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.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption in a Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption.Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method(HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

Upshot of Chemical Species and Nonlinear Thermal Radiation on Oldroyd-B Nanofluid Flow Past a Bi-directional Stretched Surface with Heat Generation/Absorption ina Porous Media

A three-dimensional mathematical model is developed to examine the flow of nonlinear thermal radiation Oldroyd-B nanofluid past a bidirectional linearly stretched surface in a porous medium. The flow is induced by temperature dependent thermal conductivity, chemical reaction and convective heat and mass conditions. Novel characteristics of Brownian motion and thermophoresis are accompanied by magnetohydrodynamic and heat generation/absorption. Self-similar transformations are employed to convert the system of nonlinear partial differential equations to a system of ordinary differential equations with high nonlinearity and are solved by strong analytic technique named as Homotopy Analysis method (HAM). Effects of varied arising parameters on involved distributions are reflected through graphical illustrations. From this study, it is perceived that strong magnetic field hinders the fluid's motion and leads to rise in temperature that eventually lowers heat transfer rate from the surface. Further, decrease in heat transfer rate is also observed for enhanced values of thermal radiation parameter. To validate our results, a comparison with already published paper in limiting case is also given and results are found in excellent oncurrence; hence reliable results are being presented.     

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.     

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.     

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.     

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.     

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.     

Mixed convection of a three-dimensional stagnation point flow on a vertical plate with surface slip in a hybrid nanofluid

Hybrid nanofluid has become one of the major interest topics among researchers nowadays due to its significant impact in myriad applications. This paper modeled and explored the properties of flow and heat transfer of mixed convection stagnation point flow for hybrid nanofluid (alumina-copper/water) on a vertical plate with slips and suction. By using the method of similarity transformation, the governing set of partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). These derived equations are then evaluated numerically by adopting the bvp4c function that is available in Matlab software. In the presence of slips together with the opposing flow of mixed convection, the local Nusselt number (heat transfer rate) can be augmented by increasing the solid volume fraction of copper. The surge of 0.5% of copper volume fraction can accelerate the heat transfer rate by approximately 1.3% in this present analysis within the specified value of slips, mixed convection, and suction. The stability analysis is conducted due to the existence of dual solutions and only the first solution is stable for practical application.     

Impact of nanoparticles and radiative heat flux in von Kármán swirling flow of Maxwell fluid

In this paper, the classical von Kármán swirling flow problem due to a rotating disk is modeled and studied for the rate type Maxwell nanofluid together with heat and mass transfer mechanisms. The model under consideration predicts the relaxation time characteristics. The novel aspects of thermophoresis and Brownian motion features due to nanoparticles are investigated by employing an innovative Buongiorno’s model. The analysis further explores the impact of linear Rosseland radiation on heat transfer characteristics. The concept of boundary layer approximations is utilized to formulate the basic governing equations of Maxwell fluid. The dimensionless form of a system of ordinary differential equations is obtained through similarity approach adopted by von Kármán. The system of equations is integrated numerically in domain [0,∞) by using bvp midrich scheme in Maple software. The obtained results intimate that higher rotation raises the radial and angular velocity components. The nano-particles concentration enhances with Brownian motion parameter. Further, the heat transfer rate at the disk surface diminishes with thermophoresis parameter. The achieved numerical computations of velocity profiles, friction coefficient and Nusselt number are matched in limiting cases with previously published literature and an outstanding agreement is observed.     

Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications.     

Thermally stratified flow of hybrid nanofluids with radiative heat transport and slip mechanism: multiple solutions

Research on flow and heat transfer of hybrid nanofluids has gained great significance due to their efficient heat transfer capabilities.In fact,hybrid nanofluids are a novel type of fluid designed to enhance heat transfer rate and have a wide range of engineering and industrial applications.Motivated by this evolution,a theoretical analysis is performed to explore the flow and heat transport characteristics of Cu/Al₂O₃ hybrid nanofluids driven by a stretching/shrinking geometry.Further,this work focuses on the physical impacts of thermal stratification as well as thermal radiation during hybrid nanofluid flow in the presence of a velocity slip mechanism.The mathematical modelling incorporates the basic conservation laws and Boussinesq approximations.This formulation gives a system of governing partial differential equations which are later reduced into ordinary differential equations via dimensionless variables.An efficient numerical solver,known as bvp4c in MATLAB,is utilized to acquire multiple(upper and lower)numerical solutions in the case of shrinking flow.The computed results are presented in the form of flow and temperature fields.The most significant findings acquired from the current study suggest that multiple solutions exist only in the case of a shrinking surface until a critical/turning point.Moreover,solutions are unavailable beyond this turning point,indicating flow separation.It is found that the fluid temperature has been impressively enhanced by a higher nanoparticle volume fraction for both solutions.On the other hand,the outcomes disclose that the wall shear stress is reduced with higher magnetic field in the case of the second solution.The simulation outcomes are in excellent agreement with earlier research,with a relative error of less than 1%.     

Modern development on the features of magnetic field and heat sink/source in Maxwell nanofluid subject to convective heat transport

Nanofluids are forthcoming new generation heat transfer fluids, which have been scrutinized precisely, in current years. Thermophysical assets of these fluids have noteworthy impact on their heat transfer features. In this current investigation a mathematical relation for two dimensional (2D) flow of magnetite Maxwell nanofluid influenced by a stretched cylinder is established. To visualize the stimulus of Brownian moment and thermophoresis phenomena on Maxwell fluid Buongiorno's relation has been considered. Moreover, heat sink/source and convective condition are also presented for heat transport mechanism. The homotopic scheme has been developed for the solutions of nonlinear ordinary differential equations (ODEs). The achieved outcomes are planned and consulted in aspects for somatic parameters. It is noteworthy that the velocity of Maxwell fluid display conflicting performance for curvature parameter and Deborah number. It is also reported that the liquid velocity decays for magnetic parameter, whereas the nanoliquid temperature and concentration field enhance for magnetic parameter. Furthermore, the liquid temperature intensifies for the progressive values of thermophoresis parameter and Brownian motion. Additionally, endorsement of current significances is organized via benchmarking with earlier famous limiting situations and we pledge a marvelous communication with these outcomes.     

Flow and heat transfer over a rotating porous disk in a nanofluid

The steady flow of an incompressible viscous fluid due to a rotating disk in a nanofluid is studied. The transformed boundary layer equations are solved numerically by a finite difference scheme, namely the Keller-box method. Numerical results for the flow and heat transfer characteristics are obtained for various values of the nanoparticle volume fraction parameter φ and suction/injection parameter h₀. Two models for the effective thermal conductivity of the nanofluid, namely the Maxwell-Garnett model and the Patel model, are considered. It is found that for the Patel model, the heat transfer rate at the surface increases for both suction and injection, whereas different behaviors are observed for the Maxwell-Garnett model, i.e. increasing the values of φ leads to a decrease in the heat transfer rate at the surface for suction, but increases for injection. The results of this study can be used in the design of an effective cooling system for electronic components to help ensure effective and safe operational conditions.     

Hybrid nanofluid flow over two different geometries with Cattaneo–Christov heat flux model and heat generation: A model with correlation coefficient and probable error

The authors scrutinize the steady, MHD flow of SiO₂−MoS₂/water hybrid nanofluid towards two different geometries i.e. a wedge and a cone. The Tiwari and Das model is implemented with a generalized–Fourier's model, popularized as Cattaneo-Christov heat flux model. Analysis of heat transfer also incorporates the effects of suction, heat generation and thermal radiation. To showcase the relationship between engineering quantities and pertinent parameters involved in the study, the correlation coefficient for heat transfer coefficient and the skin friction coefficient is computed followed by the computation of probable error and statistical declaration. Similarity transformations are utilized to remodel the constitutive laws of flow in non-dimensional form. Numerical computation of non-linear, coupled O.D.E.’s is performed with the support of the Runge-Kutta-Fehlberg scheme and shooting method. Graphical and tabular illustrations of computed results are provided to report the variation in flow properties with the fluctuation in physical parameters. In both cases, i.e. flow close to a wedge and a cone, the temperature of hybrid nanofluid enhances on intensifying the thermal radiation and experiences a decrement with thermal relaxation parameter and magnetic field. Rising values of the suction parameter, thermal relaxation parameter, and thermal radiation cause increment in heat transfer coefficient. Interestingly, it was spotted that the heat generation parameter has contrary effects on temperature distribution over the two geometries.     

Investigation of Ti6Al4V and AA7075 alloy embedded nanofluid flow over longitudinal porous fin in the presence of internal heat generation and convective condition

The thermal attributes of porous fin due to radiation and natural convection have been carried out in the presence of nanofluid flow. The geometry of the fin taken for the analysis is rectangular profiled longitudinal fin. The temperature-dependent internal heat generation condition is also considered along with Darcy's model. The two types of nanofluid containing titanium alloy(Ti6Al4V) and aluminium alloy(AA7075) immersed in water is considered for the investigation.The modelled nonlinear ordinary differential equation is numerically solved by the Runge–Kutta–Fehlberg technique. The impact of geometric parameter on the heat transfer analysis of the fin due to the flow of both nanofluids is plotted and consequences are physically interpreted. It is observed that the presence of the water-based titanium alloy better enhances the fin heat transfer rate.     

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.     

Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition

The present work deals with the three-dimensional hybrid Cu-Al₂O₃/water nanofluid flow towards a stretching/shrinking sheet with the presence of velocity slip and convective conditions. A permeable sheet is considered to maintain the shrinking flow through an adequate wall mass suction. The nonlinear governing boundary layer coupled with energy equations are transformed into the ordinary differential equations using similarity transformation. Numerical computations are performed with the aid of boundary value problem solver (bvp4c) in the Matlab software and the results are presented in the tables and graphs. The boundary layer separation occurs in the shrinking flow region. An upsurge of slip and copper nanoparticle volume fraction parameters can increase the range of first and second solutions whereas Biot parameter give zero impact on delaying the boundary layer separation. However, an increase of Biot and slip parameters can boost the heat transfer rate while opposite result is obtained with the augmentation of the copper solid volume fraction. The stability of both solutions are examined, and it is validated that the first (upper branch) solution is more stable than second solution.     

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.