scholarly journals Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy–Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 18 ◽  
Author(s):  
Ghulam Rasool ◽  
Ting Zhang ◽  
Ali J. Chamkha ◽  
Anum Shafiq ◽  
Iskander Tlili ◽  
...  
Keyword(s):  
Entropy Generation ◽  
Second Law Of Thermodynamics ◽  
Magnetic Reynolds Number ◽  
Random Motion ◽  
Weissenberg Number ◽  
Brownian Diffusion ◽  
Bejan Number ◽  
Nanofluid Flow ◽  
Highly Nonlinear ◽  
Buongiorno Model

The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

scholarly journals Entropy Generation and Consequences of MHD in Darcy–Forchheimer Nanofluid Flow Bounded by Non-Linearly Stretching Surface

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 652 ◽  
Author(s):  
Ghulam Rasool ◽  
Anum Shafiq ◽  
Ilyas Khan ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Thermal Radiation ◽  
Second Law Of Thermodynamics ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Brownian Diffusion ◽  
Bejan Number ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Entropy Optimization ◽  
Stream Lines

Present communication aims to inspect the entropy optimization, heat and mass transport in Darcy-Forchheimer nanofluid flow surrounded by a non-linearly stretching surface. Navier-Stokes model based governing equations for non-Newtonian nanofluids having symmetric components in various terms are considered. Non-linear stretching is assumed to be the driving force whereas influence of thermal radiation, Brownian diffusion, dissipation and thermophoresis is considered. Importantly, entropy optimization is performed using second law of thermodynamics. Governing problems are converted into nonlinear ordinary problems (ODEs) using suitably adjusted transformations. RK-45 based built-in shooting mechanism is used to solve the problems. Final outcomes are plotted graphically. In addition to velocity, temperature, concentration and Bejan number, the stream lines, contour graphs and density graphs have been prepared. For their industrial and engineering importance, results for wall-drag force, heat flux (Nusselt) rate and mass flux (Sherwood) rate are also given in tabular data form. Outputs indicate that velocity reduces for Forchheimer number as well as for the porosity factor. However, a rise is noted in temperature distribution for elevated values of thermal radiation. Entropy optimization shows enhancement for larger values of temperature difference ratio. Skin-friction enhances for all relevant parameters involved in momentum equation.

scholarly journals Slip flow of Jeffrey nanofluid with activation energy and entropy generation applications

2021 ◽  
Vol 13 (3) ◽  
pp. 168781402110065
Author(s):  
Hu Ge-JiLe ◽  
Sumaira Qayyum ◽  
Faisal Shah ◽  
M Ijaz Khan ◽  
Sami Ullah Khan
Keyword(s):  
Activation Energy ◽  
Entropy Generation ◽  
Slip Flow ◽  
Graphical Analysis ◽  
Thermal Engineering ◽  
Bejan Number ◽  
Nano Technology ◽  
Flow Equations ◽  
Jeffrey Nanofluid ◽  
Buongiorno Model

The growing development in the thermal engineering and nano-technology, much attention has been paid on the thermal properties of nanoparticles which convey many applications in industrial, technological and medical era of sciences. The noteworthy applications of nano-materials included heat transfer enhancement, thermal energy, solar systems, cooling of electronics, controlling the heat mechanisms etc. Beside this, entropy generation is an optimized scheme which reflects significances in thermodynamics systems to control the higher energy efficiency. On this end, present work presents the slip flow of Jeffrey nanofluid over a stretching sheet with applications of activation energy and viscous dissipation. The entropy generation features along with Bejan number significance is also addressed in present analysis. Buongiorno model of nanofluid is used to discuss the heat and mass transfer. The formulated flow equations are attained into non-dimensional form. An appropriate ND MATHEMATICA built-in scheme is used to find the solution. The solution confirmation is verified by performing the error analysis. For developed flow model and impacted parameters, a comprehensive graphical analysis is performed. It is observed that slip phenomenon is used to decays the velocity profile. Temperature and concentration are in direct relation with Brownian motion parameter and activation energy respectively. Entropy and Bejan number have same results for greater diffusion parameter.

Thermodynamic optimization of nanofluid flow over a non-isothermal wedge with nonlinear radiation and activation energy

2021 ◽  
Author(s):  
M R Acharya ◽  
P Mishra ◽  
Satyananda Panda
Keyword(s):  
Heat Transfer ◽  
Activation Energy ◽  
Reynolds Number ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Mathematical Formulation ◽  
Bejan Number ◽  
Nanofluid Flow ◽  
Entropy Generation Number ◽  
Generation Number

Abstract This paper analyses the augmentation entropy generation number for a viscous nanofluid flow over a non-isothermal wedge including the effects of non-linear radiation and activation energy. We discuss the influence of thermodynamically important parameters during the study, namely, the Bejan number, entropy generation number, and the augmentation entropy generation number. The mathematical formulation for thermal conductivity and viscosity of nanofluid for Al2O3 − EG mixture has been considered. The results were numerically computed using implicit Keller-Box method and depicted graphically. The important result is the change in augmentation entropy generation number with Reynolds number. We observed that adding nanoparticles (volume fraction) tend to enhance augmentation entropy generation number for Al2O3 − EG nanofluid. Further, the investigation on the thermodynamic performance of non-isothermal nanofluid flow over a wedge reveals that adding nanoparticles to the base fluid is effective only when the contribution of heat transfer irreversibility is more than fluid friction irreversibility. This work also discusses the physical interpretation of heat transfer irreversibility and pressure drop irreversibility. This dependency includes Reynolds number and volume fraction parameter. Other than these, the research looked at a variety of physical characteristics associated with the flow of fluid, heat and mass transfer.

scholarly journals Analysis of entropy generation minimization (EGM) in flow of Ree-Eyring nanofluid between two coaxially rotating disks

2020 ◽  
pp. 57-57
Author(s):  
Muhammad Khan ◽  
Riaz Muhammad ◽  
Sumaira Qayyum ◽  
Niaz Khan ◽  
M. Jameel
Keyword(s):  
Ohmic Heating ◽  
Skin Friction Coefficient ◽  
Random Motion ◽  
Brownian Diffusion ◽  
Physical Parameters ◽  
Rotating Disks ◽  
Rotational Parameter ◽  
Transfer Rates ◽  
Homotopy Analysis ◽  
Buongiorno Model

The present communication addresses MHD radiative nanomaterial flow of Ree-Eying fluid between two coaxially rotating disks. Both disks are stretchable. Buongiorno model is used for nanofluids. Nanofluid aspects comprise random motion of particles (Brownian diffusion) and thermophoresis. MHD fluid is considered. Furthermore, dissipation, radiative heat flux and Ohmic heating effects are considered to model the energy equation. Total entropy rate is calculated through implementation of second thermodynamics law. Series solutions are developed through homotopy analysis method. Impacts of physical parameters on the velocity, temperature, entropy and concentration fields are discussed graphically. Skin friction coefficient and heat and mass transfer rates are numerically calculated through Tables 2-4. It is noticed that the velocity of liquid particles decreases versus higher estimations of magnetic parameter while it enhances via larger rotational parameter. Temperature field significantly increases in the presence of both Brownian diffusion and thermophoresis parameters.

scholarly journals Diffusive Bejan number and second law of thermodynamics toward a new dimensionless formulation of fluid dynamics laws

2019 ◽  
Vol 23 (6 Part B) ◽  
pp. 4005-4022 ◽  
Author(s):  
Michele Trancossi ◽  
Jose Pascoa
Keyword(s):  
Fluid Dynamics ◽  
Entropy Generation ◽  
Fluid Dynamic ◽  
Second Law Of Thermodynamics ◽  
Integral Form ◽  
Second Law ◽  
Bejan Number ◽  
Definition Of ◽  
New Formulation ◽  
Dimensionless Formulation

In a recent paper, Liversage and Trancossi have defined a new formulation of drag as a function of the dimensionless Bejan and Reynolds numbers. Further analysis of this hypothesis has permitted to obtain a new dimensionless formulation of the fundamental equations of fluid dynamics in their integral form. The resulting equations have been deeply discussed for the thermodynamic definition of Bejan number evidencing that the proposed formulation allows solving fluid dynamic problems in terms of entropy generation, allowing an effective optimization of design in terms of the Second law of thermodynamics. Some samples are discussed evidencing how the new formulation can support the generation of an optimized configuration of fluidic devices and that the optimized configurations allow minimizing the entropy generation.

scholarly journals Assisting and Opposing Stagnation Point Pseudoplastic Nano Liquid Flow towards a Flexible Riga Sheet: A Computational Approach

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aysha Rehman ◽  
Azad Hussain ◽  
Sohail Nadeem
Keyword(s):  
Brownian Motion ◽  
Mixed Convection ◽  
Hartmann Number ◽  
Lewis Number ◽  
Weissenberg Number ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Diverse Range ◽  
Flow Equations ◽  
Buongiorno Model

Nanofluids are used as coolants in heat transport devices like heat exchangers, radiators, and electronic cooling systems (like a flat plate) because of their improved thermal properties. The preeminent perspective of this study is to highlight the influence of combined convection on heat transfer and pseudoplastic non-Newtonian nanofluid flow towards an extendable Riga surface. Buongiorno model is incorporated in the present study to tackle a diverse range of Reynolds numbers and to analyze the behavior of the pseudoplastic nanofluid flow. Nanofluid features are scrutinized through Brownian motion and thermophoresis diffusion. By the use of the boundary layer principle, the compact form of flow equations is transformed into component forms. The modeled system is numerically simulated. The effects of various physical parameters on skin friction, mass transfer, and thermal energy are numerically computed. Fluctuations of velocity increased when modified Hartmann number and mixed convection parameter are boosted, where it collapses for Weissenberg number and width parameter. It can be revealed that the temperature curve gets down if modified Hartmann number, mixed convection, and buoyancy ratio parameters upgrade. Concentration patterns diminish when there is an incline in width parameter and Lewis number; on the other hand, it went upward for Brownian motion parameter, modified Hartmann, and Prandtl number.

scholarly journals Regular perturbation solution of Couette flow (non-Newtonian) between two parallel porous plates: a numerical analysis with irreversibility

2020 ◽  
Vol 42 (1) ◽  
pp. 127-142
Author(s):  
M. Nazeer ◽  
M. I. Khan ◽  
S. Kadry ◽  
Yuming Chu ◽  
F. Ahmad ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Entropy Generation ◽  
Shear Thickening ◽  
Second Law Of Thermodynamics ◽  
Perturbation Solution ◽  
Bejan Number ◽  
Regular Perturbation ◽  
Thickening Behavior ◽  
Upper Lid ◽  
The Given

AbstractThe unavailability of wasted energy due to the irreversibility in the process is called the entropy generation. An irreversible process is a process in which the entropy of the system is increased. The second law of thermodynamics is used to define whether the given system is reversible or irreversible. Here, our focus is how to reduce the entropy of the system and maximize the capability of the system. There are many methods for maximizing the capacity of heat transport. The constant pressure gradient or motion of the wall can be used to increase the heat transfer rate and minimize the entropy. The objective of this study is to analyze the heat and mass transfer of an Eyring-Powell fluid in a porous channel. For this, we choose two different fluid models, namely, the plane and generalized Couette flows. The flow is generated in the channel due to a pressure gradient or with the moving of the upper lid. The present analysis shows the effects of the fluid parameters on the velocity, the temperature, the entropy generation, and the Bejan number. The nonlinear boundary value problem of the flow problem is solved with the help of the regular perturbation method. To validate the perturbation solution, a numerical solution is also obtained with the help of the built-in command NDSolve of MATHEMATICA 11.0. The velocity profile shows the shear thickening behavior via first-order Eyring-Powell parameters. It is also observed that the profile of the Bejan number has a decreasing trend against the Brinkman number. When ηi → 0 (i = 1, 2, 3), the Eyring-Powell fluid is transformed into a Newtonian fluid.

scholarly journals Characterization of Marangoni Forced Convection in Casson Nanoliquid Flow with Joule Heating and Irreversibility

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 433
Author(s):  
Muhammad Adil Sadiq ◽  
Tasawar Hayat
Keyword(s):  
Forced Convection ◽  
Entropy Generation ◽  
Joule Heating ◽  
Concentration Gradient ◽  
Marangoni Number ◽  
Casson Fluid ◽  
Bejan Number ◽  
Entropy Optimization ◽  
Highly Nonlinear ◽  
Nonlinear Pde’S

The Marangoni forced convective inclined magnetohydrodynamic flow is examined. Marangoni forced convection depends on the differences in surface pressure computed by magnetic field, temperature, and concentration gradient. Casson nanoliquid flow by an infinite disk is considered. Viscous dissipation, heat flux, and Joule heating are addressed in energy expressions. Thermophoresis and Brownian motion are also examined. Entropy generation is computed. The physical characteristics of entropy optimization with Arrhenius activation energy are discussed. Nonlinear PDE’s are reduced to highly nonlinear ordinary systems with appropriate transformations. A nonlinear system is numerically computed by the NDSolve technique. The salient characteristics of velocity, temperature, concentration, entropy generation, and Bejan number are explained. The computational results of the heat-transfer rate and concentration gradient are examined through tables. Velocity and temperature have reverse effects for the higher approximation of the Marangoni number. Velocity is a decreasing function of the Casson fluid parameter. Temperature is enhanced for higher radiation during reverse hold for concentration against the Marangoni number. The Bejan number and entropy generation have similar effects for Casson fluid and radiation parameters. For a higher estimation of the Brinkman number, the entropy optimization is augmented.

scholarly journals Thermal analysis of an Eyring-Powell fluid flow-through a constricted channel

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1207-1216 ◽  
Author(s):  
Sufian Munawar ◽  
Najma Saleem
Keyword(s):  
Entropy Generation ◽  
Perturbation Technique ◽  
Second Law Of Thermodynamics ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Regular Perturbation ◽  
Entropy Generation Number ◽  
Irregular Shapes ◽  
Flow Through ◽  
Constricted Channel

This paper is aimed to investigate the entropy generation in a MHD convective flow of Eyring-Powell fluid through a mildly constricted channel. The constriction is assumed to be of regular or irregular shape and is presented inside the channel wall. Mathematical model is developed using the basic laws of conservation of mass, momentum, and energy. The governing equations are normalized using appropriate set of dimensionless variables and solutions are obtained by regular perturbation technique. The solutions are further used to calculate the entropy expression associated with the Second law of thermodynamics. The heat transfer characteristics, like, temperature, isotherms, entropy generation number entropy lines and the Bejan number are analyzed for the variation in magnetic field, shape parameter, and material constants. It is observed that entropy production is maximum in the narrow part of the channel. Moreover, entropy generation rate is higher for the regular parabolic shape as compared to irregular shapes of constriction.

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