The Overlapping Grid Spectral Collocation Method for Solving Entropy Generation in Casson Nanofluid Flow Past a Stretching Plate

2021 ◽  
Vol 10 (1) ◽  
pp. 45-57
Author(s):  
Zack M. Mburu ◽  
Sabyasachi Mondal ◽  
Precious Sibanda ◽  
Ram Prakash Sharma
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Thermal Radiation ◽  
Collocation Method ◽  
Entropy Generation ◽  
Applied Magnetic Field ◽  
Spectral Collocation Method ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Spectral Collocation

The current study investigates the intrinsic irreversibility phenomenon of a mixed convection and electrically conducting couple stress Casson fluid motion over a thermally stretching sheet. We have considered the combined effect of applied magnetic field, Brownian motion, thermal radiation, permeability, Casson parameter, and the stretching parameter on the entropy generation rate of the model. The first and second laws of thermodynamics have been applied to examine the flow problem. The obtained dimensionless structure of highly nonlinear ordinary differential equations is then solved numerically applying the overlapping grid spectral collocation method. This method has high accuracy and converges fast. The approximate solutions for velocity, temperature and concentration are used to evaluate the rate of entropy generation and some physical parameters of the flow. For engineering interest, we have obtained tabular results for the skin friction coefficient, Nusselt number, and the Sherwood number for pertinent parameters. We found that entropy generation rate is minimized when there is an increase in the applied magnetic field, thermophoresis parameter, Casson parameter, Brownian motion, and the energy variance parameter. Further, the entropy generation rate is increased by enhancing the stretching parameter, permeability parameter, the Biot number, and thermal radiation parameter.

Thermodynamics Analysis of Unsteady MHD Mixed Convection with Slip and Thermal Radiation over a Permeable Surface

2017 ◽  
Vol 374 ◽  
pp. 29-46 ◽  
Author(s):  
Ahmad Muhammad ◽  
Oluwole Daniel Makinde
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Local Similarity

This paper discusses the thermodynamics irreversibility in an unsteady hydromagnetic mixed convective flow of an electrically conducting optically dense fluid over a permeable vertical surface under the combined influence of thermal radiation, velocity slip, temperature jump, buoyancy force, viscous dissipation, Joule heating and magnetic field. The governing partial differential equations are reduced to ordinary differential equations by using similarity variable. A local similarity solution is obtained numerically using shooting technique coupled with Runge-Kutta Fehlberg integration method. The influence of various thermophysical parameters on velocity and temperature profiles, skin friction, Nusselt number, entropy generation rate and Bejan number are presented graphically and discussed quantitatively. It is found that velocity slip, surface injection and temperature jump can successfully reduce entropy generation rate in the presence of an applied magnetic field. A comparison of numerical solution is made with the exact solution under a special case scenario and excellent agreement is found.

Entropy generation of nanofluid flow and heat transfer driven through a paralleled microchannel

2019 ◽  
Vol 97 (6) ◽  
pp. 678-691 ◽  
Author(s):  
Hang Xu ◽  
Ammarah Raees ◽  
Xiao-Hang Xu
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Current Model ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Buongiorno’S Model ◽  
Flow Models ◽  
Flow And Heat Transfer

In this paper, a fully-developed, immiscible nanofluid flow in a paralleled microchannel in the presence of a magnetic field is investigated. Buongiorno’s model is applied to describe the behaviors of the nanofluid flow. Different from most previous studies on microchannel flow, here the pressure term is considered as unknown, which makes the current model compatible with the commonly accepted channel flow models. The influences of various physical parameters on important physical quantities are given. The entropy generation analysis is performed. Variations of local and global entropy generations with the magnetic field parameter, the electric field, and the viscous dissipation parameter under various ratios of the thermophoresis parameter to the Brownian motion parameter are illustrated. The results indicate that the entropy generation rate strongly depends on the thermophoresis and the Brownian motion parameters. Their increase enhances the total irreversibility of entropy generation.

Entropy generation and thermo-diffusion effects on unsteady chemically reactive slip flow between two rotating disks

2019 ◽  
Vol 29 (10) ◽  
pp. 3795-3821
Author(s):  
Sumaira Qayyum ◽  
Muhammad Ijaz Khan ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi
Keyword(s):  
Magnetic Field ◽  
Entropy Generation ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Thermal Equation ◽  
Content Type ◽  
Flow Variables

Purpose The purpose of this study is to analyze the Entropy generation analysis and heat transport in three-dimensional flow between two stretchable disks. Joule heating and heat generation/absorption are incorporated in the thermal equation. Thermo-diffusion effect is also considered. Flow is conducting for time-dependent applied magnetic field. Induced magnetic field is not taken into consideration. Velocity and thermal slip conditions at both the disks are implemented. The flow problem is modeled by using Navier–Stokes equations with entropy generation rate and Bejan number. Design/methodology/approach Von Karman transformations are used to reduce the nonlinear governing expressions into an ordinary one and then tackled by homotopy analysis method for convergent series solutions. The nonlinear expressions for total entropy generation rate are obtained with appropriate transformations. The impacts of different flow variables on velocity, temperature, entropy generation rate and Bejan number are described graphically. Velocity, temperature and concentration gradients are discussed in the presence of flow variables. Findings Axial, radial and tangential velocity profiles show decreasing trend for larger values of velocity slip parameters. For a larger Brinkman number, the entropy generation increases, while a decreasing trend is noticed for Bejan number. Originality/value To the best of the authors’ knowledge, no such analyses have been reported in the literature.

scholarly journals Entropy Generation in MHD Eyring–Powell Fluid Flow over an Unsteady Oscillatory Porous Stretching Surface under the Impact of Thermal Radiation and Heat Source/Sink

2018 ◽  
Vol 8 (12) ◽  
pp. 2588 ◽  
Author(s):  
Sayer Alharbi ◽  
Abdullah Dawar ◽  
Zahir Shah ◽  
Waris Khan ◽  
Muhammad Idrees ◽  
...  
Keyword(s):  
Heat Source ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Stretching Sheet ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Temperature Function ◽  
Source Sink ◽  
The Impact

In this article, we have briefly examined the entropy generation in magnetohydrodynamic (MHD) Eyring–Powell fluid over an unsteady oscillating porous stretching sheet. The impact of thermal radiation and heat source/sink are taken in this investigation. The impact of embedded parameters on velocity function, temperature function, entropy generation rate, and Bejan number are deliberated through graphs, and discussed as well. By studying the entropy generation in magnetohydrodynamic Eyring–Powell fluid over an unsteady oscillating porous stretching sheet, the entropy generation rate is reduced with escalation in porosity, thermal radiation, and magnetic parameters, while increased with the escalation in Reynolds number. Also, the Bejan number is increased with the escalation in porosity and magnetic parameter, while increased with the escalation in thermal radiation parameter. The impact of skin fraction coefficient and local Nusselt number are discussed through tables. The partial differential equations are converted to ordinary differential equation with the help of similarity variables. The homotopy analysis method (HAM) is used for the solution of the problem. The results of this investigation agree, satisfactorily, with past studies.

Entropy analysis of Poiseuille nanofluid flow in a porous channel with slip and convective boundary conditions under magnetic field

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
S. Das ◽  
S. Chakraborty ◽  
R. N. Jana
Keyword(s):  
Magnetic Field ◽  
Entropy Generation ◽  
Poiseuille Flow ◽  
Magnetic Parameter ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Convective Heating ◽  
Bejan Number ◽  
Content Type ◽  
Hydrodynamic Slip

Purpose This study aims to expose the flow phenomena and entropy generation during a; magnetohydrodynamic (MHD) Poiseuille flow of water-based nanofluids (NFs) in a porous channel subject to hydrodynamic slip and convective heating boundary conditions. The flow caused by the uniform pressure; gradient between infinite parallel plates is considered steady and fully developed. The nanoparticles; namely, copper, alumina and titanium oxide are taken with pure water as the base fluid. Viscous dissipation and Joule heating impacts are also incorporated in this investigation. Design/methodology/approach The reduced governing equations are solved analytically in closed form. The physical insights of noteworthy parameters on the important flow quantities are demonstrated through graphs and analyzed elaborately. The thermodynamic analysis is performed by calculating entropy generation; rate and Bejan number. A graphical comparison between solutions corresponding to NFs and regular fluid in the channel is also provided. Findings The analysis of the results divulges that entropy generation minimization can be achieved by an appropriate combination of the geometrical and physical parameters of thermomechanical systems. It is reported that ascent in magnetic parameter number declines the velocity profiles, while the inverse pattern is witnessed with augmentation in hydrodynamic slip parameters. The temperature dissemination declines with the growth of Biot numbers. It is perceived that the entropy generation rate lessens with an upgrade in magnetic parameter, whereas the reverse trend of Bejan number is perceived with expansion in magnetic parameter and Biot number. The important contribution of the result is that the entropy generation rate is controlled with an appropriate composition of thermo-physical parameter values. Moreover, in the presence of a magnetic field and suction/injection at the channel walls, the shear stresses at the channel walls are reduced about two times. Practical implications In various industrial applications, minimizing entropy generation plays a significant role. Miniaturization of entropy is the utilization of the energy of thermal devices such as micro heat exchangers, micromixers, micropumps and cooling microelectromechanical devices. Originality/value An attentive review of the literature discloses that quite a few studies have been conducted on entropy generation analysis of a fully developed MHD Poiseuille flow of NFs through a permeable channel subject to the velocity slip and convective heating conditions at the walls.

Entropy Analysis of a Radiating Variable Viscosity EG/Ag Nanofluid Flow in Microchannels with Buoyancy Force and Convective Cooling

2018 ◽  
Vol 387 ◽  
pp. 273-285 ◽  
Author(s):  
R.L. Monaledi ◽  
Oluwole Daniel Makinde
Keyword(s):  
Thermal Stability ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Buoyancy Force ◽  
Volume Fraction ◽  
Flow System ◽  
Variable Viscosity ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Convective Cooling

The inherent irreversibility of a variable viscosity ethylene glycol/silver (EG/Ag) nanofluid single-phase Poiseuille flow in a vertical microchannel with convective cooling under the combined influence of buoyancy force, nonlinear thermal radiation, nanoparticles shape and volume fraction is investigated. The nonlinear model equations are obtained and numerically solved via shooting method with Runge-Kutta-Fehlberg integration scheme. Pertinent results with respect to the effects of emerging thermophysical parameters on the nanofluid velocity, temperature, skin friction, Nusselt number, thermal stability criteria, entropy generation rate and Bejan number are presented graphically and discussed. It is observed that thermal radiation, Biot number and buoyancy force boost the release of heat energy thereby cooling the flow system. Meanwhile, an increase in nanoparticles volume fraction lessens the entropy generation rate which augment the exergetic effectiveness and thermal stability of the flow system.

scholarly journals Analysis of entropy generation with heat generation in time dependent hydromagnetic flow of nanofluid in an oscillatory  semi- porous curved channel

2021 ◽  
Author(s):  
Muhammad Imran ◽  
Zaheer Abbas ◽  
Muhammad Naveed
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Brownian Motion ◽  
Entropy Generation ◽  
Heat Production ◽  
Time Dependent ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Radius Of Curvature ◽  
Curved Channel

The present study focusses on the investigation of thermodynamic optimization of hydromagnetic time dependent boundary layer nanofluid flow by employing entropy generation method (EMG) in semi- permeable oscillatory curved channel. We used Buongiorno model for nanofluid to address the impact of the parameters of Brownian motion and thermophoresis. The consequences of heat production are also taken into consideration in energy the equation. The mathematical form of boundary layer equations is accomplished by following the curvilinear coordinates scheme for the considered flow problem. The analytical convergent solution of the determined nonlinear PDEs is achieved through the process of homotopy analysis (HAM). A detailed analysis is conducted out to analyze the consequences of dissimilar variables concerned, such as non-dimensional radius of curvature, Lewis number, magnetic parameter, relation of wall oscillation frequency to its parameter of velocity, Reynolds number, Prandtl number, heat production and thermophoresis parameters, entropy generation rate, Brownian motion parameter and Brickman number, concentration and temperature difference parameters on temperature, velocity profile, concentration, pressure, drag surface force, Bejan number, entropy generation, rate of mass and heat transport are addressed in detail via tables and graphs. It is noted that, the magnitude of heat transmission rate (local Nusselt number) steadily decays for advanced values of radius of curvature variable and Reynolds number.

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