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.

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 The Impact of Sinusoidal Surface Temperature on the Natural Convective Flow of a Ferrofluid along a Vertical Plate

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1014 ◽  
Author(s):  
Essam R. EL-Zahar ◽  
Ahmed M. Rashad ◽  
Laila F. Seddek
Keyword(s):  
Magnetic Field ◽  
Nusselt Number ◽  
Surface Temperature ◽  
Drag Coefficient ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Grid Points ◽  
The Impact ◽  
Sinusoidal Surface ◽  
The Magnetic Field

The spotlight of this investigation is primarily the effectiveness of the magnetic field on the natural convective for a Fe3O4 ferrofluid flow over a vertical radiate plate using streamwise sinusoidal variation in surface temperature. The energy equation is reduplicated by interpolating the non-linear radiation effectiveness. The original equations describing the ferrofluid motion and energy are converted into non-dimensional equations and solved numerically using a new hybrid linearization-differential quadrature method (HLDQM). HLDQM is a high order semi-analytical numerical method that results in analytical solutions in η -direction, and so the solutions are valid overall in the η domain, not only at grid points. The dimensionless velocity and temperature curves are elaborated. Furthermore, the engineering curiosity of the drag coefficient and local Nusselt number are debated and sketched in view of various emerging parameters. The analyzed numerical results display that applying the magnetic field to the ferroliquid generates a dragging force that diminishes the ferrofluid velocity, whereas it is found to boost the temperature curves. Furthermore, the drag coefficient sufficiently minifies, while an evolution in the heat transfer rate occurs as nanoparticle volume fraction builds. Additionally, the augmentation in temperature ratio parameter signifies a considerable growth in the drag coefficient and Nusselt number. The current theoretical investigation may be beneficial in manufacturing processes, development of transport of energy, and heat resources.

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.

scholarly journals Mixed Convection of a Radiating Magnetic Nanofluid past a Heated Permeable Stretching/Shrinking Sheet in a Porous Medium

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Feleke Buta Tadesse ◽  
Oluwole Daniel Makinde ◽  
Lemi Guta Enyadene
Keyword(s):  
Magnetic Field ◽  
Porous Medium ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Volume Fraction ◽  
Flow Stability ◽  
Collective Effects ◽  
Shrinking Sheet ◽  
Convective Heating

This paper analyzes the collective effects of buoyancy force, thermal radiation, convective heating, and magnetic field on stagnation point flow of an electrically conducting nanofluid past a permeable stretching/shrinking sheet in a porous medium. Similarity transformations are used on the resulting nonlinear partial differential equations to transfer into a system of coupled nonlinear ordinary differential equations. The fourth-fifth-order Runge–Kutta–Fehlberg method with shooting technique is applied to solve numerically. Results are obtained for dimensionless velocity, temperature, and nanoparticle volume fraction as well as the skin friction and local Nusselt and Sherwood numbers. The results indicate the existence of two real solutions for the shrinking sheet in the range of λ c < λ < 0 . The fluid flow stability is maintained by increasing the magnetic field effect, whereas the porous medium parameter inflates the flow stability. It is also noted that both the skin friction coefficient and the local Sherwood number approximately decline with the intensification of thermal radiation within the range from 9.83% to 14% and the range from 48.86% to 78.66%, respectively. It is also evident in the present work that the local Nusselt number upsurges with the porous and suction/injection parameters.

Analytical Investigation of Nusselt Number and Skin Friction of Fluid Flow Over a Stretching Sheet Using Optimal Homotopy Asymptotic Method

2020 ◽  
Vol 12 (5) ◽  
pp. 657-661
Author(s):  
Zohreh Aliannejadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Differential Equations ◽  
Skin Friction ◽  
Flow And Heat Transfer ◽  
Optimal Homotopy Asymptotic Method ◽  
The Magnetic Field

In many cases such as production of metal sheets, the behavior of fluid flow and heat transfer in the neighborhood of a hot plate is very important. The CFD simulation of fluid flow is a widespread study that reveals detail information about the fluid flow in the calculated domain. In this study, the flow and heat transfer of a specific fluid in the above area of a stretching plate is examined analytically to find the variation of skin friction and Nusselt number. For this purpose, the similarity transformations can be employed to achieve the ordinary differential equations from the governing partial differential equations. The optimal homotopy asymptotic method (OHAM) is used to solve the ordinary differential equations which is applicable in solving of nonlinear equations. The effects of magnetic field on the analytical results from solving the equations are evaluated in detail. It is found that the thickness of the flow boundary layer decreases and the thickness of the thermal boundary layer increases by increasing in the magnetic field. Moreover, the Nusselt number is lower and skin friction is higher for the higher values of the magnetic field.

scholarly journals Hydrothermal and Entropy Investigation of Ag/MgO/H2O Hybrid Nanofluid Natural Convection in a Novel Shape of Porous Cavity

2021 ◽  
Vol 11 (4) ◽  
pp. 1722
Author(s):  
Nidal Abu-Libdeh ◽  
Fares Redouane ◽  
Abderrahmane Aissa ◽  
Fateh Mebarek-Oudina ◽  
Ahmad Almuhtady ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Hybrid Nanofluid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Nanofluid Flow ◽  
The Magnetic Field

In this study, a new cavity form filled under a constant magnetic field by Ag/MgO/H2O nanofluids and porous media consistent with natural convection and total entropy is examined. The nanofluid flow is considered to be laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The results of the values of Darcy (Da), Hartmann (Ha) and Rayleigh (Ra) numbers, porosity (εp), and the properties of solid volume fraction (ϕ) and flow fields were studied. The findings show that with each improvement in the Ha number, the heat transfer rate becomes more limited, and thus the magnetic field can be used as an outstanding heat transfer controller.

scholarly journals Heat transfer augmentation of magnetohydrodynamics natural convection in L-shaped cavities utilizing nanofluids

2012 ◽  
Vol 16 (2) ◽  
pp. 489-501 ◽  
Author(s):  
Ehsan Sourtiji ◽  
Seyed Hosseinizadeh
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Flow Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
The Magnetic Field

A numerical study of natural convection heat transfer through an alumina-water nanofluid inside L-shaped cavities in the presence of an external magnetic field is performed. The study has been carried out for a wide range of important parame?ters such as Rayleigh number, Hartmann number, aspect ratio of the cavity and solid volume fraction of the nanofluid. The influence of the nanoparticle, buoyancy force and the magnetic field on the flow and temperature fields have been plotted and discussed. The results show that after a critical Rayleigh number depending on the aspect ratio, the heat transfer in the cavity rises abruptly due to some significant changes in flow field. It is also found that the heat transfer enhances in the presence of the nanoparticles and increases with solid volume fraction of the nanofluid. In addition, the performance of the nanofluid utilization is more effective at high Ray?leigh numbers. The influence of the magnetic field has been also studied and de?duced that it has a remarkable effect on the heat transfer and flow field in the cavity that as the Hartmann number increases the overall Nusselt number is significantly decreased specially at high Rayleigh numbers.

scholarly journals A Tilted Lorentz Force Effect on Porous Media Filled with Nanofluid

2018 ◽  
Vol 48 (2) ◽  
pp. 50-71
Author(s):  
M. Muthtamilselvan ◽  
S. Sureshkumar
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Inclination Angle ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Staggered Grid ◽  
Convection Flow ◽  
The Magnetic Field

Abstract This paper is intended to investigate the effects of an inclined magnetic field on the mixed convection flow in a lid-driven porous enclosure filled with nanofluid. Both the left and right vertical walls of the cavity are thermally insulated while the bottom and top horizontal walls are maintained at constant but different temperatures. The governing equations are solved numerically by using finite volume method on a uniformly staggered grid system. The computational results are obtained for various combinations of Richardson number, Darcy number, Hartmann number, inclination angle of magnetic field, and solid volume fraction. It is found that the presence of magnetic field deteriorates the fluid flow, which leads to a significant reduction in the overall heat transfer rate. The inclination angle of magnetic field plays a major role in controlling the magnetic field strength and the overall heat transfer rate is enhanced with the increase of inclination angle of magnetic field. Adding the nanoparticles in the base fluid significantly increases the overall heat transfer rate in the porous medium whether the magnetic field is considered or not.

scholarly journals Slip Microrotation Flow of Silver-Sodium Alginate Nanofluid via Mixed Convection in a Porous Medium

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3232
Author(s):  
Hossam A. Nabwey ◽  
Ahmed M. Rashad ◽  
Waqar A. Khan
Keyword(s):  
Porous Medium ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Skin Friction ◽  
Sodium Alginate ◽  
Volume Fraction ◽  
Colloidal Suspension ◽  
Solid Volume Fraction ◽  
Velocity Slip ◽  
Research Attention

In the previous decennium, considerable applications ofnanoparticles have been developed in the area of science. Nanoparticles with micropolar fluid suspended in conventional fluids can increase the heat transfer. Micropolar fluids have attracted much research attention because of their use in industrial processes. Exotic lubricants, liquid crystal solidification, cooling of a metallic plate in a bath, extrusion of metals and polymers, drawing of plastic films, manufacturing of glass and paper sheets, and colloidal suspension solutions are just a few examples. The primary goal of this studywas to see how radiation and velocity slip affect the mixed convection of sodium alginate nanofluid flow over a non-isothermal wedge in a saturated porous media.In this communication, theTiwari and Das model was employed to investigate the micropolarnanofluid flow via mixed convection over aradiated wedge in a saturated porous medium with the velocity slip condition. Nanoparticles of silver (Ag) wreused in asodium alginate base fluid. The intended system of governing equations is converted to a set of ordinary differential equations and then solved applying the finite difference method. Variousfluid flows, temperatures, and physical quantities of interest were examined. The effects of radiation on the skin friction are negligible in the case of forced and mixed convection, whereas radiation increases the skin friction in free convection. It is demonstrated that the pressure gradient, solid volume fraction, radiation, and slip parameters enhance the Nusselt number, whereas the micropolar parameter reduces the Nusselt number.

Natural convection analysis flow of Al2O3-Cu/water hybrid nanofluid in a porous conical enclosure subjected to the magnetic field

2020 ◽  
Vol 92 (1) ◽  
pp. 10904 ◽  
Author(s):  
Rabeh Slimani ◽  
Abderrahmane Aissa ◽  
Fateh Mebarek-Oudina ◽  
Umair Khan ◽  
M. Sahnoun ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Hybrid Nanofluid ◽  
Porosity Ratio ◽  
The Magnetic Field

The current study investigates MHD natural convection heat transfer of a hybrid nanofluid in a truncated cone along with transparent domains having the stimulus of an inherent constant magnetic field. The governing equations subject to the physical boundary conditions are solved numerically by using the Galerkin finite element method. The effects of the various parameters involved in the problem such as the Rayleigh number Ra (ranging between 103 and 106), the Hartmann number Ha (ranging between 0 and 60), and the porosity ratio ε (0.1–0.9) are examined. Moreover, the effects of Da which represents the Darcy number (between 10‑3 and 10‑1) and the volume fraction of nanoparticles ϕ for the dissipated nanoparticles of Al2O3-Cu are reported in terms of the streamlines and isotherms distributions as well as the Nusselt number. Such parameters are critical control parameters for both the fluid flow and the rate of heat transfer of the natural convection in the annular space. The solution outcomes proof that the average Nusselt number varies directly with the dynamic field flowing through a porous media, whereas it behaves inversely with the magnetic field.

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