scholarly journals Entropy Generation in Cu-Al2O3-H2O Hybrid Nanofluid Flow over a Curved Surface with Thermal Dissipation

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 941 ◽  
Author(s):  
Muhammad Idrees Afridi ◽  
Tawfeeq Abdullah Alkanhal ◽  
Muhammad Qasim ◽  
Iskander Tlili
Keyword(s):  
Differential Equations ◽  
Entropy Generation ◽  
Numerical Results ◽  
Curvilinear Coordinates ◽  
Curved Surface ◽  
Thermal Dissipation ◽  
Solid Boundary ◽  
Radius Of Curvature ◽  
Physical Parameters ◽  
Hybrid Nanofluid

Heat transfer and entropy generation in a hybrid nanoliquid flow caused by an elastic curved surface is investigated in the present article. To examine the effects of frictional heating on entropy generation, the energy dissipation function is included in the energy equation. The Tiwari and Dass model for nanofluid is used by taking water as a base fluid. A new class of nanofluid (hybrid nanofluid) with two kinds of nanoparticles, Copper (Cu) and Aluminum oxide (Al2O3), is considered. Curvilinear coordinates are used in the mathematical formulation due to the curved nature of the solid boundary. By utilizing similarity transformations, the modelled partial differential equations are converted into ordinary differential equations. Shooting and the Runge-Kutta-Fehlberg method (FRKM) have been used to solve the transformed set of non-linear differential equations. The expression for entropy generation is derived in curvilinear coordinates and computed by using the numerical results obtained from dimensionless momentum and energy equations. Comparisons of our numerical results and those published in the previous literature demonstrate excellent agreements, validating our numerical simulation. In addition, we have also conducted parametric studies and find that entropy generation and temperature suppress with increasing values of dimensionless radius of curvature. Furthermore, it is found that less entropy is generated in regular nanofluid as compare to hybrid nanofluid. To examine the influences of a set of embedding physical parameters on quantities of interest, different graphs are plotted and discussed.

scholarly journals Irreversibility Analysis of Hybrid Nanofluid Flow over a Thin Needle with Effects of Energy Dissipation

Symmetry ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 663 ◽  
Author(s):  
Muhammad Idrees Afridi ◽  
I. Tlili ◽  
Marjan Goodarzi ◽  
M. Osman ◽  
Najeeb Alam Khan
Keyword(s):  
Entropy Generation ◽  
Numerical Solutions ◽  
Free Stream ◽  
Thermal Dissipation ◽  
Heat Transfer Analysis ◽  
Stream Velocity ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The flow and heat transfer analysis in the conventional nanofluid A l 2 O 3 − H 2 O and hybrid nanofluid C u − A l 2 O 3 − H 2 O was carried out in the present study. The present work also focused on the comparative analysis of entropy generation in conventional and hybrid nanofluid flow. The flows of both types of nanofluid were assumed to be over a thin needle in the presence of thermal dissipation. The temperature at the surface of the thin needle and the fluid in the free stream region were supposed to be constant. Modified Maxwell Garnet (MMG) and the Brinkman model were utilized for effective thermal conductivity and dynamic viscosity. The numerical solutions of the self-similar equations were obtained by using the Runge-Kutta Fehlberg scheme (RKFS). The Matlab in-built solver bvp4c was also used to solve the nonlinear dimensionless system of differential equations. The present numerical results were compared to the existing limiting outcomes in the literature and were found to be in excellent agreement. The analysis demonstrated that the rate of entropy generation reduced with the decreasing velocity of the thin needle as compared to the free stream velocity. The hybrid nanofluid flow with less velocity was compared to the regular nanofluid under the same circumstances. Furthermore, the enhancement in the temperature profile of the hybrid nanofluid was high as compared to the regular nanofluid. The influences of relevant physical parameters on flow, temperature distribution, and entropy generation are depicted graphically and discussed herein.

MHD and nonlinear thermal radiation effects on hybrid nanofluid past a wedge with heat source and entropy generation

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Fazle Mabood ◽  
Anum Shafiq ◽  
Waqar Ahmed Khan ◽  
Irfan Anjum Badruddin
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Thermal Radiation ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Design Parameters ◽  
Hybrid Nanofluid ◽  
Nonlinear Thermal Radiation ◽  
Content Type

Purpose This study aims to investigate the irreversibility associated with the Fe3O4–Co/kerosene hybrid-nanofluid past a wedge with nonlinear radiation and heat source. Design/methodology/approach This study reports the numerical analysis of the hybrid nanofluid model under the implications of the heat source and magnetic field over a static and moving wedge with slips. The second law of thermodynamics is applied with nonlinear thermal radiation. The system that comprises differential equations of partial derivatives is remodeled into the system of differential equations via similarity transformations and then solved through the Runge–Kutta–Fehlberg with shooting technique. The physical parameters, which emerges from the derived system, are discussed in graphical formats. Excellent proficiency in the numerical process is analyzed by comparing the results with available literature in limiting scenarios. Findings The significant outcomes of the current investigation are that the velocity field uplifts for higher velocity slip and magnetic strength. Further, the heat transfer rate is reduced with the incremental values of the Eckert number, while it uplifts with thermal slip and radiation parameters. An increase in Brinkmann’s number uplifts the entropy generation rate, while that peters out the Bejan number. The results of this study are of importance involving in the assessment of the effect of some important design parameters on heat transfer and, consequently, on the optimization of industrial processes. Originality/value This study is original work that reports the hybrid nanofluid model of Fe3O4–Co/kerosene.

Entropy Generation on Maxwell Fluid Flow Past an Inclined Stretching Plate with Slip and Convective Surface Conditon: Darcy-Forchheimer Model

2019 ◽  
Vol 26 ◽  
pp. 62-83
Author(s):  
Tunde Abdulkadir Yusuf ◽  
Jacob Abiodun Gbadeyan
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Entropy Generation ◽  
Mhd Flow ◽  
Maxwell Fluid ◽  
Entropy Generation Rate ◽  
Physical Parameters ◽  
Convective Boundary ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study the effect of entropy generation on two dimensional magnetohydrodynamic (MHD) flow of a Maxwell fluid over an inclined stretching sheet embedded in a non-Darcian porous medium with velocity slip and convective boundary condition is investigated. Darcy-Forchheimer based model was employed to describe the flow in the porous medium. The non-linear thermal radiation is also taken into account. Similarity transformation is used to convert the non-linear partial differential equations to a system of non-linear ordinary differential equations. The resulting transformed equations are then solved using the Homotopy analysis method (HAM). Influence of various physical parameters on the dimensionless velocity profile, temperature profile and entropy generation are shown graphically and discussed in detail while the effects of these physical parameters on velocity gradient and temperature gradient are aided with the help of Table. Furthermore, comparison of some limiting cases of this model was made with existing results. The results obtained are found to be in good agreement with previously published results. Moreover, increase in local inertial coefficient parameter is found to decrease the entropy generation rate.

Impact of Entropy Generation on Stagnation-Point Flow of Sutterby Nanofluid: A Numerical Analysis

2016 ◽  
Vol 71 (9) ◽  
pp. 837-848 ◽  
Author(s):  
Ehtsham Azhar ◽  
Z. Iqbal ◽  
E.N. Maraj
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Computational Analysis ◽  
Similarity Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Physical Parameters ◽  
Stretching Plate

AbstractThe present article dicusses the computational analysis of entropy generation for the stagnation-point flow of Sutterby nanofluid over a linear stretching plate. The Sutterby fluid is chosen to study the effect for three major classes of non-Newtonian fluids, i.e. pseudoplastic, Newtonian, and dilatant. The effects of pertinent physical parameters are examined under the approximation of boundary layer. The system of coupled nonlinear partial differential equations is simplified by incorporating suitable similarity transformation into a system of non-linear-coupled ordinary differential equations. Entropy generation analysis is conducted numerically, and the results are displayed through graphs and tables. Significant findings are listed in the closing remarks.

scholarly journals Influence of heat generation/absorption and stagnation point on polystyrene–TiO2/H2O hybrid nanofluid flow

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Sadaf Masood ◽  
Muhammad Farooq ◽  
Aisha Anjum
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Entropy Generation ◽  
Heat Generation ◽  
Velocity Ratio ◽  
Hybrid Nanofluid ◽  
Engineering System ◽  
Nanofluid Flow ◽  
Homotopy Analysis

AbstractThis article focuses on hybrid nanofluid flow induced by stretched surface. The present context covers stagnation point flow of a hybrid nanofluid with the effect of heat generation/absorption. Currently most famous class of nanofluids is Hybrid nanofluid. It contains polystyrene and titanium oxide as a nanoparticles and water as a base fluid. First time attributes of heat transfer are evaluated by utilizing polystyrene–TiO2/H2O hybrid nanofluid with heat generation/absorption. Partial differential equations are converted into ordinary differential equation by using appropriate transformations for heat and velocity. Homotopy analysis method is operated for solution of ordinary differential equations. Flow and heat are disclosed graphically for unlike parameters. Resistive force and heat transfer rate is deliberated mathematically and graphically. It is deduced that velocity field enhanced for velocity ratio parameter whereas temperature field grows for heat generation/absorption coefficient. To judge the production of any engineering system entropy generation is also calculated. It is noticed that entropy generation grows for Prandtl number and Eckert number while it shows opposite behavior for temperature difference parameter.

scholarly journals Darcy-Forchheimer hybrid nanofluid flow over a stretching curved surface with heat and mass transfer

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0249434
Author(s):  
Anwar Saeed ◽  
Wajdi Alghamdi ◽  
Safyan Mukhtar ◽  
Syed Imad Ali Shah ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Curved Surface ◽  
Hybrid Nanofluid ◽  
Porous Space ◽  
Highly Nonlinear ◽  
Homotopy Analysis ◽  
Curvature Parameter ◽  
Swcnts And Mwcnts

The present article provides a detailed analysis of the Darcy Forchheimer flow of hybrid nanoliquid past an exponentially extending curved surface. In the porous space, the viscous fluid is expressed by Darcy-Forchheimer. The cylindrical shaped carbon nanotubes (SWCNTs and MWCNTs) and Fe3O4 (iron oxide) are used to synthesize hybrid nanofluid. At first, the appropriate similarity transformation is used to convert the modeled nonlinear coupled partial differential equations into nonlinear coupled ordinary differential equations. Then the resulting highly nonlinear coupled ordinary differential equations are analytically solved by the utilization of the “Homotopy analysis method” (HAM) method. The influence of sundry flow factors on velocity, temperature, and concentration profile are sketched and briefly discussed. The enhancement in both volume fraction parameter and curvature parameter k results in raises of the velocity profile. The uses of both Fe3O4 and CNTs nanoparticles are expressively improving the thermophysical properties of the base fluid. Apart from this, the numerical values of some physical quantities such as skin friction coefficients, local Nusselt number, and Sherwood number for the variation of the values of pertinent parameters are displayed in tabular forms. The obtained results show that the hybrid nanofluid enhances the heat transfer rate 2.21%, 2.1%, and 2.3% using the MWCNTs, SWCNTs, and Fe3O4 nanomaterials.

MHD Slip Flow of Cu-Kerosene Nanofluid in a Channel with Stretching Walls Using 3-Stage Lobatto IIIA Formula

2018 ◽  
Vol 387 ◽  
pp. 51-62 ◽  
Author(s):  
Jawad Reza ◽  
Fateh Mebarek-Oudina ◽  
Oluwole Daniel Makinde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Transverse Magnetic ◽  
Numerical Results ◽  
Physical Parameters ◽  
Boundary Layer Equations ◽  
Energy Equations

In this paper, rheology of laminar incompressible Copper-Kerosene nanofluid in a channel with stretching walls under the influence of transverse magnetic field is investigated. The main structure of the partial differential equations was taken from the law of conservation of mass, momentum and energy equations. Governing boundary layer equations are transformed into nonlinear ordinary differential equations by using similarity variables and then solved with 3-stage Lobatto IIIA formula. Numerical results were compared with another numerical method (Runge-Kutta-Fehlberg) and found excellent agreement. The influence of physical parameters Reynolds number, magnetic number, solid volume fraction, momentum and thermal slip parameters on velocity and temperature profile considered. Numerical results revealed that solid volume fraction decreases the velocity of nanofluid particles near the lower wall of the channel and increase the thermal boundary layer thickness in the channel.

Instability of Variable Thermal Conductivity Magnetohydrodynamic Nanofluid Flow in a Vertical Porous Channel of Varying Width

2017 ◽  
Vol 378 ◽  
pp. 85-101
Author(s):  
Md. Sarwar Alam ◽  
Oluwole Daniel Makinde ◽  
Md. Abdul Hakim Khan
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Entropy Generation ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Porous Wall ◽  
Variable Thermal Conductivity ◽  
Physical Parameters

A numerical investigation is performed into the heat transfer and entropy generation of a variable thermal conductivity magnetohydrodynamic flow of Al2O3-water nanofluid in a vertical channel of varying width with right porous wall, which enable the fluid to enter. The effects of the Lorentz force, buoyancy force, viscous dissipation and Joule heating are considered and modeled using the transverse momentum and energy balance equations respectively. The governing nonlinear partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations using appropriate similarity transformations and then solved numerically using power series with Hermite-Padé approximation method. A stability analysis has been performed for the local rate of shear stress and Nusselt number that indicates the existence of dual solution branches. Numerical results are achieved for the fluid velocity, temperature as well as the rate of heat transfer at the wall and the entropy generation of the system. The present results are original and new for the flow and heat transfer past a channel of varying width in a nanofluid which shows that the physical parameters have significant effects on the flow field.

Curvilinear flow of micropolar fluid with Cattaneo–Christov heat flux model due to oscillation of curved stretchable sheet

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Muhammad Naveed ◽  
Muhammad Imran ◽  
Zaheer Abbas
Keyword(s):  
Heat Flux ◽  
Micropolar Fluid ◽  
Fluid Velocity ◽  
Thermal Relaxation ◽  
Curvilinear Coordinates ◽  
Curved Surface ◽  
Radius Of Curvature ◽  
Published Data ◽  
Flux Model ◽  
Heat Flux Model

Abstract This paper aims to investigate the transfer of heat phenomenon in a hydromagnetic time dependent flow of micropolar fluid across an oscillating stretchable curved surface by using the Cattaneo–Christov heat flux model, which considers thermal relaxation time. An elastic curved surface that stretches back and forth causes the flow situation. The flow equations are derived as nonlinear partial differential equations by incorporating a curvilinear coordinates system, which is then solved analytically via the homotopy analysis method (HAM). The accuracy of the derived analytical results is also examined by using a finite-difference technique known as the Keller box method, and it is found to be in strong agreement. The influences of various physical characteristics such as material parameter, magnetic parameter, thermal relaxation parameter, a dimensionless radius of curvature, Prandtl number and ratio of surface’s oscillating frequency to its stretching rate parameter on angular velocity, fluid velocity, pressure, temperature, heat transmission rate, and skin friction and couple stress coefficient are depicted in detail with the help of graphs and tables. Furthermore, for the verification and validation of the current results, a tabular comparison of the published data in the literature for the case of flat oscillating surface versus curved oscillating surface is carried out and found to be in good agreement.

Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis

2021 ◽  
Author(s):  
Fazal Haq ◽  
Muhammad Ijaz Khan ◽  
Sami Ullah Khan ◽  
Khadijah M. Abualnaja ◽  
M. A. El-Shorbagy
Keyword(s):  
Differential Equations ◽  
Entropy Generation ◽  
Nonlinear Differential Equations ◽  
Transportation Systems ◽  
Physical Parameters ◽  
Bejan Number ◽  
Convective Boundary ◽  
Homotopy Analysis ◽  
Permeability Parameter ◽  
Thermal Features

Abstract This analysis presents the applications of entropy generation phenomenon in incompressible flow of Jeffrey nanofluid in presence of distinct thermal features. The novel aspects of various features like Joule heating, porous medium, dissipation features and radiative mechanism is addressed. In order to improve the thermal transportation systems based on nanomaterials, the convective boundary conditions are introduced. The thermal viscoelastic nanofluid model is expressed in term of differential equations. The problem is presented via nonlinear differential equations for which analytical expressions are obtained by using homotopy analysis method(HAM). The accuracy of solution is ensured. The effective outcomes of all physical parameters associated with the flow model are carefully examined and underlined through various curves. The observations summarized from current analysis reveal that presence of permeability parameter offers resistance to the flow. A monotonic decrement in local Nusselt number is noted with Hartmann number and Prandtl number. Moreover, entropy generation and Bejan number increases with radiation parameter and fluid parameter.

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