scholarly journals Magnetohydrodynamic Flow of a Bingham Fluid in a Vertical Channel: Mixed Convection

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 154
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria
Keyword(s):  
Magnetic Field ◽  
Mixed Convection ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Reverse Flow ◽  
Vertical Channel ◽  
Bingham Fluid ◽  
Induced Magnetic Field ◽  
Bingham Number ◽  
External Uniform Magnetic Field

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.

Reverse Flow in Magnetoconvection of Two Immiscible Fluids in a Vertical Channel

2017 ◽  
Vol 139 (10) ◽  
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Mixed Convection ◽  
Newtonian Fluid ◽  
Hartmann Number ◽  
Reverse Flow ◽  
Vertical Channel ◽  
Boussinesq Approximation ◽  
Immiscible Fluids ◽  
Induced Magnetic Field

This paper concerns the study of the influence of an external magnetic field on the reverse flow occurring in the steady mixed convection of two Newtonian immiscible fluids filling a vertical channel under the Oberbeck–Boussinesq approximation. The two isothermal boundaries are kept either at different or at equal temperatures. The velocity, the temperature, and the induced magnetic field are obtained analytically. The results are presented graphically and discussed for various values of the parameters involved in the problem (in particular, the Hartmann number and the buoyancy coefficient) and are compared with those for a single Newtonian fluid. The occurrence of the reverse flow is explained and carefully studied.

Mixed Magnetoconvection of Nanofluids in a Long Vertical Porous Channel

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria
Keyword(s):  
Magnetic Field ◽  
Uniform Magnetic Field ◽  
Volume Fraction ◽  
Reverse Flow ◽  
Boussinesq Approximation ◽  
Porous Channel ◽  
Nanoparticle Volume Fraction ◽  
Induced Magnetic Field ◽  
Two Phase ◽  
External Uniform Magnetic Field

Abstract This paper aimed to study the flow of a nanofluid in a long vertical porous channel when an external uniform magnetic field is impressed. The Buongiorno two-phase model of nanofluid is supposed to be slightly compressible in order to assume the Oberbeck–Boussinesq approximation. The velocity, the induced magnetic field, the temperature, and the nanoparticle volume fraction are analytically obtained. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of plots illustrating the influence of various parameters involved in the problem is presented and discussed.

Electrically driven cylindrical free shear flows under an axial uniform magnetic field

2021 ◽  
Vol 57 (2) ◽  
pp. 229-250
Keyword(s):  
Magnetic Field ◽  
Electric Current ◽  
Applied Field ◽  
Uniform Magnetic Field ◽  
Shear Flows ◽  
Hartmann Number ◽  
Induced Magnetic Field ◽  
Free Shear Layers ◽  
Moderate Magnetic Field ◽  
Almost All

We consider a mathematical model of two-dimensional electrically driven laminar axisymmetric circular free shear flows in a cylindrical vessel under the action of an applied axial uniform magnetic field. The mathematical approach is based on the studies by J.C.R. Hunt and W.E. Williams (J. Fluid. Mech., 31, 705, 1968). We solve a system of stationary partial differential equations with two unknown functions of velocity and induced magnetic field. The flows are generated as a result of the interaction of the electric current injected into the liquid and the applied field using one or two pairs of concentric annular electrodes located apart on the end walls. Two lateral free shear layers and two Hartmann layers on the end walls and a quasi-potential flow core between them emerge when the Hartmann number Ha >> 1. As a result, almost all injected current passes through these layers. Depending on the direction of the current injection, coinciding or two counter flows between the end walls are realized. The Hartmann number varies in a range from 2 to 300. When a moderate magnetic field (Ha = 50) is reached, the flow rate and the induced magnetic field flux cease to depend on the magnitude of the applied field but depend on the injected electric current value. Increasing magnetic field leads only to inner restructuring of the flows. Redistributions of velocities and induced magnetic fields, electric current density versus Hartmann number are analyzed. Figs 18, Refs 21.

MHD natural convection of Cu/H2O nanofluid in a horizontal semi-cylinder with a local triangular heater

2018 ◽  
Vol 28 (12) ◽  
pp. 2979-2996 ◽  
Author(s):  
A.S. Dogonchi ◽  
Mikhail A. Sheremet ◽  
Ioan Pop ◽  
D.D. Ganji
Keyword(s):  
Magnetic Field ◽  
Rayleigh Number ◽  
Free Convection ◽  
Shape Factor ◽  
Uniform Magnetic Field ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Horizontal Cylinder ◽  
Content Type ◽  
Nanoparticles Volume Fraction

Purpose The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM). Design/methodology/approach Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM. Findings The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number. Originality/value A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Reverse Flow ◽  
Second Order ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Variable Surface

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

scholarly journals Effects of Thermal Radiation, Heat Generation, and Induced Magnetic Field on Hydromagnetic Free Convection Flow of Couple Stress Fluid in an Isoflux-Isothermal Vertical Channel

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Hasan Nihal Zaidi ◽  
Mohammed Yousif ◽  
S. Nazia Nasreen
Keyword(s):  
Magnetic Field ◽  
Couple Stress ◽  
Channel Wall ◽  
Vertical Channel ◽  
Convection Flow ◽  
Induced Current ◽  
Induced Magnetic Field ◽  
Radiation Heat ◽  
Free Convection Flow ◽  
Radiation Heat Generation

The study scrutinizes the effects of thermal radiation, heat generation, and induced magnetic field on steady, fully developed hydromagnetic free convection flow of an incompressible viscous and electrically conducting couple stress fluid in a vertical channel. The channel walls are maintained at an isoflux-isothermal condition, such that the left channel wall is maintained at a constant heat flux. In contrast, the right channel wall is maintained at a constant temperature. The governing simultaneous equations are solved analytically utilizing the method of undetermined coefficient, and closed form solutions in dimensionless form have been acquired for the velocity field, the induced magnetic field, and the temperature field. The expression for the induced current density has been also obtained. A parametric study for the velocity, temperature, and induced magnetic field profiles, as well as for the skin-friction coefficient, Nusselt number, and induced current density, is conducted and discussed graphically.

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