scholarly journals Combined Effect of Buoyancy Force and Navier Slip on MHD Flow of a Nanofluid over a Convectively Heated Vertical Porous Plate

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Winifred Nduku Mutuku-Njane ◽  
Oluwole Daniel Makinde
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Porous Plate ◽  
Mhd Flow ◽  
Slip Boundary Condition ◽  
Navier Slip ◽  
Vertical Porous Plate ◽  
Water Based

We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ), magnetic field parameter (Ha), buoyancy effect (Gr), Eckert number (Ec), suction/injection parameter (fw), Biot number (Bi), and slip parameter (β), on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.

Analytical Solution of Slip Flow of Nanofluids over a Permeable Wedge in the Presence of Magnetic field

2011 ◽  
Vol 354-355 ◽  
pp. 45-48 ◽  
Author(s):  
Jia Jia Niu ◽  
Lian Cun Zheng ◽  
Xin Xin Zhang ◽  
Chun Rui Li
Keyword(s):  
Magnetic Field ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Slip Flow ◽  
Slip Boundary Condition ◽  
Skin Friction Coefficient ◽  
Nonlinear Ordinary Differential Equation ◽  
Local Similarity ◽  
Slip Boundary ◽  
Layer Analysis

In this paper, a boundary layer analysis is presented for the slip flow of three types of incompressible viscous nanofluids past a permeable wedge in the presence of a magnetic field. Due to the appearance of a slip boundary condition at the surface, local similarity solution of the reduced nonlinear ordinary differential equation is obtained by the HAM coupled with minimizing the square residual error. The effects of pertinent parameters, such as the magnetic parameter, the solid volume fraction of nanoparticles, the slip parameter and the type of nanofluid on the flow, are analyzed and studied in details. It is found that Ag-water has the highest skin friction coefficient at the surface compared with the others.

scholarly journals MHD Stagnation Point Flow over a Nonlinear Stretching/Shrinking Sheet in Nanofluids

2020 ◽  
Vol 76 (3) ◽  
pp. 139-152
Author(s):  
Nor Hathirah Abd Rahman ◽  
Norfifah Bachok ◽  
Haliza Rosali
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Problem Solver ◽  
Shrinking Sheet ◽  
The Impact ◽  
The Magnetic Field

In this study, an investigation of the steady 2-D magnetohydrodynamiic (MHD) flow of stagnation point past a nonlinear sheet of stretching/shrinking within of a non-uniform transverse magnetic intensity in nanofluids had been analysed. Considered material of nanoparticles such as copper (Cu) in water base fluid with Pr = 6.2 to analyze the influence of volume fraction parameter of nanoparticles and the stretching/shrinking sheet parameter. The governing nonlinear partial differential equations (PDEs) are converted in to the nonlinear ordinary differential equations (ODEs) and use the boundary value problem solver bvp4c in Matlab program to solve numerically through the use of a similarity transformation. The impact of the parameter of the magnetic field on the coefficient of skin friction, the local number of Nusselt and the profiles of velocity and temperature are portrayed and explained physically. The analysis reveals that the magnetic field and volume fraction of nanoparticles affect the velocity and temperature. The dual solutions are achieved where for the shrinking sheet case and the solutions are non-unique, different from a stretching sheet.

Free convection effects on steady MHD flow past a vertical porous plate

1974 ◽  
Vol 66 (3) ◽  
pp. 541-551 ◽  
Author(s):  
V. M. Soundalgekar
Keyword(s):  
Magnetic Field ◽  
Free Convection ◽  
Porous Plate ◽  
Mhd Flow ◽  
Approximate Solutions ◽  
Magnetic Reynolds Number ◽  
Plate Temperature ◽  
Electrically Conducting ◽  
Vertical Porous Plate ◽  
The Difference

An analysis of two-dimensional steady flow of an incompressible, viscous, electrically conducting fluid past an infinite vertical porous plate is carried out under the following assumptions: (i) that the suction velocity normal to the plate is constant, (ii) that the plate temperature is constant, (iii) that the difference between the temperatures of the plate and the free stream is moderately large, causing free convection currents, (iv) that the transversely applied magnetic field and magnetic Reynolds number are very small and hence the induced magnetic field is negligible.Approximate solutions to the coupled nonlinear equations governing the steady velocity and temperature are derived. They are shown graphically. During the course of discussion, the effects of positive and negative G (the Grashof number: G > 0 implies cooling of the plate, G < 0 heating of the plate), of P (the Prandtl number), of positive and negative E (the Eckert number) and of M (the magnetic field parameter) are presented quantitatively.

scholarly journals Lie Group Analysis of Unsteady Flow of Kerosene/Cobalt Ferrofluid Past A Radiated Stretching Surface with Navier Slip and Convective Heating

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 826
Author(s):  
Hossam A. Nabwey ◽  
Waqar A. Khan ◽  
Ahmed M. Rashad
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Skin Friction ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convective Heating ◽  
Navier Slip ◽  
Dimensionless Velocity ◽  
The Mathematical Model ◽  
The Magnetic Field

In this work, we identified the characteristics of unsteady magnetohydrodynamic (MHD) flow of ferrofluid past a radiated stretching surface. Cobalt–kerosene ferrofluid is considered and the impacts of Navier slip and convective heating are additionally considered. The mathematical model which describes the problem was built from some partial differential equations and then converted to self-similar equations with the assistance of the Lie group method; after that, the mathematical model was solved numerically with the aid of Runge–Kutta–Fehlberg method. Graphical representations were used to exemplify the impact of influential parameters on dimensionless velocity and temperature profiles; the obtained results for the skin friction coefficient and Nusselt number were also examined graphically. It was demonstrated that the magnetic field, Navier slip, and solid volume fraction of ferroparticles tended to reduce the dimensionless velocity, while the radiation parameter and Biot number had no effects on the dimensionless velocity. Moreover, the magnetic field and solid volume fraction increase skin friction whereas Navier slip reduces the skin friction. Furthermore, the Navier slip and magnetic field reduce the Nusselt number, whereas solid volume fraction of ferroparticles, convective heating, and radiation parameters help in increasing the Nusselt number.

scholarly journals Dual Solutions and Stability Analysis of a Hybrid Nanofluid over a Stretching/Shrinking Sheet Executing MHD Flow

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 276 ◽  
Author(s):  
Liaquat Ali Lund ◽  
Zurni Omar ◽  
Ilyas Khan ◽  
El-Sayed M. Sherif
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Temporal Stability ◽  
Mhd Flow ◽  
Numerical Results ◽  
Dual Solutions ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

In this paper, the unsteady magnetohydrodynamic (MHD) flow of hybrid nanofluid (HNF) composed of C u − A l 2 O 3 /water in the presence of a thermal radiation effect over the stretching/shrinking sheet is investigated. Using similarity transformation, the governing partial differential equations (PDEs) are transformed into a system of ordinary differential equations (ODEs), which are then solved by using a shooting method. In order to validate the obtained numerical results, the comparison of the results with the published literature is made numerically as well as graphically and is found in good agreements. In addition, the effects of many emerging physical governing parameters on the profiles of velocity, temperature, skin friction coefficient, and heat transfer rate are demonstrated graphically and are elucidated theoretically. Based on the numerical results, dual solutions exist in a specific range of magnetic, suction, and unsteadiness parameters. It was also found that the values of f ″ ( 0 ) rise in the first solution and reduce in the second solution when the solid volume fraction ϕ C u is increased. Finally, the temporal stability analysis of the solutions is conducted, and it is concluded that only the first solution is stable.

Radiation and non-uniform heat sink/source effects on 2D MHD flow of CNTs-H2O nanofluid over a flat porous plate

2019 ◽  
Vol 16 (4) ◽  
pp. 791-809
Author(s):  
Himanshu Upreti ◽  
Sawan Kumar Rawat ◽  
Manoj Kumar
Keyword(s):  
Magnetic Field ◽  
Heat Sink ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Porous Plate ◽  
Mhd Flow ◽  
Particle Volume ◽  
Content Type ◽  
Uniform Heat ◽  
The Impact

Purpose The purpose of this paper is to examine the velocity and temperature profile for a two-dimensional flow of single- and multi-walled nanotubes (CNTs)/H2O nanofluid over a flat porous plate, under the impact of non-uniform heat sink/source and radiation. The influence of suction/blowing, viscous dissipation and magnetic field is also incorporated. Design/methodology/approach The solution of the PDEs describing the flow of nanofluid is accomplished using Runge–Kutta–Fehlberg approach with shooting scheme. Findings Quantities of physical importance such as local Nusselt number and skin friction coefficient for both types of nanotubes are computed and shown in tables. Also, the impact of copious factors like Prandtl number, magnetic field, Eckert number, porosity parameter, radiation parameter, non-linear stretching parameter, injection/suction, heating variable, particle volume fraction and non-uniform heat sink/source parameter on temperature and velocity profile is explained in detail with the aid of graphs. Originality/value Till date, no study has been reported that examines the role of radiation and non-uniform heat sink/source on MHD flow of CNTs‒water nanofluid over a porous plate. The numerical outcomes attained for the existing work are original and their originality is authenticated by comparing them with earlier published work. This problem is of importance, as there are many applications of the fluid flowing over a flat porous plate.

MHD Flow of Non-Newtonian Molybdenum Disulfide Nanofluid in a Converging/Diverging Channel with Rosseland Radiation

2020 ◽  
Vol 401 ◽  
pp. 92-106 ◽  
Author(s):  
J. Raza ◽  
Fateh Mebarek-Oudina ◽  
Paras Ram ◽  
S. Sharma
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Molybdenum Disulfide ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Mhd Flow ◽  
Opening Angle ◽  
Physical Parameters ◽  
Two Dimensional Flow

The steady two-dimensional flow of an incompressible non-Newtonian Molybdenum Disulfide nanofluid in the presence of source or sink between two stretchable or shrinkable walls under the influence of thermal radiation is investigated numerically. A generalized transformation is applied to convert the constructed set of partial differential equations (PDEs) into the system of non-linear coupled ordinary differential equations (ODEs). The obtained system of ODEs are solved by using Runge-Kutta 4th and 5th order. The influence of physical parameters, shrinking/ stretching parameter, Casson parameter, Hartmann number, Reynolds number, solid volume fraction, opening angle of the channel and radiation parameter on the velocity and temperature distribution are observed for converging and diverging channels. It is noticed that thermal boundary layer thickness is diminished for increased thermal radiation resulting in gradual temperature fall. The results also reveal that velocity and temperature profile both are elevated on raising the stretching parameter and Hartmann number. A comparative analysis is made out to validate the present results.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subramanian Muthukumar ◽  
Selvaraj Sureshkumar ◽  
Arthanari Malleswaran ◽  
Murugan Muthtamilselvan ◽  
Eswari Prem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Bottom Wall ◽  
Uniform Heating ◽  
The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

scholarly journals Numerical study of thermal radiation and mass transfer effects on free convection flow over a moving vertical porous plate using cubic B-spline collocation method

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
M. Abu zeid ◽  
Khalid K. Ali ◽  
M. A. Shaalan ◽  
K. R. Raslan
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Free Convection ◽  
Thermal Radiation ◽  
Porous Plate ◽  
Convection Flow ◽  
Spline Collocation ◽  
Free Convection Flow ◽  
B Spline ◽  
Vertical Porous Plate

Abstract In this paper, we present a numerical method based on cubic B-spline function for studying the effects of thermal radiation and mass transfer on free convection flow over a moving vertical porous plate. Similarity transformations reduced the governing partial differential equations of the fluid flow to a system of nonlinear ordinary differential equations which are solved numerically using a cubic B-spline collocation method. The effects of various physical parameters on the velocity, temperature, and concentration distributions are shown graphically, and the numerical values of physical quantities like skin friction, Nusselt number, and Sherwood number for various parameters are presented in tabular form and discussed.

NUMERICAL SIMULATION OF MARANGONI MAGNETOHYDRODYNAMIC BIO-NANOFLUID CONVECTION FROM A NON-ISOTHERMAL SURFACE WITH MAGNETIC INDUCTION EFFECTS: A BIO-NANOMATERIAL MANUFACTURING TRANSPORT MODEL

2014 ◽  
Vol 14 (03) ◽  
pp. 1450039 ◽  
Author(s):  
O. ANWAR BÉG ◽  
M. FERDOWS ◽  
S. SHAMIMA ◽  
M. NAZRUL ISLAM
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Prandtl Number ◽  
Stream Function ◽  
Magnetic Induction ◽  
Body Force ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Force Parameter

Laminar magnetohydrodynamic Marangoni-forced convection boundary layer flow of a water-based biopolymer nanofluid containing nanoparticles from a non-isothermal plate is studied. Magnetic induction effects are incorporated. A variety of nanoparticles are studied, specifically, silver, copper, aluminium oxide and titanium oxide. The Tiwari–Das model is utilized for simulating nanofluid effects. The normalized ordinary differential boundary layer equations (mass, magnetic field continuity, momentum, induced magnetic field and energy conservation) are solved subject to appropriate boundary conditions using Maple shooting quadrature. The influence of Prandtl number (Pr), magnetohydrodynamic body force parameter (β), reciprocal of magnetic Prandtl number (α) and nanofluid solid volume fraction (φ) on velocity, temperature and magnetic stream function distributions is investigated in the presence of strong Marangoni effects (ξ i.e., Marangoni parameter is set as unity). Magnetic stream function is accentuated with body force parameter. The flow is considerably decelerated as is magnetic stream function gradient, with increasing nanofluid solid volume fraction, whereas temperatures are significantly enhanced. Interesting features in the flow regime are explored. The study finds applications in the fabrication of complex biomedical nanofluids, biopolymers, etc.

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