Research

18 pages, 2774 KiB

Open AccessArticle

Darcy–Forchheimer MHD Couple Stress 3D Nanofluid over an Exponentially Stretching Sheet through Cattaneo–Christov Convective Heat Flux with Zero Nanoparticles Mass Flux Conditions

by Muhammad Wakeel Ahmad, Poom Kumam, Zahir Shah, Ali Ahmad Farooq, Rashid Nawaz, Abdullah Dawar, Saeed Islam and Phatiphat Thounthong

Entropy 2019, 21(9), 867; https://doi.org/10.3390/e21090867 - 06 Sep 2019

Cited by 31 | Viewed by 3603

Abstract

In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the [...] Read more.

In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in x- and y-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the y-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

21 pages, 5016 KiB

Open AccessArticle

Hall and Ion-Slip Effect on CNTS Nanofluid over a Porous Extending Surface through Heat Generation and Absorption

by Ibni Ameen, Zahir Shah, Saeed Islam, Saleem Nasir, Waris Khan, Poom Kumam and Phatiphat Thounthong

Entropy 2019, 21(8), 801; https://doi.org/10.3390/e21080801 - 16 Aug 2019

Cited by 25 | Viewed by 3962

Abstract

In this research work, a 3D rotating flow of carbon nanotubes (CNTs) over a porous stretchable sheet for heat and mass transfer is investigated. Kerosene oil is considered as a base liquid and two types of CNTs, (Single & Multi) WCNTs are added [...] Read more.

In this research work, a 3D rotating flow of carbon nanotubes (CNTs) over a porous stretchable sheet for heat and mass transfer is investigated. Kerosene oil is considered as a base liquid and two types of CNTs, (Single & Multi) WCNTs are added as the additives to the base liquid. The present analysis further comprises the combined effect of the Hall, ion-slip, and thermal radiation, along with heat generation/absorption. The appropriate ordinary differential system of equations after applying appropriate transformation is calculated. The resulting nonlinear system of equations (conservation of mass, momentum, temperature) is explained by HAM (Homotopy Analysis Method). Solution of velocities and thermal fields are obtained and discussed graphically. Expression of

C_{f}

and

N u

are intended for both type of nanoliquids. The influences of prominent physical factors are plotted for velocities and thermal profiles using Methematica. These graphical results are qualitatively in excellent agreement with the previous published results. Also, single wall nanoparticles are found to have higher temperatures than multi wall CNTs nanoparticles. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

17 pages, 2920 KiB

Open AccessArticle

Entropy Generation Optimization in Squeezing Magnetohydrodynamics Flow of Casson Nanofluid with Viscous Dissipation and Joule Heating Effect

by Muhammad Zubair, Zahir Shah, Abdullah Dawar, Saeed Islam, Poom Kumam and Aurangzeb Khan

Entropy 2019, 21(8), 747; https://doi.org/10.3390/e21080747 - 30 Jul 2019

Cited by 25 | Viewed by 3999

Abstract

In this research article, the investigation of the three-dimensional Casson nanofluid flow in two rotating parallel plates has been presented. The nanofluid has been considered in steady state. The rotating plates have been considered porous. The heat equation is considered to study the [...] Read more.

In this research article, the investigation of the three-dimensional Casson nanofluid flow in two rotating parallel plates has been presented. The nanofluid has been considered in steady state. The rotating plates have been considered porous. The heat equation is considered to study the magnetic field, joule heating, and viscous dissipation impacts. The nonlinear ordinary system of equations has been solved analytically and numerically. For skin friction and Nusslt number, numerical results are tabulated. It is found that velocity declines for higher values of magnetic and porosity parameter while it is heightened through squeezing parameter. Temperature is an enhancing function for Eckert number and nanoparticles volume fraction. Entropy generation is augmented with radiation parameter, Prandtl, and Eckert numbers. The Casson, porosity, magnetic field, and rotation parameters were reduced while the squeezing and suction parameters increased the velocity profile along x-direction. The porosity parameter increased the Bejan number while the Eckert and Prandtl numbers decreased the Bejan number. Skin friction was enhanced with increasing the Casson, porosity, and magnetic parameters while it decreased with enhancing rotation and squeezing parameters. All these impacts have been shown via graphs. The influences by fluid flow parameters over skin friction and Nusselt number are accessible through tables. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

21 pages, 1455 KiB

Open AccessArticle

Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method

by Hassan Khan, Rasool Shah, Poom Kumam and Muhammad Arif

Entropy 2019, 21(6), 597; https://doi.org/10.3390/e21060597 - 16 Jun 2019

Cited by 50 | Viewed by 4376

Abstract

In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure [...] Read more.

In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

15 pages, 4421 KiB

Open AccessArticle

Entropy Generation via Ohmic Heating and Hall Current in Peristaltically-Flowing Carreau Fluid

by Saima Noreen, Asif Abbas and Abid Hussanan

Entropy 2019, 21(5), 529; https://doi.org/10.3390/e21050529 - 24 May 2019

Cited by 5 | Viewed by 3784

Abstract

The core objective of the present study is to examine entropy generation minimization via Hall current and Ohmic heating. Carreau fluid considerations interpret the unavailability of systems’ thermal energy (for mechanical work). The magneto hydrodynamic flow is in the channel, which is not [...] Read more.

The core objective of the present study is to examine entropy generation minimization via Hall current and Ohmic heating. Carreau fluid considerations interpret the unavailability of systems’ thermal energy (for mechanical work). The magneto hydrodynamic flow is in the channel, which is not symmetric. We have solved analytically the resulting nonlinear mathematical model. Moreover, physical exploration of important parameters on total entropy generation, temperature, and Bejan number is plotted and discussed. We observed that the generation of entropy takes place throughout the confined flow field y = W₁ and y = W₂ because of the viscous dissipation effect. In addition, reducing the operating temperature minimizes the entropy. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

20 pages, 6749 KiB

Open AccessArticle

Entropy Generation and Heat Transfer Analysis in MHD Unsteady Rotating Flow for Aqueous Suspensions of Carbon Nanotubes with Nonlinear Thermal Radiation and Viscous Dissipation Effect

by Muhammad Jawad, Zahir Shah, Aurungzeb Khan, Waris Khan, Poom Kumam and Saeed Islam

Entropy 2019, 21(5), 492; https://doi.org/10.3390/e21050492 - 13 May 2019

Cited by 30 | Viewed by 4793

Abstract

The impact of nonlinear thermal radiations rotating with the augmentation of heat transfer flow of time-dependent single-walled carbon nanotubes is investigated. Nanofluid flow is induced by a shrinking sheet within the rotating system. The impact of viscous dissipation is taken into account. Nanofluid [...] Read more.

The impact of nonlinear thermal radiations rotating with the augmentation of heat transfer flow of time-dependent single-walled carbon nanotubes is investigated. Nanofluid flow is induced by a shrinking sheet within the rotating system. The impact of viscous dissipation is taken into account. Nanofluid flow is assumed to be electrically conducting. Similarity transformations are applied to transform PDEs (partial differential equations) into ODEs (ordinary differential equations). Transformed equations are solved by the homotopy analysis method (HAM). The radiative source term is involved in the energy equation. For entropy generation, the second law of thermodynamics is applied. The Bejan number represents the current investigation of non-dimensional entropy generation due to heat transfer and fluid friction. The results obtained indicate that the thickness of the boundary layer decreases for greater values of the rotation parameter. Moreover, the unsteadiness parameter decreases the temperature profile and increases the velocity field. Skin friction and the Nusselt number are also physically and numerically analyzed. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

25 pages, 5900 KiB

Open AccessArticle

Second Law Analysis of Unsteady MHD Viscous Flow over a Horizontal Stretching Sheet Heated Non-Uniformly in the Presence of Ohmic Heating: Utilization of Gear-Generalized Differential Quadrature Method

by Muhammad Qasim, Muhammad Idrees Afridi, Abderrahim Wakif, T. Nguyen Thoi and Abid Hussanan

Entropy 2019, 21(3), 240; https://doi.org/10.3390/e21030240 - 02 Mar 2019

Cited by 30 | Viewed by 3575

Abstract

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport [...] Read more.

In this article, the entropy generation characteristics of a laminar unsteady MHD boundary layer flow are analysed numerically for an incompressible, electrically conducting and dissipative fluid. The Ohmic heating and energy dissipation effects are added to the energy equation. The modelled dimensional transport equations are altered into dimensionless self-similar partial differential equations (PDEs) through suitable transformations. The reduced momentum and energy equations are then worked out numerically by employing a new hybrid method called the Gear-Generalized Differential Quadrature Method (GGDQM). The obtained numerical results are incorporated in the calculation of the Bejan number and dimensionless entropy generation. Quantities of physical interest, like velocity, temperature, shear stress and heat transfer rate, are illustrated graphically as well as in tabular form. Impacts of involved parameters are examined and discussed thoroughly in this investigation. Exact and GGDQM solutions are compared for special cases of initial unsteady flow and final steady state flow. Furthermore, a good harmony is observed between the results of GGDQM and those given previously by the Spectral Relaxation Method (SRM), Spectral Quasilinearization Method (SQLM) and Spectral Perturbation Method (SPM). Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

15 pages, 6903 KiB

Open AccessFeature PaperArticle

Natural Convection and Irreversibility Evaluation in a Cubic Cavity with Partial Opening in Both Top and Bottom Sides

by Hakan F. Oztop, Mohammed A. Almeshaal, Lioua Kolsi, Mohammed Mehdi Rashidi and Mohamed E. Ali

Entropy 2019, 21(2), 116; https://doi.org/10.3390/e21020116 - 27 Jan 2019

Cited by 17 | Viewed by 4192

Abstract

A numerical study on natural convection in a cubical cavity with partial top and bottom openings is performed in this paper. One of the vertical walls of the cavity has higher temperature than that of the opposite one; the remaining walls are insulated [...] Read more.

A numerical study on natural convection in a cubical cavity with partial top and bottom openings is performed in this paper. One of the vertical walls of the cavity has higher temperature than that of the opposite one; the remaining walls are insulated perfectly. Three-dimensional simulations of governing equations have been performed using a finite volume technique. The results are presented for different parameters such as opening length and Rayleigh number. It is observed that heat transfer rate and fluid flow can be controlled via opening ratio size and Rayleigh number. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

15 pages, 369 KiB

Open AccessArticle

Doubly Nonnegative and Semidefinite Relaxations for the Densest k-Subgraph Problem

by Chuan-Hao Guo, Yuan Guo and Bei-Bei Liu

Entropy 2019, 21(2), 108; https://doi.org/10.3390/e21020108 - 24 Jan 2019

Viewed by 2259

Abstract

The densest k-subgraph (DkS) maximization problem is to find a set of k vertices with maximum total weight of edges in the subgraph induced by this set. This problem is in general NP-hard. In this paper, two relaxation methods for solving the [...] Read more.

The densest k-subgraph (DkS) maximization problem is to find a set of k vertices with maximum total weight of edges in the subgraph induced by this set. This problem is in general NP-hard. In this paper, two relaxation methods for solving the DkS problem are presented. One is doubly nonnegative relaxation, and the other is semidefinite relaxation with tighter relaxation compare with the relaxation of standard semidefinite. The two relaxation problems are equivalent under the suitable conditions. Moreover, the corresponding approximation ratios’ results are given for these relaxation problems. Finally, some numerical examples are tested to show the comparison of these relaxation problems, and the numerical results show that the doubly nonnegative relaxation is more promising than the semidefinite relaxation for solving some DkS problems. Full article

(This article belongs to the Special Issue Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Challenges and Progresses in the Modelling of Entropy Generation in Fluid Mechanics, Heat Transfer and Porous Media

Share This Special Issue

Special Issue Editors

Special Issue Information

Keywords

Published Papers (9 papers)

Research

Further Information

Guidelines

MDPI Initiatives

Follow MDPI