermal enhancement of many industrial systems and they have been used extensively in energy applications during recent years. Keeping such applications in mind, the present work exhibits a two-dimensional numerical simulation for the boundary layer flow of Graphene oxide (GO)-nanofluids adjacent to a thin needle along with heat transfer. Influence of heat generation/absorption and viscous dissipation have been included to explore the heat transport analysis. The nanofluid flow is generated due to a continuously moving horizontal thin needle. The non-linear expressions governing the flow and heat transfer analysis are changed into dimensionless form by introducing new dimensionless variables. The novelty of current study is to predict the multiple numerical solutions for dimensionless velocity and temperature fields. Numerical computations and graphical delineations were done with the assistance of MATLAB software. This study explores the impacts of several dimensionless key parameters, like, magnetic parameter, Prandtl number, nanoparticles volume fraction and ratio of needle's velocities on the flow and thermal distributions. The computational results have proved that the fluid temperature enhances for higher values of nanoparticles volume fraction while an opposite is true for velocity distributions. In addition, the computed outcomes revealed that for the case of upper branch solution, significant reduction in skin-friction coefficient is seen for higher magnetic parameter.     

Numerical simulation of Electrokinetically Driven Peristaltic Pumping of Silver-Water Nanofluids in an asymmetric microchannel

This article intends to focus on the theoretical and numerical investigation of the peristaltic pumping of water-based silver nanofluid in the presence of electroosmotic forces. The investigation is carried out in an asymmetric microchannel subject to the influence of mixed convection and viscous dissipation. No-slip boundary conditions for velocity, temperature, and nanoparticle volume fraction are imposed on channel walls. The lubrication approach is utilized to simplify the normalized constitutive equations. The distribution of electric potential in the electric double layer is characterized by Poisson-Boltzmann ionic distribution which is further linearized by Debye-Hückel approximation. Nanofluid properties are predicted by a combination of the Buongiorno two-phase mixture model and homogeneous flow model. Additionally, the effective thermal conductivity and dynamic viscosity of silver-water nanofluid are characterized by the Corcione model. Silver nanoparticles of 20nm diameter are utilized in this suspension. The transformed set of nonlinear and coupled equations is numerically executed for axial velocity, temperature, and nanoparticle volume fraction by employing the mathematical software Maple 17. Pumping and trapping phenomena are also investigated. A comparison between the thermal conductivity of nanofluid predicted by the Corcione model and the Maxwell model is further presented. The influence of various flow parameters is outlined through graphical results. It has been observed that the thermal conductivity of silver-water nanofluid enhances with increasing nanoparticle volume fraction and temperature but decreases for larger sized nanoparticles. Moreover, the heat transfer rate rises significantly when smaller silver nanoparticles are suspended in water. Furthermore, the temperature of nanofluid is directly related to the Debye length parameter and the Helmholtz- Smoluchowski velocity parameter.     

Hydromagnetic flow of a variable viscosity nanofluid in a rotating permeable channel with hall effects

The flow, heat and mass transfer of water-based nanofluid are examined between two horizontal parallel plates in a rotating system. The effects of Brownian motion, thermophoresis, viscosity and Hall current parameters are considered. The governing partial differential equations are reduced to ordinary differential equations that are then solved numerically using the Runge–Kutta–Fehlberg method. Validation of numerical solution is achieved with an exact solution of primary velocity and found to be in good agreement. Results show that both surfaces experience opposite behavior regarding skin friction, Nusselt and Sherwood numbers in both primary and secondary flows. These physical quantities depend upon dimensionless parameters and numbers.     

MHD flow study of viscous fluid through a complex wavy curved surface due to biomimetic propulsion under porosity and second-order slip effects

The steady laminar flow of viscous fluid from a curved porous domain under a radial magnetic field is considered. The fluid flow by a curved domain is due to peristaltic waves present at the boundary walls. The whole analysis is based on porosity(Darcy number) effects. Moreover, the effects of second-order slip on the rheology analysis are also discussed. Due to the complex nature of the flow regime, we have governed the rheological equations by using curvilinear coordinates in the fixed frame. The physical influence of magnetic(Hartmann number) and porosity(Darcy number)parameters on the rheological features of peristaltic transportation are argued in detailed(in the wave frame). Additionally, in the current study, the complex wavy pattern on both boundary walls of the channel is used. The whole rheological study is based on ancient, but medically valid,assumptions of creeping phenomena and long wavelength assumptions. Analytical solutions of the governing equations are obtained by using the simple integration technique in Mathematica software 11.0. The core motivation of the present analysis is to perceive the physical influence of embedded parameters, such as the dimensionless radius of the curvature parameter, magnetic parameter, porosity parameter, different amplitude ratios of complex peristaltic waves, first-and second-order slip parameters, on the axial velocity, pressure gradient, local wall shear stress,tangential component of the extra-stress tensor, pumping and trapping phenomena.