scholarly journals Transpiration and Viscous Dissipation Effects on Entropy Generation in Hybrid Nanofluid Flow over a Nonlinear Radially Stretching Disk

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 668 ◽  
Author(s):  
Umer Farooq ◽  
Muhammad Afridi ◽  
Muhammad Qasim ◽  
D. Lu
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Research Work ◽  
Dissipation Function ◽  
Hybrid Nanofluid ◽  
Layer Flow

The present research work explores the effects of suction/injection and viscous dissipation on entropy generation in the boundary layer flow of a hybrid nanofluid (Cu–Al2O3–H2O) over a nonlinear radially stretching porous disk. The energy dissipation function is added in the energy equation in order to incorporate the effects of viscous dissipation. The Tiwari and Das model is used in this work. The flow, heat transfer, and entropy generation analysis have been performed using a modified form of the Maxwell Garnett (MG) and Brinkman nanofluid model for effective thermal conductivity and dynamic viscosity, respectively. Suitable transformations are utilized to obtain a set of self-similar ordinary differential equations. Numerical solutions are obtained using shooting and bvp4c Matlab solver. The comparison of solutions shows excellent agreement. To examine the effects of principal flow parameters like suction/injection, the Eckert number, and solid volume fraction, different graphs are plotted and discussed. It is concluded that entropy generation inside the boundary layer of a hybrid nanofluid is high compared to a convectional nanofluid.

scholarly journals The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

scholarly journals Entropy Generation in a Dissipative Nanofluid Flow under the Influence of Magnetic Dissipation and Transpiration

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5506
Author(s):  
Dianchen Lu ◽  
Muhammad Idrees Afridi ◽  
Usman Allauddin ◽  
Umer Farooq ◽  
Muhammad Qasim
Keyword(s):  
Boundary Layer ◽  
Viscous Dissipation ◽  
Entropy Generation ◽  
Ultrafine Particles ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Suction Parameter ◽  
Self Similar

The present study explores the entropy generation, flow, and heat transfer characteristics of a dissipative nanofluid in the presence of transpiration effects at the boundary. The non-isothermal boundary conditions are taken into consideration to guarantee self-similar solutions. The electrically conducting nanofluid flow is influenced by a magnetic field of constant strength. The ultrafine particles (nanoparticles of Fe3O4/CuO) are dispersed in the technological fluid water (H2O). Both the base fluid and the nanofluid have the same bulk velocity and are assumed to be in thermal equilibrium. Tiwari and Dass’s idea is used for the mathematical modeling of the problem. Furthermore, the ultrafine particles are supposed to be spherical, and Maxwell Garnett’s model is used for the effective thermal conductivity of the nanofluid. Closed-form solutions are derived for boundary layer momentum and energy equations. These solutions are then utilized to access the entropy generation and the irreversibility parameter. The relative importance of different sources of entropy generation in the boundary layer is discussed through various graphs. The effects of space free physical parameters such as mass suction parameter (S), viscous dissipation parameter (Ec), magnetic heating parameter (M), and solid volume fraction (ϕ) of the ultrafine particles on the velocity, Bejan number, temperature, and entropy generation are elaborated through various graphs. It is found that the parabolic wall temperature facilitates similarity transformations so that self-similar equations can be achieved in the presence of viscous dissipation. It is observed that the entropy generation number is an increasing function of the Eckert number and solid volume fraction. The entropy production rate in the Fe3O4−H2O nanofluid is higher than that in the CuO−H2O nanofluid under the same circumstances.

scholarly journals Boundary layer flow on permeable flat surface in Ag-Al2O3/water hybrid nanofluid with viscous dissipation

2021 ◽  
Vol 2 (1) ◽  
pp. 11-19
Author(s):  
MUHAMMAD KHAIRUL ANUAR MOHAMED ◽  
A. Hussanan ◽  
H.T. Alkasasbeh ◽  
B. Widodo ◽  
M.Z. Salleh
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Flat Surface ◽  
Volume Fraction ◽  
Transfer Characteristic ◽  
Hybrid Nanofluid ◽  
Water Based ◽  
Layer Flow

Seeking the better performance nanofluid but with low cost of production, presence challenged. Metal nanomaterial is good in both thermal and electric conductivity but expensive while oxide nanomaterial does oppositely. The present study solved numerically the laminar boundary layer flow over a permeable flat surface in a blended metal-oxide hybrid nanofluid plate with viscous dissipation effects. The similarity equations in the form of the set of ordinary differential equations are reduced from the non-linear partial differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the reduced skin friction coefficient and reduced Nusselt number as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the Eckert number, permeability parameter and nanoparticle volume fraction are analyzed and discussed. The Ag-Al2O3 water-based hybrid nanofluid tested in this study shows competitive results with the Ag water-based nanofluid in certain cases.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals Marangoni Mixed Convection Boundary Layer Flow in a Nanofluid

2014 ◽  
Vol 9 (2) ◽  
Author(s):  
Amirah Remeli ◽  
Norihan Md Arifin ◽  
Roslinda Nazar ◽  
Fudziah Ismail
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mixed Convection ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Immiscible Fluids ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow

The problem of Marangoni mixed convection boundary layer flow and heat transfer that can be formed along the interface of two immiscible fluids in a nanofluid is studied using different types of nanoparticles. Numerical solutions of the similarity equations are obtained using the shooting method. Three types of metallic or nonmetallic nanoparticles, namely copper (Cu), alumina (23AlO) and titania (2TiO) are consideredby using a water-based fluid to investigate the effect of the solid volume fraction or nanoparticle volume fraction parameter ϕ of the nanofluid. The influences of the interest parameters on the reduced velocity along the interface, velocity profiles as well as the reduced heat transfer at the interface and temperature profiles were presented in tables and figures.

scholarly journals Heat Transfer in Hydromagnetic Flow over an Unsteady Stretching Permeable Sheet

2019 ◽  
Vol 4 (4) ◽  
pp. 1018-1030
Author(s):  
Susheela Chaudhary ◽  
Santosh Chaudhary ◽  
Sawai Singh
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Research Work ◽  
Magnetic Field Effect ◽  
Skin Friction Coefficient ◽  
Local Skin ◽  
Layer Flow ◽  
Fourth Order Method

Unsteady laminar boundary layer flow of viscous incompressible electrically conducting fluid along a continuous stretched permeable surface with the magnetic field effect is investigated. The defining characteristics of unsteady laminar boundary layer flow are governed a more than one independent variables, stretching velocity and surface temperature of the field. Governing equations are obtained for influencing parameters and transformed into ordinary differential equations by taking convenient similarity variables. Runge-Kutta fourth order method in corporation by the shooting technique is introduced to carry out numerical computations of the investigation. Velocity and temperature profiles are computed and represented graphically for the influences of suction/injection parameter, unsteadiness parameter, magnetic parameter and Prandtl number, while numerical solutions of local skin friction coefficient and local Nusselt number are discussed through tables. For non-magnetic condition, results are found in concordance with earlier research work.

Mixed convection boundary layer flow along vertical thin needles in nanofluids

2014 ◽  
Vol 24 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Radu Trimbitas ◽  
Teodor Grosan ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Heat Transfer Characteristics ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Convection Boundary ◽  
Layer Flow

Purpose – The purpose of this paper is to theoretically study the problem of mixed convection boundary layer flow and heat transfer past a vertical needle with variable wall temperature using nanofluids. The similarity equations are solved numerically for copper nanoparticles in the based fluid of water to investigate the effect of the solid volume fraction parameter of the fluid and heat transfer characteristics. The skin friction coefficient, Nusselt number, and the velocity and temperature profiles and are graphically presented and discussed. Design/methodology/approach – The transformed system of ordinary differential equations was solved using the function bvp4c from Matlab. The relative tolerance was set to 1e-10. For the study of the stability the authors also used the bvp4c function in combination with chebfun package from Matlab. Findings – It is found that the solid volume fraction affects the fluid flow and heat transfer characteristics. The numerical results for a regular fluid and forced convection flow are compared with the corresponding results reported by Chen and Smith. The solutions exists up to a critical value of λ, beyond which the boundary layer separates from the surface and the solution based upon the boundary-layer approximations is not possible Originality/value – The paper describes how multiple (dual) solutions for the flow reversals are obtained. A stability analysis for this flow reversal has been also done showing that the lower solution branches are unstable, while the upper solution branches are stable.

Physical insights into the heat and mass transfer in Casson hybrid nanofluid flow induced by a Riga plate with thermophoretic particle deposition

2021 ◽  
pp. 095440892110393
Author(s):  
JK Madhukesh ◽  
A Alhadhrami ◽  
R Naveen Kumar ◽  
RJ Punith Gowda ◽  
BC Prasannakumara ◽  
...  
Keyword(s):  
Particle Deposition ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Boundary Layer Separation ◽  
Hybrid Nanofluid ◽  
Flow Equations ◽  
Pressure Drag ◽  
Similarity Transformations ◽  
Riga Plate

In applied physics, Riga plate was one of the trademark inventions to overcome the poor conductivity of fluids. This provided an aid to avoid the boundary layer separation, reduce the friction as well as the pressure drag of submarines. This particular study has a lot of importance in numerous manufacturing, industrial and engineering fields. The current study deals with the laminar, steady flow of a Casson hybrid nanoliquid induced by a Riga plate in the presence of a porous medium. Appropriate similarity transformations are used to reduce the fluid flow equations into a system of ordinary differential equations. Later, for these reduced equations, an effective numerical method called the fourth fifth-order Runge–Kutta–Fehlberg process with shooting technique is used to obtain the numerical solutions. The influences of involved parameters on the flow fields are demonstrated graphically. Results reveal that the velocity of the Casson hybrid nanofluid declines with an increase in the solid volume fraction and porosity parameter. The velocity gradient increases for an increase in values of the modified Hartmann number. Thermal distribution enhances with an increase in the values of Biot number as well as heat source/sink parameter.

scholarly journals Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Norihan Md. Arifin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Convection Boundary Layer ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Layer Flow

The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl numberPr=6.2. The effects of the nanoparticle volume fractionϕand the constant exponentmon the flow and heat transfer characteristics are obtained and discussed.

Second Law Analysis of Boundary Layer Flow With Variable Fluid Properties

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
M. I. Afridi ◽  
M. Qasim ◽  
O. D. Makinde
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Entropy Generation ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Entropy Generation Rate ◽  
Bejan Number ◽  
Entropy Generation Number ◽  
Layer Flow

An entropy generation analysis of steady boundary layer flow of viscous fluid with variable properties over an exponentially stretching sheet is presented. The basic nonlinear partial differential equations that govern the flow are reduced to ordinary differential equations by using appropriate transformations. Numerical solutions are obtained by using shooting technique along with Runge–Kutta method. Expressions for the dimensionless volumetric entropy generation rate (NG) and Bejan number are also obtained. The effects of different dimensionless emerging parameters on entropy generation number (NG) and Bejan number (Be) are investigated graphically in detail.

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