scholarly journals Statistical Criteria of Nanofluid Flows over a Stretching Sheet with the Effects of Magnetic Field and Viscous Dissipation

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1367 ◽  
Author(s):  
Alias Jedi ◽  
Noorhelyna Razali ◽  
Wan Mohd Faizal Wan Mahmood ◽  
Nor Ashikin Abu Bakar
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Eckert Number ◽  
Boundary Layer Problem

In this study, the heat and mass transfer characteristics of nanofluid flow over a nonlinearly stretching sheet are investigated. The important effects of axisymmetric of thermal conductivity and viscous dissipation have been included in the model of nanofluids. The Buongiorno model is considered to solve the nanofluid boundary layer problem. The governing nonlinear partial differential equations have been transformed into a system of ordinary differential equations and are solved numerically via the shooting technique. The validity of this method was verified by comparison with previous work performed for nanofluids without the effects of the magnetic field and viscous dissipation. The analytical investigation is carried out for different governing parameters, namely, the Brownian motion parameter, thermophoresis parameter, magnetic parameter, Biot number, and Eckert number. The results indicate that the skin friction coefficient has a direct relationship with the Brownian motion number and thermophoresis number. Moreover, it can be seen that the Nusselt number decreases with the increase of the magnetic parameter and Eckert number.

scholarly journals Influence of Joule Heating and Non-Linear Radiation on MHD 3D Dissipating Flow of Casson Nanofluid past a Non-Linear Stretching Sheet

2019 ◽  
Vol 8 (1) ◽  
pp. 661-672
Author(s):  
Pandikunta Sreenivasulu ◽  
Tamalapakula Poornima ◽  
Nandanoor Bhaskar Reddy
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Joule Heating ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Skin Friction Coefficient ◽  
Casson Nanofluid ◽  
Similarity Transformations ◽  
Non Linear

Abstract Present analysis is to study the combined effects of viscous dissipation and Joule heating on MHD three-dimensional laminar flow of a viscous incompressible non-linear radiating Casson nanofluid past a nonlinear stretching porous sheet. Present model describes that flow generated by bi-directional non-linear stretching sheet with thermophoresis and Brownian motion effects. The governing nonlinear partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations by similarity transformations and then solved by employing shooting method. The effects of the flow parameters on the velocity, temperature and concentration as well as the skin friction coefficient, Nusselt number and Sherwood number near the wall are computed for various values of the fluid properties. This study reveals that the temperature of Casson nanofluid increases with combination of viscous dissipation and Joule heating. Increasing thermophoresis parameter increases the species concentration of the nanoflow. The comparison of present results have been made with the published work and the results are found to be very good agreement.

scholarly journals Role of Brownian Motion and Thermophoresis Effects on Hydromagnetic Flow of Nanofluid Over a Nonlinearly Stretching Sheet with Slip Effects and Solar Radiation

2019 ◽  
Vol 24 (3) ◽  
pp. 489-508
Author(s):  
S.P. Anjali Devi ◽  
S. Mekala
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Velocity Slip ◽  
Physical Parameters ◽  
Nonlinear Thermal Radiation ◽  
Hydromagnetic Flow ◽  
Nonlinearly Stretching Sheet

Abstract Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

Casson Liquid Flow due to Porous Stretching Sheet with Suction/Injection

2018 ◽  
Vol 388 ◽  
pp. 420-432
Author(s):  
Vinay Kumar Poorigaly Nanjundaswamy ◽  
Ulavathi Shettar Mahabaleshwar ◽  
Patil Mallikarjun ◽  
Mohaddeseh Mousavi Nezhad ◽  
Giulio Lorenzini
Keyword(s):  
Differential Equations ◽  
Stretching Sheet ◽  
Theoretical Study ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Casson Fluid ◽  
Skin Friction Coefficient ◽  
Boundary Layer Flows ◽  
Similarity Transformations ◽  
Casson Fluid Model

The theoretical study of laminar boundary layer flows of a non-Newtonian fluid past a stretching sheet in an embedded porous medium in the presence of suction/injection is of significant importance in the crystal growing, geothermal, metallurgical, polymer extrusion and several other technological processes. Casson fluid model is one such fluid model used to characterize the behaviour of non-Newtonian fluids. The present article discusses the Casson fluid flow past a permeable stretching sheet in the presence of mass transpiration. The physical problem is modelled into a system of nonlinear partial differential equations which are analytically solved by transforming them into nonlinear ordinary differential equations with constant coefficient by means of similarity transformations. The analysis reveals the effect of Casson parameter on the velocity boundary. In fact, the increasing Casson parameter results in the suppression of velocity boundary. It is found that the skin friction coefficient decreases with the decreasing values of Casson parameter. The effects of Darcy drag force and the mass transpiration are also analyzed by means of various plots.

Double Diffusive Convection in Flow Couple Stress Nanofluid in a Permeable Wall Vertical Channel in the Presence of a Magnetic Field

2019 ◽  
Vol 26 ◽  
pp. 30-44
Author(s):  
Noureddine Messaoudi ◽  
Mohamed Nadjib Bouaziz ◽  
Hamza Ali Agha
Keyword(s):  
Magnetic Field ◽  
Mass Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Couple Stress ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Vertical Channel ◽  
Strong Impact

In this work, the flow of a couple stress nanofluid in a vertical channel with heat and mass transfer in the presence of a magnetic field and taking account the Brownian motion, the thermophoresis as well as the effect of Soret and Dufour was simulated numerically using Matlab following the code bvp4c. The nonlinear partial differential equations governing this particular flow are transformed into a system of ordinary differential equations via the similarity technique. The influence of the parameters describing the behavior of the problem studied on the velocity, temperature, concentration and volume fraction fields of the nanoparticles, as well as on the coefficient of friction, Nusselt and Sherwood numbers, were highlighted for the end of the study. understand their effect on heat and mass transfer. The rheology of the nanofluid and the magnetic field have a strong impact on the velocity and temperature profiles, while the parameters of Brownian motion and thermophoresis promote heat transfer.

Magnetohydrodynamic convection in a porous square cavity filled by a nanofluid with viscous dissipation effects

2018 ◽  
Vol 233 (3) ◽  
pp. 474-488 ◽  
Author(s):  
Balla Chandra Shekar ◽  
C Haritha ◽  
Naikoti Kishan
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Viscous Dissipation ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Square Cavity ◽  
Local Skin ◽  
Left Wall ◽  
Energy Equations

The present paper investigates the incompressible, laminar, natural convection flow in a porous square cavity filled with a nanofluid in the presence of magnetic field and viscous dissipation. The nanofluid mathematical model proposed by Buongiorno is considered. The left wall of the enclosure is heated, while the right wall is cooled and the bottom and upper walls are adiabatic. The analysis is formulated in terms of vorticity stream function procedure. The governing equations, which are continuity, momentum, and energy equations, are solved by finite element method based on Galerkin weighted residual approach. The relevant parameters considered for computations are magnetic field, Rayleigh number, thermophoresis, Brownian motion, buoyancy ratio, Lewis number, and Eckert number. The numerical results in terms of streamlines, isotherms, isoconcentrations, the average and local skin friction coefficient and Nusselt numbers are reported for various values of Nt, Nb, Ra, Le, M, and Ec. It is found that the magnetic field, Brownian motion, thermophoretic force, and viscous dissipation show significant effect on the velocity, temperature, and concentration distributions in the cavity.

scholarly journals Numerical Solution of MHD Viscoelastic Nanofluid Flow over a Stretching Sheet with Partial Slip and Heat Source/Sink

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Mania Goyal ◽  
Rama Bhargava
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Brownian Motion ◽  
Differential Equations ◽  
Heat Source ◽  
Uniform Magnetic Field ◽  
Stretching Sheet ◽  
Partial Slip ◽  
Local Similarity ◽  
Source Sink

We analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet with a heat source/sink, under the action of a uniform magnetic field, orientated normally to the plate. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of local similarity transformations. The differential equations are solved by the variational finite element method (FEM). We have examined the effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, uniform magnetic field, viscoelastic parameter, Prandtl number, heat source/sink parameter, Lewis number, and the slip parameter on the flow field and heat transfer characteristics. Graphical display of the numerical examination is performed to illustrate the influence of various flow parameters on the velocity, temperature, concentration, and Nusselt and Sherwood numbers distributions. The present study has many applications in coating and suspensions, cooling of metallic plate, paper production, heat exchangers technology, and materials processing exploiting.

Flow and Heat Transfer in a Newtonian Nanoliquid due to a Curved Stretching Sheet

2017 ◽  
Vol 72 (9) ◽  
pp. 833-842 ◽  
Author(s):  
Pradeep Ganapathi Siddheshwar ◽  
Meenakshi Nerolu ◽  
Igor Pažanin
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Skin Friction Coefficient ◽  
Variable Coefficients

AbstractFlow of a Newtonian nanoliquid due to a curved stretching sheet and heat transfer in it is studied. The governing nonlinear partial differential equations are reduced to nonlinear ordinary differential equations with variable coefficients by using a similarity transformation. The flow characteristics are studied using plots of flow velocity components and the skin-friction coefficient as a function of suction-injection parameter, curvature, and volume fraction. Prescribed surface temperature and prescribed surface heat flux are considered for studying the temperature distribution in the flow. The thermophysical properties of 20 nanoliquids are considered in the investigation by modeling them through the use of phenomenological laws and mixture theory. The results of the corresponding problem involving a plane stretching sheet is obtained as a particular case of those obtained in the present paper. Skin friction coefficient and Nusselt number are evaluated and it is observed that skin friction coefficient decreases with concentration of nanoparticles in the absence as well as presence of suction where as Nusselt number increases with increase in concentration of nanoparticles in a dilute range.

scholarly journals A novel application of Lobatto IIIA solver for numerical treatment of mixed convection nanofluidic model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Iftikhar Ahmad ◽  
Tahir Nawaz Cheema ◽  
Muhammad Asif Zahoor Raja ◽  
Saeed Ehsan Awan ◽  
Norma Binti Alias ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Mixed Convection ◽  
Variable Viscosity ◽  
Fluid Model ◽  
Nonlinear Partial Differential Equations ◽  
Transverse Magnetic ◽  
Skin Friction Coefficient ◽  
Temperature Dependent Viscosity ◽  
Numerical Computing

AbstractThe objective of the current investigation is to examine the influence of variable viscosity and transverse magnetic field on mixed convection fluid model through stretching sheet based on copper and silver nanoparticles by exploiting the strength of numerical computing via Lobatto IIIA solver. The nonlinear partial differential equations are changed into ordinary differential equations by means of similarity transformations procedure. A renewed finite difference based Lobatto IIIA method is incorporated to solve the fluidic system numerically. Vogel's model is considered to observe the influence of variable viscosity and applied oblique magnetic field with mixed convection along with temperature dependent viscosity. Graphical and numerical illustrations are presented to visualize the behavior of different sundry parameters of interest on velocity and temperature. Outcomes reflect that volumetric fraction of nanoparticles causes to increase the thermal conductivity of the fluid and the temperature enhances due to blade type copper nanoparticles. The convergence analysis on the accuracy to solve the problem is investigated viably though the residual errors with different tolerances to prove the worth of the solver. The temperature of the fluid accelerates due the blade type nanoparticles of copper and skin friction coefficient is reduced due to enhancement of Grashof Number.

scholarly journals Heat and Mass Transfer in the Boundary Layer of Unsteady Viscous Nanofluid along a Vertical Stretching Sheet

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Eshetu Haile ◽  
B. Shankar
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Skin Friction Coefficient ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Layer Flow

Heat and mass transfer in the boundary-layer flow of unsteady viscous nanofluid along a vertical stretching sheet in the presence of magnetic field, thermal radiation, heat generation, and chemical reaction are presented in this paper. The sheet is situated in the xz-plane and y is normal to the surface directing towards the positive y-axis. The sheet is continuously stretching in the positive x-axis and the external magnetic field is applied to the system parallel to the positive y-axis. With the help of similarity transformations, the partial differential equations are transformed into a couple of nonlinear ordinary differential equations. The new problem is then solved numerically by a finite-difference scheme known as the Keller-box method. Effects of the necessary parameters in the flow field are explicitly studied and briefly explained graphically and in tabular form. For the selected values of the pertinent parameters appearing in the governing equations, numerical results of velocity, temperature, concentration, skin friction coefficient, Nusselt number, and Sherwood number are obtained. The results are compared to the works of others (from previously published journals) and they are found in excellent agreement.

Effect of Induced Magnetic Field on Magnetohydrodynamic Stagnation Point Flow and Heat Transfer on a Stretching Sheet

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
A. Sinha ◽  
J. C. Misra
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Stagnation Point Flow ◽  
Induced Magnetic Field ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Electrically Conducting Fluid

In this paper, the steady magnetohydrodynamic (MHD) stagnation point flow of an incompressible viscous electrically conducting fluid over a stretching sheet has been investigated. Velocity and thermal slip conditions have been incorporated in the study. The effects of induced magnetic field and thermal radiation have also been duly taken into account. The nonlinear partial differential equations arising out of the mathematical analysis of the problem are transformed into a system of nonlinear ordinary differential equations by using similarity transformation and boundary layer approximation. These equations are solved by developing an appropriate numerical method. Considering an illustrative example, numerical results are obtained for velocity, temperature, skin friction, and Nusselt number by considering a chosen set of values of various parameters involved in the study. The results are presented graphically/in tabular form.

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