Entropy generation applications in flow of viscoelastic nanofluid past a lubricated disk in presence of nonlinear thermal radiation and Joule heating

Entropy generation is the loss of energy in thermodynamical systems due to resistive forces,diffusion processes, radiation effects and chemical reactions. The main aim of this research is to address entropy generation due to magnetic field, nonlinear thermal radiation, viscous dissipation, thermal diffusion and nonlinear chemical reaction in the transport of viscoelastic fluid in the vicinity of a stagnation point over a lubricated disk. The conservation laws of mass and momentum along with the first law of thermodynamics and Fick's law are used to discuss the flow, heat and mass transfer, while the second law of thermodynamics is used to analyze the entropy and irreversibility. The numbers of independent variables in the modeled set of nonlinear partial differential equations are reduced using similarity variables and the resulting system is numerically approximated using the Keller box method. The effects of thermophoresis,Brownian motion and the magnetic parameter on temperature are presented for lubricated and rough disks. The local Nusselt and Sherwood numbers are documented for both linear and nonlinear thermal radiation and lubricated and rough disks. Graphical representations of the entropy generation number and Bejan number for various parameters are also shown for lubricated and rough disks. The concentration of nanoparticles at the lubricated surface reduces with the magnetic parameter and Brownian motion. The entropy generation declines for thermophoresis diffusion and Brownian motion when lubrication effects are dominant. It is concluded that both entropy generation and the magnitude of the Bejan number increase in the presence of slip. The current results present many applications in the lubrication phenomenon,heating processes, cooling of devices, thermal engineering, energy production, extrusion processes etc.     

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.     

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 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.     

Chemical reaction and heat source/sink effect on magnetonano Prandtl-Eyring fluid peristaltic propulsion in an inclined symmetric channel

The main emphasis of this article is to examine the peristaltic transport of magnetohydrodynamic (MHD) Prandtl-Eyring nanofluid in an inclined symmetric channel with compliant walls. Nanofluid including thermophoresis and Brownian motion is taken into account. Two-dimensional governing equations for the peristaltic motion of Prandtl-Eyring nanofluid are modeled in the presence of chemical reaction. The resulting dimensionless nonlinear system is numerically solved for velocity, temperature, and concentration. The effects of various dimensionless parameters on fluid flow are featured through graphs. This analysis reveals that the influence of wall tension and wall mass parameters on axial velocity are increasing whereas the impact of wall damping parameter on velocity is decaying. The opposite effect of thermophoresis parameter and Brownian motion parameter on both temperature and heat transfer coefficient are observed. The destructive chemical reaction causes decay in temperature, nanoparticle concentration, and heat transfer coefficient.     

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.     

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.     

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.     

Heat and mass transfer analysis of time-dependent tangent hyperbolic nanofluid flow past a wedge

The candid intension of this article is to inspect the heat and mass transfer of a magnetohydrodynamic tangent hyperbolic nanofluid. The nanofluid flow has been assumed to be directed by a wedge on its way. In addition, the collective stimulus of the convective heating mode with thermal radiation is inspected. The governing set of PDEs is rendered into that of the coupled nonlinear ODEs. The resulting ordinary differential equations are then solved by the well known shooting technique for two different cases; the flow over a static wedge and flow over a stretching wedge. The impact of intricate physical parameters on the velocity, temperature and concentration profiles is analyzed graphically. It is noticed that the intensifying values of the generalized Biot number, Brownian motion parameter, thermophoresis parameter and Weissenberg number enhances the dimensionless temperature profile.     

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.     

A meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids

Decline in the theoretical and empirical review of Brownian motion is worth noticing, not just because its relevance lies in the field of mathematical physics but due to unavailability of statistical technique. The ongoing debate on transport phenomenon and thermal performance of various fluids in the presence of haphazard motion of tiny particles as explained by Albert Einstein using kinetic theory and Robert Brown is further clinched in this report. This report presents the outcome of detailed inspections of the significance of Brownian motion on the flow of various fluids as reported in forty-three (43) published articles using the method of slope linear regression through the data point. The technique of slope regression through the data points of each physical property of the flow and Brownian motion parameter was established and used to generate four forest plots. The outcome of the study indicates that an increase in Brownian motion corresponds to an enhancement of haphazard motion of tiny particles. In view of this, there would always be a significant difference between the corresponding effects when Brownian motion is small and large in magnitude. Maximum heat transfer rate can be achieved due to Brownian motion in the presence of thermal radiation, thermal convective and mass convective at the wall in three-dimensional flow. In the presence of heat convective and mass convective at the wall, and thermal radiation, a significant increase in Nusselt number due to Brownian motion is guaranteed. A decrease in the concentration of fluid substance due to an increase in Brownian motion is bound to occur. This is not achievable in the case of high entropy generation and homogeneous-heterogeneous quartic autocatalytic kind of chemical reaction.     

Transverse Transport of Polymeric Nanofluid under Pure Internal Heating: Keller Box Algorithm

The present work aims to investigate transverse Oldroyd-B nanofluid flow on a stretched panel with consideration of internal heat generation. Buongiorno model is utilized to study influence of thermophoresis and Brownian motion effects. A numerical procedure known as Keller box algorithm is used to solve the governed physical model.Graphically velocity, temperature and concentration of nanoparticles are expressed. Also, concerned physical measures such as heat and mass transfer are investigated numerically. The simulations performed revealed that fluid parameters play a significant role in heat transfer under Brownian motion and thermophoresis effects. Local heat flux is elevated while local mass flux is suppressed with enhancing Brownian motion parameter. Streamlines pattern exhibits that flow is more inclined in the presence of Deborah number effects. To the best of our knowledge, transverse flow of an Oldroyd-B type fluid which incorporates the thermal relaxation effects has never been reported before in the presence of Brownian motion and internal heating phenomenon. Therefore we intend to discuss these features in detail. The obtained results are a novel contribution, which can be benchmark for further relevant academic research related to polymer industry.     

Transverse Transport of Polymeric Nanofluid under Pure Internal Heating: Keller Box Algorithm

The present work aims to investigate transverse Oldroyd-B nanofluid flow on a stretched panel with consideration of internal heat generation. Buongiorno model is utilized to study influence of thermophoresis and Brownian motion effects. A numerical procedure known as Keller box algorithm is used to solve the governed physical model. Graphically velocity, temperature and concentration of nanoparticles are expressed. Also, concerned physical measures such as heat and mass transfer are investigated numerically. The simulations performed revealed that fluid parameters play a significant role in heat transfer under Brownian motion and thermophoresis effects. Local heat flux is elevated while local mass flux is suppressed with enhancing Brownian motion parameter. Streamlines pattern exhibits that flow is more inclined in the presence of Deborah number effects. To the best of our knowledge, transverse flow of an Oldroyd-B type fluid which incorporates the thermal relaxation effects has never been reported before in the presence of Brownian motion and internal heating phenomenon. Therefore we intend to discuss these features in detail. The obtained results are a novel contribution, which can be benchmark for further relevant academic research related to polymer industry.     

Casson fluid flow: Free convective heat and mass transfer over an unsteady permeable stretching surface considering viscous dissipation

The present study investigates a Casson fluid flow in the presence of free convection of combined heat and mass transfer toward an unsteady permeable stretching sheet with thermal radiation, viscous dissipation and chemical reaction. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations and then solved by an efficient Runge–Kutta–Fehlberg method. The dimensionless velocity is decreased by increasing values of the chemical reaction and magnetic parameter while fluid temperature is significantly reduced by increasing values of the Prandtl number. The heat transfer rate is reduced with increasing values of thermal radiation and magnetic parameters.     

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.     

Modeling Chemically Reactive Flow of Sutterby Nanofluid by a Rotating Disk in Presence of Heat Generation/Absorption

In this article we investigate the flow of Sutterby liquid due to rotating stretchable disk. Mass and heat transport are analyzed through Brownian diffusion and thermophoresis. Further the effects of magnetic field, chemical reaction and heat source are also accounted. We employ transformation procedure to obtain a system of nonlinear ODE's. This system is numerically solved by Built-in-Shooting method. Impacts of different involved parameter on velocity, temperature and concentration are described. Velocity, concentration and temperature gradients are numerically computed. Obtained results show that velocity is reduced through material parameter. Temperature and concentration are enhanced with thermophoresis parameter.