scholarly journals Lie Group Solution for Free Convective Flow of a Nanofluid Past a Chemically Reacting Horizontal Plate in a Porous Media

2014 ◽  
Vol 2014 ◽  
pp. 1-21 ◽  
Author(s):  
M. M. Rashidi ◽  
E. Momoniat ◽  
M. Ferdows ◽  
A. Basiriparsa
Keyword(s):  
Lie Group ◽  
Convective Flow ◽  
Volume Fraction ◽  
Group Analysis ◽  
Numerical Results ◽  
Thermal Slip ◽  
Nanoparticle Volume Fraction ◽  
Horizontal Plate ◽  
Free Convective Flow ◽  
Chemically Reacting

The optimal homotopy analysis method (OHAM) is employed to investigate the steady laminar incompressible free convective flow of a nanofluid past a chemically reacting upward facing horizontal plate in a porous medium taking into account heat generation/absorption and the thermal slip boundary condition. Using similarity transformations developed by Lie group analysis, the continuity, momentum, energy, and nanoparticle volume fraction equations are transformed into a set of coupled similarity equations. The OHAM solutions are obtained and verified by numerical results using a Runge-Kutta-Fehlberg fourth-fifth order method. The effect of the emerging flow controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction have been presented graphically and discussed. Good agreement is found between analytical and numerical results of the present paper with published results. This close agreement supports our analysis and the accuracy of the numerical computations. This paper also includes a representative set of numerical results for reduced Nusselt and Sherwood numbers in a table for various values of the parameters. It is concluded that the reduced Nusselt number increases with the Lewis number and reaction parameter whist it decreases with the order of the chemical reaction, thermal slip, and generation parameters.

Lie group analysis and numerical solutions for magneto-convective slip flow of nanofluid over a moving plate with Newtonian heating boundary condition

2015 ◽  
Vol 93 (12) ◽  
pp. 1501-1509 ◽  
Author(s):  
M.J. Uddin ◽  
O. Anwar Bég ◽  
N. Amran ◽  
A.I.MD. Ismail
Keyword(s):  
Boundary Condition ◽  
Lie Group ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Flow ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Nanoparticle Volume Fraction ◽  
Newtonian Heating ◽  
Moving Plate

Magnetohydrodynamic laminar boundary layer slip flow of a nanofluid over a moving plate with Newtonian heating boundary condition in the presence of heat generation–absorption effects is studied using Lie group analysis and a numerical method. The model used for the nanofluid includes the effects of Brownian motion and thermophoresis. The governing transport equations are non-dimensionalized and transformed into a set of similarity equations using similarity transformations generated by Lie group transformations. The transformed equations are then solved using the Runge–Kutta–Fehlberg fourth- and fifth-order numerical method in Maple 17, which is also used to generate relevant graphs and tables. The flow, heat, and nanoparticle volume fraction characteristics are shown to depend on a number of thermophysical parameters, namely, Brownian motion, thermophoresis, Lewis number, Prandtl number, linear momentum slip, magnetic field, suction–injection, Newtonian heating, and heat generation–absorption. The effects of these parameters on the dimensionless stream function, velocity, temperature, nanoparticle volume fraction, wall heat, and mass transfer rates are investigated. Comparisons of the present numerical solutions with published works show very good correlation. The study finds applications in nano-technological magnetic materials processing.

scholarly journals Lie Group Analysis of Natural Convective Flow from a Convectively Heated Upward Facing Radiating Permeable Horizontal Plate in Porous Media Filled with Nanofluid

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Md. Jashim Uddin ◽  
W. A. Khan ◽  
A. I. Md. Ismail
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Lie Group ◽  
Convective Flow ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Horizontal Plate ◽  
Transfer Rates ◽  
Special Cases

Two-dimensional, steady, laminar and incompressible natural convective flow of a nanofluid over a connectively heated permeable upward facing radiating horizontal plate in porous medium is studied numerically. The present model incorporates Brownian motion and thermophoresis effects. The similarity transformations for the governing equations are developed by Lie group analysis. The transformed equations are solved numerically by Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. Effects of the governing parameters on the dimensionless velocity, temperature and nanoparticle volume fraction as well as on the dimensionless rate of heat and mass transfer are presented graphically and the results are compared with the published data for special cases. Good agreement is found between numerical results of the present paper and published results. It is found that Lewis number, Brownian motion and convective heat transfer parameters increase the heat and mass transfer rates whilst thermophoresis decreases both heat and mass transfer rates.

scholarly journals Two parameters Lie group analysis and numerical solution of unsteady free convective flow of non-Newtonian fluid

2016 ◽  
Vol 55 (3) ◽  
pp. 2299-2308 ◽  
Author(s):  
M.J. Uddin ◽  
M.M. Rashidi ◽  
Hamed H. Alsulami ◽  
S. Abbasbandy ◽  
N. Freidoonimeh
Keyword(s):  
Numerical Solution ◽  
Newtonian Fluid ◽  
Lie Group ◽  
Convective Flow ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Free Convective Flow ◽  
Two Parameters

Transient Free Convective Flow of CNT Water Nanofluid with Heat Transfer from a Moving Cylinder

2020 ◽  
Vol 10 ◽  
Author(s):  
C. Sridevi ◽  
A. Sailakumari
Keyword(s):  
Carbon Nanotubes ◽  
Heat Generation ◽  
Convective Flow ◽  
Volume Fraction ◽  
Vertical Cylinder ◽  
Single Wall Carbon Nanotubes ◽  
Free Convective Flow ◽  
Multi Wall Carbon Nanotubes ◽  
Moving Cylinder ◽  
Variable Surface

Background: In this paper, transient two-dimensional laminar boundary layer viscous incompressible free convective flow of water based nanofluid with carbon nanotubes (CNTs) past a moving vertical cylinder with variable surface temperature is studied numerically in the presence of thermal radiation and heat generation. Methods: The prevailing partial differential equations which model the flow with initial and boundary conditions are solved by implicit finite difference method of Crank Nicolson type which is unconditionally stable and convergent. Results: Influence of Grashof number (Gr), nanoparticle volume fraction ( ), heat generation parameter (Q), temperature exponent (m), radiation parameter (N) and time (t) on velocity and temperature profiles are sketched graphically and elaborated comprehensively. Conclusion: Analysis of Nusselt number and Skin friction coefficient are also discussed numerically for both single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes (MWCNTs).

scholarly journals Statistical Modeling for Nanofluid Flow: A Stretching Sheet with Thermophysical Property Data

2020 ◽  
Vol 4 (1) ◽  
pp. 3 ◽  
Author(s):  
Alias Jedi ◽  
Azhari Shamsudeen ◽  
Noorhelyna Razali ◽  
Haliza Othman ◽  
Nuryazmin Ahmat Zainuri ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Nonlinear Ordinary Differential Equation ◽  
Numerical Results ◽  
Nanoparticle Volume Fraction ◽  
Nanofluid Flow ◽  
Property Data ◽  
Layer Flow

This paper reports the use of a numerical solution of nanofluid flow. The boundary layer flow over a stretching sheet in combination of two nanofluids models is studied. The partial differential equation that governs this model was transformed into a nonlinear ordinary differential equation by using similarity variables, and the numerical results were obtained by applying the shooting technique. Copper (Cu) nanoparticles (water-based fluid) were used in this study. This paper presents and discusses all numerical results, including those for the local Sherwood number and the local Nusselt number. Additionally, the effects of the nanoparticle volume fraction, Brownian motion Nb, and thermophoresis Nt on the performance of heat transfer are discussed. The results show that the stretching sheet has a unique solution: as the nanoparticle volume fraction φ (φ = 0), Nt (Nt = 0.1), and Nb decrease, the rate of heat transfer increases. Furthermore, as φ (φ = 0) and Nb decrease, the rate of mass transfer increases. The data of the Nusselt and Sherwood numbers were tested using different statistical distributions, and it is found that both datasets fit the Weibull distribution for different values of Nt and rotating φ.

scholarly journals Group Analysis of Free Convection Flow of a Magnetic Nanofluid with Chemical Reaction

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Md. Jashim Uddin ◽  
O. A. Bég ◽  
A. Aziz ◽  
A. I. Md. Ismail
Keyword(s):  
Chemical Reaction ◽  
Volume Fraction ◽  
Convective Heat Transfer Coefficient ◽  
Group Analysis ◽  
Momentum Conservation ◽  
Convection Flow ◽  
Axial Distance ◽  
Nanoparticle Volume Fraction ◽  
Convective Boundary ◽  
Transfer Velocity

A theoretical study of two-dimensional magnetohydrodynamics viscous incompressible free convective boundary layer flow of an electrically conducting, chemically reacting nanofluid from a convectively heated permeable vertical surface is presented. Scaling group of transformations is used in the governing equations and the boundary conditions to determine absolute invariants. A third-order ordinary differential equation which corresponds to momentum conservation and two second-order ordinary differential equations which correspond to energy and nanoparticle volume fraction (species) conservation are derived. Our (group) analysis indicates that, for the similarity solution, the convective heat transfer coefficient and mass transfer velocity are proportional tox-1/4whilst the reaction rate is proportional tox-1/2, wherexis the axial distance from the leading edge of the plate. The effects of the relevant controlling parameters on the dimensionless velocity, temperature, and nanoparticle volume fraction are examined. The accuracy of the technique we have used was tested by performing comparisons with the results of published work and the results were found to be in good agreement. The present computations indicate that the flow is accelerated and temperature enhanced whereas nanoparticle volume fractions are decreased with increasing order of chemical reaction. Furthermore the flow is strongly decelerated, whereas the nanoparticle volume fraction and temperature are enhanced with increasing magnetic field parameter. Increasing convection-conduction parameter increases velocity and temperatures but has a weak influence on nanoparticle volume fraction distribution. The present study demonstrates the thermal enhancement achieved with nanofluids and also magnetic fields and is of relevance to nanomaterials processing.

scholarly journals Boundary-Layer Flow and Heat Transfer of Nanofluids over a Permeable Moving Surface in the Presence of a Coflowing Fluid

2014 ◽  
Vol 6 ◽  
pp. 521236 ◽  
Author(s):  
Amin Noor ◽  
Roslinda Nazar ◽  
Khamisah Jafar ◽  
Ioan Pop
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Free Stream ◽  
Volume Fraction ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Numerical Results ◽  
Nanoparticle Volume Fraction ◽  
Flow And Heat Transfer ◽  
Layer Flow

The steady boundary-layer flow of a nanofluid past a permeable moving flat plate in the presence of a coflowing fluid is theoretically investigated. The plate is assumed to move in the same or opposite direction of the free stream. The governing partial differential equations are first transformed into ordinary differential (similarity) equations before they are solved numerically using a finite-difference scheme along with a shooting method. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and nanoparticle volume fraction profiles for some values of the governing parameters, namely, the plate velocity parameter, the Prandtl number, the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the nanoparticle volume fraction parameter. The numerical results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.

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