This study is interested in the effect of an axial magnetic field imposed on incompressible flow of electrically conductive fluid between two horizontal coaxial cylinders. The imposed magnetic field is assumed uniform and constant. The effect of heat generation due to viscous dissipation is also taken into account. The inner and outer cylinders are maintained at different uniform temperatures. The movement of the fluid is due to rotation of the cylinder with a constant speed. An exact solution of the equations governing the flow was obtained in the form of Bessel functions. A finite difference implicit scheme was used in the numerical solution. The velocity and temperature distributions were obtained with and without the magnetic field. The results show that for different values of the Hartmann number, the velocity between the two cylinders decreases as the Hartmann number increases. Also, it is found that by increasing the Hartmann number, the average Nusselt number decreases. On the other hand, the Hartmann number does not affect the temperature.
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... Using external forces method to control the flow and solute distribution in the melt has been experimentally and numerically investigated (Brown 1989;Muller and Ostrogorsky 1994;Lukka 2006;Stelian and Duffar 2015;Aberkane et al. 2015). Among the studied methods for optimization of crystal growth, the most important are the magnetic fields (Lan 2006;Inatomi et al. 2000;Khan et al. 2013) and vibration (Lan 2000). ...
The present work is proposed a numerical parametric study of heat and mass transfer in a rotating vertical cylinder during the solidification of a binary metallic alloy. The aim of this paper is to present an enthalpy formulation based on the fixed grid methodology for the numerical solution of convective-diffusion during the phase change in the case of the steady crucible rotation. The extended Darcy model including the time derivative and Coriolis terms was applied as momentum equation. It was found that the buoyancy driven flow and solute distribution can be affected significantly by the rotating cylinder. The problem is governed by the Navier-Stokes equations coupled with the conservation laws of energy and solute. The resulting system was discretized by the control volume method and solved by the SIMPLER algorithm proposed by Patankar. A computer code was developed and validated by comparison with previous studies. It can be observed that the forced convection introduced by rotation, dramatically changes the flow and solute distribution at the interface (liquid-mushy zone). The effect of Reynolds number on the Nusselt number, flow and solute distribution is presented and discussed.
The effects of joule heating on MHD natural convection flow from a horizontal circular cylinder along the outer
surface from the lower stagnation point to the upper stagnation point in presence of pressure stress work and viscous
dissipation is investigated. The results have been obtained by transforming the governing boundary layer equations
into a system of non-dimensional equations and by applying implicit finite difference method together with Newton’s
linearization approximation. Numerical results for different values of the magnetic parameter, joule heating parameter
and Prandtl number have been obtained. The velocity profiles, temperature distributions, skin friction co-efficient and
the rate of heat transfer have been presented graphically for the effects of the aforementioned parameters. Results are
compared with previous investigation.
Unsteady hydromagnetic Couette flow of class-II of a viscous incompressible electrically conducting fluid in a rotating system with Hall effects in the presence of a uniform transverse magnetic field is studied. Both the fluid and plates of the channel are assumed to be at rest when time t'≤0 and fluid flow within the channel is induced due to non-torsional oscillations of the upper plate in its own plane with a velocity U(t') about a non-zero uniform velocity U0 at time t'>0. Exact solution of the governing equations is obtained by Laplace transform technique. Asymptotic behavior of the solution is analyzed for small and large values of rotation parameter K2 and magnetic parameter M2 when time t>>1. The numerical values of the fluid velocity are depicted graphically whereas that of shear stress at the plates are presented in tabular form for various values of Hall current parameter m, rotation parameter K2, magnetic parameter M2 and frequency parameter ω.
This work concerns the dynamic and the thermal study between a heated rotating solid and a pulsatile flow evolving periodically in a cylindrical cavity. The reference frequency of pulsatile flow was determined by the evolution regime to his stationary state. The frequency varied from the 1/3 reference frequency to 10 once this value. The periodicity is assured by the periodical inlet conditions. The numerical study concerns the Reynolds number less than 100 and the Taylor number less than 500, in order to avoid the presence of instabilities in the flow. Two numerical methods have been used; the finite-elements method and the finite-differences combined with ADI scheme. The fluid considered is the air with constant physiques proprieties. The influence of ratio conductivity, K, between solid conductivity and fluid conductivity, has taken from K = 10⁻² to K = 10⁺³. The influence of the two periodical combined motions; rotation of the solid and axial flow, on the thermal transfer mechanism is studied. The results show that the velocity components are in phase with the rate flow but the pressure and the different thermal parameters are in difference of phase. We note also the oscillatory shape of different dynamical and thermal parameters. The frequency influence appears at the greater values. The Nusselt number is proportional to the frequencies. The results are in good agreement with previous numerical and experimental studies.
Exact solutions for fully developed natural convection
in open-ended vertical concentric annuli under a
radial magnetic field are presented. Expressions for velocity
field, temperature field, mass flow rate and skin-friction
are given, under more general thermal boundary
conditions. It is observed that both velocity as well as
temperature of the fluid is more in case of isothermal
condition compared with constant heat flux case when gap
between cylinders is less or equal to radius of inner cylinder
while reverse phenomena occur when the gap between
cylinders is greater than radius of inner cylinder.
In the present paper, first of all, it is proved that the 'principle of the exchange of stabilities' is not, in general valid, for the case of free boundaries and then a sufficient condition is derived for the validity of this principle in ferromagnetic convection, for the case of free boundaries, in a horizontal ferrofluid saturated porous layer in the presence of a uniform vertical magnetic field and uniform rotation about the vertical axis.
In the present work, effects of using magnetic nanofluid and also applying an external magnetic field on the critical heat flux (CHF) of subcooled flow boiling has been studied experimentally. The experiments have been applied in upward flow direction in a 12 mm I.D., 19 mm O.D. and 0.75 m length annular test section. Inlet subcooling was kept constant and the mass flux was varied in the range of 0-150 kg/m2.s while the exit was at atmospheric pressure. Ferrofluids with water as a base fluid and 0.01 and 0.1% volume fractions of Fe3O4 nanoparticles were utilized. The results indicates that the CHF of subcooled flow boiling was increased by using nanofluid as a working fluid, which was mainly due to the deposition of the nanoparticles on the surface of inner tube, and consequently, increasing the surface wettability. Furthermore, an external magnetic field by utilizing quadrupole magnet was applied on the subcooled boiling flow at the near exit of the test section. The obtained results indicated that applying magnetic field caused an enhancement in CHF values of both pure water and ferrofluids. The main reasons for such effect of magnetic field can be justified to changing water properties under action of the magnetic field, single-phase convection heat transfer enhancement, suppression of nucleate boiling, and stabilization of boiling flow.
In this study magnetohydrodynamic effect on free convection of nanofluid in an eccentric semi-annulus filled is considered. The effective thermal conductivity and viscosity of nanofluid are calculated by the Maxwell–Garnetts (MG) and Brinkman models, respectively. Lattice Boltzmann method is applied to simulate this problem. This investigation compared with other works and found to be in excellent agreement. Effects of the Hartmann number, nanoparticle volume fraction, Rayleigh numbers and position of the inner circular cylinder on flow and heat transfer characteristics are examined. Also a correlation of Nusselt number corresponding to active parameters is presented. The results show that Nusselt number has direct relationship with nanoparticle volume fraction and Rayleigh number but it has inverse relationship with Hartmann number and position of inner cylinder at high Rayleigh number. Also it can be concluded that heat transfer enhancement increases with increase of Hartmann number and decreases with augment of Raleigh number.
In this paper, the effect of a magnetic field on natural convection in a half-annulus enclosure with one wall under constant heat flux using control volume based finite element method. The fluid in the enclosure is a water-based nanofluid containing Cu nanoparticles. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Numerical simulations were performed for different governing parameters namely the Hartmann number, Rayleigh number and inclination angle of enclosure. The results indicate that Hartmann number and the inclination angle of the enclosure can be control parameters at different Rayleigh number. In presence of magnetic field velocity field retarded and hence convection and Nusselt number decreases.
Effect of static radial magnetic field on natural convection heat transfer in a horizontal cylindrical annulus enclosure filled with nanofluid is investigated numerically using the Lattice Boltzmann method (LBM). The inner and outer cylinder surfaces are maintained at the different uniform temperatures. The surfaces are non-magnetic material. The investigation is carried out for different governing parameters namely, Hartmann number, nanoparticle volume fraction and Rayleigh number. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The results reveal that the flow oscillations can be suppressed effectively by imposing an external radial magnetic field. Also, it is found that the average Nusselt number is an increasing function of nanoparticle volume fraction and Rayleigh number, while it is a decreasing function of Hartmann number.
In the present study, mixed convection of a fluid in the fully developed region in a horizontal concentric cylindrical annulus with different uniform wall temperatures, is numerically investigated in both steady and unsteady states in the presence of radial MHD force, as well as in consideration of heat generation due to viscous dissipation. Also, cylinder length is assumed to be infinite. Moreover, radiation heat transfer from the hot surface is assumed to be negligible. Buoyancy effects are also considered, along with Boussinesq approximation. The forced flow is induced by the cold rotating outer cylinder at slow constant angular velocity, with its axis at the center of the annulus. Investigations are made for various combinations of non-dimensional group numbers; Reynolds number (ReRe), Rayleigh number (RaRa), Hartmann number (HaHa), Eckert number (EckEck) and annulus gap width ratio (σ0σ0). These dimensionless parameters used in the present study will be investigated over a wide range to present the basic flow patterns and isotherms in a concentric cylindrical annulus. A finite volume scheme, consisting of the Tri-Diagonal Matrix Algorithm (TDMA), is used to solve governing equations, which are continuity, two-dimensional momentum and energy, by the SIMPLE algorithm. The numerical results reveal that the flow and heat transfer are suppressed more effectively by imposing an external magnetic field. Furthermore, it is found that the external magnetic field causes the fluid velocity and temperature to be suppressed more effectively. Moreover, it will be shown that viscous dissipation terms have significant effects in situations with high values of Eckert and Prandtl number and low values of Reynolds number.