Hydromagnetic Carreau Nanoliquid in Frames of Dissipation and Activation Energy

The novel characteristics of magnetic field and entropy generation in mixed convective flow of Carreau fluid towards a stretched surface are investigated.Buongiornio nanoliquid model consists of thermophoresis and Brownian movement aspects is opted for analysis.Energy expression is modeled subject to thermal radiation and viscous dissipation phenomenon.Concentration by zero mass flux condition is implemented.Consideration of chemical reaction and activation energy characterizes the mass transfer mechanism.Total entropy generation rate and Bejan number is formulated.The utilization of transformation variables reduces the PDEs into non-linear ODEs.The obtained nonlinear complex problems are computed numerically through Shooting scheme.The impact of involved variables like local Weissenberg number,magnetic parameter,thermal radiation parameter,Brownian motion parameter,thermophoresis parameter,buoyancy ratio parameter,mixed convection parameter,Prandtl parameter,Eckert number,Schmidt number,non-dimensional activation energy parameter,chemical reaction parameter,Brinkman number,dimensionless concentration ratio variable,diffusive variable and dimensionless temperature ratio variable on velocity,temperature,nanoparticles concentration,entropy generation,Bejan number,surface drag force and heat transfer rate are examined through graphs and tables.     

New thermodynamics of entropy generation minimization with nonlinear thermal radiation and nanomaterials

This research addressed entropy generation for MHD stagnation point flow of viscous nanofluid over a stretching surface. Characteristics of heat transport are analyzed through nonlinear radiation and heat generation/absorption. Nanoliquid features for Brownian moment and thermophoresis have been considered. Fluid in the presence of constant applied inclined magnetic field is considered. Flow problem is mathematically modeled and governing expressions are changed into nonlinear ordinary ones by utilizing appropriate transformations. The effects of pertinent variables on velocity, nanoparticle concentration and temperature are discussed graphically. Furthermore Brownian motion and thermophoresis effects on entropy generation and Bejan number have been examined. Total entropy generation is inspected through various flow variables. Consideration is mainly given to the convergence process. Velocity, temperature and mass gradients at the surface of sheet are calculated numerically.     

Entropy generation in radiative motion of tangent hyperbolic nanofluid in presence of activation energy and nonlinear mixed convection

In this communication, an optimization of entropy generation is performed through thermodynamics second law. Tangent hyperbolic nanomaterial model is used which describes the important slip mechanism namely Brownian and thermophoresis diffusions. MHD fluid is considered. The novel binary chemical reaction model is implemented to characterize the impact of activation energy. Nonlinear mixed convection, dissipation and Joule heating are considered. Appropriate similarity transformations are implemented to get the required coupled ODEs system. The obtained system is tackled for series solutions by homotopy method. Graphs are constructed to analyze the impact of different flow parameters on entropy number, nanoparticle volume concentration, temperature and velocity fields. Total entropy generation rate is calculated via various flow variables. It is noticed from obtained results that entropy number depend up thermal irreversibility, viscous dissipation and Joule heating irreversibility and concentration irreversibility. Decreasing behavior of concentration is witnessed for higher estimations of chemical reaction variable. Entropy number is more for higher Hartmann number, Weissenberg number and chemical reaction variable while contrast behavior is noted for Bejan number.     

Entropy generation minimization and statistical declaration with probable error for skin friction coefficient and Nusselt number

Main emphasis of present work is to analyze the novel feature of entropy generation in MHD nanomaterial flow between two rotating disks. Heat transfer process is explored in the presence of Joule heating and thermal radiation. Tiwari–Das nanofluid model is employed in mathematical modeling. Aluminum oxide and copper water nanoparticles are accounted. Statistical declaration and probable error for problem accuracy are computed. Total entropy generation subject to Bejan number is scrutinized. Suitable variables are utilized to transform nonlinear PDEs to ordinary ones. Convergent series solutions are computed. Zeroth and mth order problems are discussed for stability analysis. The impact of physical flow variables like Reynolds number, magnetic parameter, porosity parameter, stretching parameter, rotational parameter, radiation parameter, Eckert number, suction injection parameter, Brinkman number and temperature ratio parameter on velocities, temperature, total entropy generation and Bejan number are examined and discussed through graphs. Velocity and thermal gradients at the surface of disks are computed.     

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.     

Entropy generation (irreversibility) associated with flow and heat transport mechanism in Sisko nanomaterial

Here a novel applications of entropy generation optimization is presented for nonlinear Sisko nanomaterial flow by rotating stretchable disk. Flow is examined in the absence of magnetohydrodynamics and Joule heating. Total irreversibility rate (entropy generation rate) is investigated for different flow parameters. Heat source/sink and viscous dissipation effects are considered. Impacts of Brownian motion and thermophoresis on irreversibility have been analyzed. Governing flow equations comprise momentum, energy and nanoparticle concentration. Von Karman's similarity variables are implemented for reduction of PDEs into ODEs. Homotopy analysis technique for series solutions is implemented. Attention is given to the irreversibility. The impacts of different flow parameters on velocity, nanoparticle concentration, temperature and irreversibility rate are graphically presented. From obtained results it is examined that irreversibility rate enhances for larger estimation of Brinkman number and diffusion. Furthermore it is also examined that temperature and nanoparticle concentration show contrast behavior through Prandtl number and Brownian motion.     

Transient thin film flow of nonlinear radiative Maxwell nanofluid over a rotating disk

In this letter, a mathematical model for transient nature thin film flow of Maxwell nanofluid over a rotating disk is studied in the presence of a uniform magnetic field and non-linear thermal radiation. The Brownian motion and thermophoresis features due to nanofluid are captured by adopting the Buongiorno model. The prime emphasize is to explore the temperature field and nanoparticles volume fraction in nanofluid thin film flow. The reduced system of differential equations is solved numerically by finite difference based method namely bvp4c. The numerical outcomes regarding film thickness, Nusselt number, Sherwood number, velocity, temperature, and concentration are revealed for varying estimation of involved physical parameters. It is shown that the film thickness decreases with increasing values of the magnetic number. Further, the impact of thermophoresis and thermal radiation parameters is worthwhile in enhancing the fluid temperature. The Solute concentration is found to decrease with Brownian motion and Schmidt number.     

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.     

Brownian motion and thermophoresis effects on unsteady stagnation point flow of Eyring-Powell nanofluid: a Galerkin approach

This article concerns the analysis of an unsteady stagnation point flow of Eyring-Powell nanofluid over a stretching sheet. The influence of thermophoresis and Brownian motion is also considered in transport equations. The nonlinear ODE set is obtained from the governing nonlinear equations via suitable transformations. The numerical experiments are performed using the Galerkin scheme. A tabular form comparison analysis of outcomes attained via the Galerkin approach and numerical scheme (RK-4) is available to show the credibility of the Galerkin method. The numerical exploration is carried out for various governing parameters, namely, Brownian motion, steadiness, thermophoresis, stretching ratio, velocity slip, concentration slip, thermal slip, and fluid parameters, and Hartmann, Prandtl and Schmidt numbers. The velocity of fluid enhances with an increase in fluid and magnetic parameters for the case of opposing, but the behavior is reversed for assisting cases. The Brownian motion and thermophoresis parameters cause an increase in temperature for both cases (assisting and opposing). The Brownian motion parameter provides a drop-in concentration while an increase is noticed for the thermophoresis parameter. All the outcomes and the behavior of emerging parameters are illustrated graphically. The comparison analysis and graphical plots endorse the appropriateness of the Galerkin method. It is concluded that said method could be extended to other problems of a complex nature.     

Entropy analysis on unsteady MHD biviscosity nanofluid flow with convective heat transfer in a permeable radiative stretchable rotating disk

We examine the entropy analysis in three-dimensional hydromagnetic flow and convective heat transport of a biviscosity nanofluid over a rotating porous disk with a time-dependent stretching rate in the direction of the radius of the circular disk. We also examine the influence of thermal radiation and viscous dissipation due to nanoparticles and applied magnetic field. We invoked suitable self-similar transformations to covert the modeled coupled nonlinear PDEs into a set of nonlinear ODEs. The transformed system of equations is then worked out numerically by a well-known shooting technique and the fourth-order Runge–Kutta–Fehlberge method. The rotating phenomenon yields an additional parameter known as a rotation parameter, which controls the disk’s rotation. The study shows that the fluid motion is accelerated along the radial and cross-radial directions with an increase in the rotation of the disk. The skin-friction and the heat transfer rate at the disk strongly depend on the rotation of the disk, permeability of the porous medium, thermal radiation, and nanoparticle size. The Bejan number quantifies the entropy production of the system. It has a considerable impact on the magnetic field, rotation of the disk, thermal radiation, and Biot number. The efficient performance of the system is possible by a suitable choice of the physical parameters discussed in this article.     

Unsteady boundary layer flow of a nanofluid over a stretching sheet with variable fluid properties in the presence of thermal radiation

In this paper, we investigated numerically an unsteady boundary layer flow of a nanofluid over a stretching sheet in the presence of thermal radiation with variable fluid properties. Using a set of suitable similarity transformations, the governing partial differential equations are reduced into a set of nonlinear ordinary differential equations. System of the nonlinear ordinary differential equations are then solved by the Keller-box method. The physical parameters taken into consideration for the present study are: Prandtl number Pr, Lewis number Le, Brownian motion parameter N _b, thermophoresis parameter N _t, radiation parameter N _r, unsteady parameter M. In addition to these parameters, two more new parameters namely variable thermophoretic diffusion coefficient parameter e and variable Brownian motion diffusion coefficient parameter β have been introduced in the present study. Effects of these parameters on temperature, volume fraction of the nanoparticles, surface heat and mass transfer rates are presented graphically and discussed briefly. To validate our method, we have compared the present results with some previously reported results in the literature. The results are found to be in a very good agreement.     

Entropy production in the flow over a swirling stretchable cylinder

In the present work, the entropy generation due to the heat transfer and fluid friction irreversibility is investigated numerically for a three-dimensional flow induced by rotating and stretching motion of a cylinder. The isothermal boundary conditions are taken into account for the heat transfer analysis. The similarity transformations are utilized to convert the governing partial differential equations to ordinary differential equations. Resulting nonlinear differential equations are solved using a numerical scheme. Expressions for the entropy generation number, the Nusselt number and the Bejan number are obtained and discussed through graphs for various physical parameters. An analysis has been made to compare the heat transfer irreversibility with fluid friction irreversibility using the expression of the Bejan number. It is found that the surface is a durable source of irreversibility and the curvature of cylinder is to enhance the fluid friction irreversibility.     

Rapid communication: Permeability of hydrogen in two-dimensional graphene and hexagonal boron nitride sheets

This paper concerns an application to optimal energy by incorporating thermal equilibrium on MHD-generalised non-Newtonian fluid model with melting heat effect. Highly nonlinear system of partial differential equations is simplified to a nonlinear system using boundary layer approach and similarity transformations. Numerical solutions of velocity and temperature profile are obtained by using shooting method. The contribution of entropy generation is appraised on thermal and fluid velocities. Physical features of relevant parameters have been discussed by plotting graphs and tables. Some noteworthy findings are: Prandtl number, power law index and Weissenberg number contribute in lowering mass boundary layer thickness and entropy effect and enlarging thermal boundary layer thickness. However, an increasing mass boundary layer effect is only due to melting heat parameter. Moreover, thermal boundary layers have same trend for all parameters, i.e., temperature enhances with increase in values of significant parameters. Similarly, Hartman and Weissenberg numbers enhance Bejan number.     

Thermo-bioconvection transport of nanofluid over an inclined stretching cylinder with Cattaneo–Christov double-diffusion

In this paper, Newtonian nanofluid flow is observed under the effects of the magnetic field, activation energy and motile microorganisms over an inclined stretchable cylinder. The magnificent aspects of nanoliquid are demonstrated by enduring the Brownian motion and thermophoresis diffusion features.Nonlinear higher order partial differential equations are transformed into first-order ordinary differential equations with suitable similarity variables. The attained sets of governing equations are then cracked by bvp4 c procedure in MATLAB mathematical software. The numerical and graphical outcomes of controlling parameters such as Prandtl number, mixed convection, activation energy, thermophoresis,Brownian parameter, Biot number, Lewis number, Peclet number and motile concentration parameter against the velocity, temperature, volumetric concentration and motile concentration of nanoparticles of the fluid are discussed. The velocity is enhanced with the growth valuation in mixed convection and decay by rising variation of buoyancy ratio parameter, magnetic parameter and bio-convective Rayleigh parameter. The evolution in motile microorganisms is due to the increasing values of microorganisms Biot number. The presented data can be helpful in enhancement of manufacturing processes, biomolecules, extrusion systems applications and energy production improvement.     

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.     

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.     

Three-dimensional flow of Powell–Eyring nanofluid with heat and mass flux boundary conditions

This article investigates the three-dimensional flow of Powell–Eyring nanofluid with thermophoresis and Brownian motion effects. The energy equation is considered in the presence of thermal radiation. The heat and mass flux conditions are taken into account. Mathematical formulation is carried out through the boundary layer approach. The governing partial differential equations are transformed into the nonlinear ordinary differential equations through suitable variables. The resulting nonlinear ordinary differential equations have been solved for the series solutions. Effects of emerging physical parameters on the temperature and nanoparticles concentration are plotted and discussed. Numerical values of local Nusselt and Sherwood numbers are computed and examined.     

Numerical study of the onset of chemical reaction and heat source on dissipative MHD stagnation point flow of Casson nanofluid over a nonlinear stretching sheet with velocity slip and convective boundary conditions

The magnetohydrodynamic (MHD) stagnation point flow of Casson nanofluid over a nonlinear stretching sheet in the presence of velocity slip and convective boundary condition is examined. In this analysis, various effects such as velocity ratio, viscous dissipation, heat generation/absorption and chemical reaction are accentuated. Possessions of Brownian motion and thermophoresis are also depicted in this study. A uniform magnetic field as well as suction is taken into account. Suitable similarity transformations are availed to convert the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations and then series solutions are secured using a homotopy analysis method (HAM). Notable accuracy of the present results has been obtained with the earlier results. Impact of distinct parameters on velocity, temperature, concentration, skin friction coefficient,Nusselt number and Sherwood number is canvassed through graphs and tabular forms.