scholarly journals Generalization of the Convective Flow of Brinkman-Type Fluid Using Fourier’s and Fick’s Laws: Exact Solutions and Entropy Generation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah bin Sakidin
Keyword(s):  
Entropy Generation ◽  
Mass Concentration ◽  
Special Function ◽  
Time Parameter ◽  
Convection Flow ◽  
Bejan Number ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Fluid Parameter ◽  
The Given

A new scheme to formulating the Caputo time-fractional model for the flow of Brinkman-type fluid between the plates was introduced by using the generalized laws of Fourier and Fick. Within a channel, free convection flow of the electrically conducted Brinkman-type fluid was considered. A newly generated transformation was applied to the heat and mass concentration equations. The governing equations were solved by the techniques of Fourier sine and the Laplace transforms. In terms of the special function, namely, the Mittag-Leffler function, final solutions were obtained. The entropy generation and Bejan number are also calculated for the given flow. To explain the conceptual arguments of the embedded parameters, separate plots are represented in figures and are often quantitatively computed and presented in tables. It is worth noting that for increasing the values of the Brinkman-type fluid parameter, the velocity profile decreases. The regression analysis shows that the variation in the velocity for time parameter is statistically significant.

scholarly journals Entropy Generation and Natural Convection Flow of Hybrid Nanofluids in a Partially Divided Wavy Cavity Including Solid Blocks

Energies ◽  
2020 ◽  
Vol 13 (11) ◽  
pp. 2942 ◽  
Author(s):  
Ammar I. Alsabery ◽  
Ishak Hashim ◽  
Ahmad Hajjar ◽  
Mohammad Ghalambaz ◽  
Sohail Nadeem ◽  
...  
Keyword(s):  
Entropy Generation ◽  
Convection Flow ◽  
Hybrid Nanofluid ◽  
Bejan Number ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Wavy Cavity ◽  
Rayleigh Numbers

The present investigation addressed the entropy generation, fluid flow, and heat transfer regarding Cu-Al 2 O 3 -water hybrid nanofluids into a complex shape enclosure containing a hot-half partition were addressed. The sidewalls of the enclosure are made of wavy walls including cold isothermal temperature while the upper and lower surfaces remain insulated. The governing equations toward conservation of mass, momentum, and energy were introduced into the form of partial differential equations. The second law of thermodynamic was written for the friction and thermal entropy productions as a function of velocity and temperatures. The governing equations occurred molded into a non-dimensional pattern and explained through the finite element method. Outcomes were investigated for Cu-water, Al 2 O 3 -water, and Cu-Al 2 O 3 -water nanofluids to address the effect of using composite nanoparticles toward the flow and temperature patterns and entropy generation. Findings show that using hybrid nanofluid improves the Nusselt number compared to simple nanofluids. In the case of low Rayleigh numbers, such enhancement is more evident. Changing the geometrical aspects of the cavity induces different effects toward the entropy generation and Bejan number. Generally, the global entropy generation for Cu-Al 2 O 3 -water hybrid nanofluid takes places between the entropy generation values regarding Cu-water and Al 2 O 3 -water nanofluids.

The Effects of Radiation on Free Convection Flow with Ramped Wall Temperature in Brinkman Type Fluid

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Muhamad Najib Zakaria ◽  
Abid Hussanan ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Nusselt Number ◽  
Free Convection ◽  
Laplace Transform ◽  
Vertical Plate ◽  
Convection Flow ◽  
Physical Parameters ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Laplace Transform Technique ◽  
Effects Of Radiation

The present paper is on study of the influence of radiation on unsteady free convection flow of Brinkman type fluid near a vertical plate containing a ramped temperature profile. Using the appropriate variables, the basic governing equations are reduced to nondimensional equations valid with the imposed initial and boundary conditions. The exact solutions are obtained by using Laplace transform technique. The influence of radiation near a ramped temperature plate is also compared with the flow near a plate with constant temperature. The numerical computations are carried out for various values of the physical parameters such as velocity, temperature, skin friction and Nusselt number and presented graphically.

MHD Flow of Cu-Al2O3/Water Hybrid Nanofluid in Porous Channel: Analysis of Entropy Generation

2017 ◽  
Vol 377 ◽  
pp. 42-61 ◽  
Author(s):  
Sanatan Das ◽  
Rabindra Nath Jana ◽  
Oluwole Daniel Makinde
Keyword(s):  
Entropy Generation ◽  
Mhd Flow ◽  
Transverse Magnetic ◽  
Porous Channel ◽  
Hybrid Nanofluid ◽  
Bejan Number ◽  
Governing Equations ◽  
Transfer Enhancement ◽  
Entropy Generation Number ◽  
Channel Analysis

In this investigation, a magnetohydrodynamic (MHD) flow of AlO /water nanofluid and Cu-AlO /water hybrid nanofluid through a porous channel is analyzed in the presence of a transverse magnetic field. An exact solution of the governing equations has been obtained in closed form. The entropy generation number and the Bejan number are also obtained. The influences of each of the governing parameters on velocity, temperature, entropy generation and Bejan number are displayed graphically and the physical aspects are discussed. In addition, a comparison of the heat transfer enhancement level due to the suspension of AlO and Cu nanoparticles in water as regular nanofluids and as hybrid Cu-AlO /water nanofluid is reported.

scholarly journals Numerical Investigation of Entropy Generation in Unsteady MHD Generalized Couette Flow with Variable Electrical Conductivity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
T. Chinyoka ◽  
O. D. Makinde
Keyword(s):  
Electrical Conductivity ◽  
Couette Flow ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Bejan Number ◽  
Governing Equations ◽  
Entropy Generation Number ◽  
Thermophysical Parameters ◽  
Second Law Analysis ◽  
Finite Difference Techniques

The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively.

scholarly journals Numerical investigation of entropy generation in laminar forced convection flow over inclined backward and forward facing steps in a duct under bleeding condition

2014 ◽  
Vol 18 (2) ◽  
pp. 479-492 ◽  
Author(s):  
Meysam Atashafrooz ◽  
Nassab Gandjalikhan ◽  
Babak Ansari
Keyword(s):  
Numerical Investigation ◽  
Forced Convection ◽  
Entropy Generation ◽  
Fluid Dynamic ◽  
Numerical Results ◽  
Convection Flow ◽  
Bejan Number ◽  
Entropy Generation Number ◽  
Forced Convection Flow ◽  
Laminar Forced Convection

A numerical investigation of entropy generation in laminar forced convection of gas flow over a recess including two inclined backward and forward facing steps in a horizontal duct under bleeding condition is presented. For calculation of entropy generation from the second law of thermodynamics in a forced convection flow, the velocity and temperature distributions are primary needed. For this purpose, the two-dimensional Cartesian coordinate system is used to solve the governing equations which are conservations of mass, momentum and energy. These equations are solved numerically using the computational fluid dynamic techniques to obtain the temperature and velocity fields, while the blocked region method is employed to simulate the inclined surface. Discretized forms of these equations are obtained by the finite volume method and solved using the SIMPLE algorithm. The numerical results are presented graphically and the effects of bleeding coefficient and recess length as the main parameters on the distributions of entropy generation number and Bejan number are investigated. Also, the effect of Reynolds number and bleeding coefficient on total entropy generation which shows the amount of flow irreversibilities is presented for two recess length. The use of present results in the design process of such thermal system would help the system attain the high performance during exploitation. Comparison of numerical results with the available data published in open literature shows a good consistency.

scholarly journals Viscous Dissipation and Dufour Effects on MHD Free Convection Flow Through an Oscillatory Inclined Porous Plate with Hall and Ion-Slip Current

2018 ◽  
Vol 7 (4.5) ◽  
pp. 410 ◽  
Author(s):  
K. V. B. Raja kumar ◽  
K. S. Balamurugan ◽  
Ch. V. Ramana Murthy ◽  
N. Ranganath
Keyword(s):  
Viscous Dissipation ◽  
Porous Plate ◽  
Convection Flow ◽  
Governing Equations ◽  
Inclined Plate ◽  
Regular Perturbation ◽  
Rotating System ◽  
Free Convection Flow ◽  
Ion Slip ◽  
Flow Through

In this paper the viscous dissipation and Dufour effects on Unsteady MHD free convective flow through a semi-infinite Oscillatory porous inclined plate of time dependent permeability with Chemical reaction and Hall and Ion-Slip Current in a Rotating System was investigated. The dimensionless governing equations for this investigation are solved analytically by using multiple regular perturbation law. The effects of different parameters on velocity, temperature and concentration fields are shown graphically.  

scholarly journals Porosity effect on unsteady MHD free convection flow of Jeffrey fluid past an oscillating vertical plate with ramped wall temperature

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Nor Athirah Mohd Zin ◽  
Ahmad Qushairi Mohamad ◽  
Ilyas Khan ◽  
Sharidan Shafie
Keyword(s):  
Free Convection ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Convection Flow ◽  
Jeffrey Fluid ◽  
Dimensionless Time ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Permeability Parameter ◽  
The Impact

The unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid embedded in porous medium past an oscillating vertical plate generated by thermal radiation with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under the action of transverse magnetic field towards the flow. Constitutive relation of Jeffrey fluid is employed to model the governing equations in terms of partial differential equations with some physical conditions. The transformed dimensionless governing equations are solved analytically using Laplace transform technique. The impact of various pertinent parameters namely material parameter of Jeffrey fluid , dimensionless parameter of Jeffrey fluid , phase angle , Hartmann number , permeability parameter , Grashof number , Prandtl number , radiation parameter  and dimensionless time  on velocity and temperature distributions are presented graphically and discussed in details. It is observed that, the permeability parameter tend to retard the fluid velocity for ramped wall temperature but enhance the velocity for an isothermal plate. Besides that, this study shows, the amplitude of velocity and temperature fields for ramped wall temperature are always lower than isothermal plate. A comparison with the existing published work is also provided to confirm the validity of the present results and an excellent agreement are found. 

scholarly journals Free Convection MHD Flow with Thermal Radiation from an Impulsively-Started Vertical Plate

2009 ◽  
Vol 14 (1) ◽  
pp. 73-84 ◽  
Author(s):  
G. Palani ◽  
I. A. Abbas
Keyword(s):  
Free Convection ◽  
Vertical Plate ◽  
Mhd Flow ◽  
Convection Flow ◽  
Combined Effects ◽  
The Finite Element Method ◽  
Scattering Medium ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Convection Regime

This paper investigates the combined effects of magnetohydrodynamics and radiation on free convection flow past an impulsively started isothermal vertical plate with Rosseland diffusion approximation. The fluid considered is a gray, absorbingemitting radiation but a non-scattering medium, with approximate transformations the boundary layer governing the flow are reduced to non-dimensional equations valid in the free convection regime. The dimensionless governing equations are solved by the finite element method.

scholarly journals Unsteady free convective heat transfer in third-grade fluid flow from an isothermal vertical plate: A thermodynamic analysis

2019 ◽  
Vol 33 (08) ◽  
pp. 1950060
Author(s):  
Ashwini Hiremath ◽  
G. Janardhana Reddy ◽  
Mahesh Kumar ◽  
O. Anwar Bég
Keyword(s):  
Heat Transfer ◽  
Entropy Generation ◽  
Vertical Plate ◽  
Third Grade ◽  
Dimensionless Temperature ◽  
Convection Flow ◽  
Bejan Number ◽  
Third Grade Fluid ◽  
Grade Fluid ◽  
Grade Parameter

The current study investigates theoretically and numerically the entropy generation in time-dependent free-convective third-grade viscoelastic fluid convection flow from a vertical plate. The nondimensional conservation equations for mass, momentum and energy are solved using a Crank–Nicolson finite difference method with suitable boundary conditions. Expressions for known values of flow-variables coefficients are also derived for the wall heat transfer and skin friction and numerically evaluated. The effect of Grashof number, Prandtl number, group parameter (product of dimensionless temperature difference and Brinkman number) and third-grade parameter on entropy heat generation is analyzed and shown graphically. Bejan line distributions are also presented for the influence of several control parameters. The computations reveal that with increasing third-grade parameter, the entropy generation decreases and Bejan number increases. Also, the comparison graph shows that contour lines for third-grade fluid vary considerably from the Newtonian fluid. The study is relevant to non-Newtonian thermal materials processing systems.

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.

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