A Differential Quadrature Solution of MHD Natural Convection in an Inclined Enclosure With a Partition

2008 ◽  
Vol 130 (2) ◽  
Author(s):  
Kamil Kahveci ◽  
Semiha Öztuna
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Inclination Angle ◽  
Hartmann Number ◽  
Differential Quadrature ◽  
Flow And Heat Transfer ◽  
Inclined Enclosure ◽  
Vorticity Generation

Magnetohydrodynamics natural convection in an inclined enclosure with a partition is studied numerically using a differential quadrature method. Governing equations for the fluid flow and heat transfer are solved for the Rayleigh number varying from 104 to 106, the Prandtl numbers (0.1, 1, and 10), four different Hartmann numbers (0, 25, 50, and 100), the inclination angle ranging from 0degto90deg, and the magnetic field with the x and y directions. The results show that the convective flow weakens considerably with increasing magnetic field strength, and the x-directional magnetic field is more effective in reducing the convection intensity. As the inclination angle increases, multicellular flows begin to develop on both sides of the enclosure for higher values of the Hartmann number if the enclosure is under the x-directional magnetic field. The vorticity generation intensity increases with increase of Rayleigh number. On the other hand, increasing Hartmann number has a negative effect on vorticity generation. With an increase in the inclination angle, the intensity of vorticity generation is observed to shift to top left corners and bottom right corners. Vorticity generation loops in each region of enclosure form due to multicelluar flow for an x-directional magnetic field when the inclination angle is increased further. In addition, depending on the boundary layer developed, the vorticity value on the hot wall increases first sharply with increasing y and then begins to decrease gradually. For the high Rayleigh numbers, the average Nusselt number shows an increasing trend as the inclination angle increases and a peak value is detected. Beyond the peak point, the foregoing trend reverses to decrease with the further increase of the inclination angle. The results also show that the Prandtl number has only a marginal effect on the flow and heat transfer.

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.

Numerical simulation of natural convection within wavy square enclosure filled with nanofluid under magnetic field using EFGM with parallel algorithm

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Surabhi Nishad ◽  
Sapna Jain ◽  
Rama Bhargava
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Inclination Angle ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Content Type ◽  
The Magnetic Field ◽  
Field Inclination

Purpose This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach. Design/methodology/approach The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B0 has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid. Findings The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease. Originality/value The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.

Numerical investigation of magnetic field inclination angle on transient natural convection in an enclosure filled with nanofluid

2014 ◽  
Vol 31 (7) ◽  
pp. 1342-1360 ◽  
Author(s):  
Masoud Kharati Koopaee ◽  
Iman Jelodari
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Rayleigh Number ◽  
Thermal Behavior ◽  
Inclination Angle ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Field Orientation ◽  
Content Type ◽  
Maximum Value

Purpose – The objective of present research is to characterize the unsteady thermal behavior of a square enclosure filled with water-Al2O3 nanofluids in the presence of oriented magnetic fields. The purpose this paper is to study the effect of pertinent parameters on the transient natural convection in the enclosure. Design/methodology/approach – In this research, an in-house implicit finite volume code based on the SIMPLE algorithm is utilized for numerical calculations. To ensure the accuracy of results, comparisons are also made with previous works in literature. In this study, a constant strength magnetic field is concerned and for Rayleigh numbers of Ra=103, 104 and 105 the effect of magnetic field orientation with respect to the case of zero inclination on the thermal performance of cavity is investigated at Hartmann number range of Ha=15-90. In the present work, the nano-particle volume fractions range from φ=0-0.06. Findings – Results show that when Rayleigh number is Ra=103, the inclination angle, solid particles and Hartmann number has no effect on the transient behavior. It is shown that during the time advancement to steady condition, the heat transfer rate relative to zero inclination angle, may reach to a maximum value. This relative maximum heat transfer increases as the inclination angle increases and decreases as the solid volume fraction increases. The effect of increase in Hartmann number is to decrease this maximum value at Rayleigh number of Ra=104 and at Rayleigh number of Ra=105, depending on the Hartmann number, this value may increase or decrease. It is also found that an increase in Hartmann number leads to delay the appearance of the relative maximum value of heat transfer. Results show that this maximum value is of more significance at zero solid volume fraction when inclination angle is 90 degrees and Hartmann number is Ha=60. Originality/value – Limited works could be found in the literature regarding the idea of using nanofluids as the working fluid in an enclosure in the presence of magnetic field. In these works, the steady state thermal behavior of enclosures subjected to fixed magnetic fields is concerned. In the present work, the unsteady thermal behavior is concerned and the effect of magnetic field orientation angles on transient heat transfer performance of the enclosure at different Rayleigh and Hartmann numbers and solid volume fractions is explored.

scholarly journals Turbulent natural convection heat transfer in a square cavity with nanofluids in presence of inclined magnetic field

2021 ◽  
pp. 326-326
Author(s):  
Mohamed El Hattab ◽  
Zakaria Lafdaili
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Orientation Angle ◽  
Inclined Magnetic Field ◽  
Square Cavity ◽  
Turbulent Natural Convection

In this paper, we present a numerical study of turbulent natural convection in a square cavity differentially heated and filled with nanofluid and subjected to an inclined magnetic field. The standard k-? model was used as the turbulence model. The transport equations were discretized by the finite volume method using the SIMPLE algorithm. The influence of the Rayleigh number, the Hartmann number, the orientation angle of the applied magnetic field, the type of nanoparticles as well as the volume fraction of nanoparticles, on the hydrodynamic and thermal characteristics of the nanofluid was illustrated and discussed in terms of streamlines, isotherms and mean Nusselt number. The results obtained show that the heat transfer rate increases with increasing Rayleigh number and orientation angle of the magnetic field but it decreases with increasing Hartmann number. In addition, heat transfer improves with increasing volume fraction and with the use of Al2O3 nanoparticles.

Numerical Investigation of Magneto-Natural Heat Transfer in Nanofluid Filled Inclined Enclosure

2020 ◽  
Vol 9 (2) ◽  
pp. 98-105
Author(s):  
L. Eljamali ◽  
R. Sehaqui
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Inclined Enclosure ◽  
Vertical Walls

This paper examines the natural convection in an inclined enclosure that is filled with a water-copper nanofluid and influenced by a magnetic field applied normal to the plane of the cavity. The horizontal walls are assumed to be insulated while the side vertical walls of the cavity are heated differentially. The governing equations are re-formulated in functions of stream function and vorticity. The resulting boundary value problem is solved numerically using an ADI method (alternating direction implicit). A variety of plots showing the velocity and temperature profiles and the influence of Hartmann number as well as Rayleigh number on the streamlines and isotherms are shown.

Lattice Boltzmann Simulation of Magnetic Field Effect on Natural Convection of Power-Law Nanofluids in Rectangular Enclosures

2017 ◽  
Vol 9 (5) ◽  
pp. 1094-1110
Author(s):  
Lei Wang ◽  
Zhenhua Chai ◽  
Baochang Shi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Power Law ◽  
Lattice Boltzmann ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Power Law Index

AbstractIn this paper, the magnetic field effects on natural convection of power-law nanofluids in rectangular enclosures are investigated numerically with the lattice Boltzmann method. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles and the investigations are carried out for different governing parameters including Hartmann number (0.0≤Ha≤20.0), Rayleigh number (104≤Ra≤106), power-law index (0.5≤n≤1.0), nanopartical volume fraction (0.0≤ϕ≤0.1) and aspect ratio (0.125≤AR≤8.0). The results reveal that the flow oscillations can be suppressed effectively by imposing an external magnetic field and the augmentation of Hartmann number and power-law index generally decreases the heat transfer rate. Additionally, it is observed that the average Nusselt number is increased with the increase of Rayleigh number and nanoparticle volume fraction. Moreover, the present results also indicate that there is a critical value for aspect ratio at which the impact on heat transfer is the most pronounced.

scholarly journals MHD convection flow of Ag–water nanofluid in inclined enclosure with center heater

2020 ◽  
Vol 37 ◽  
pp. 13-27
Author(s):  
Mahalakshmi Thangavelu ◽  
Nithyadevi Nagarajan ◽  
Hakan F Oztop ◽  
Ruey-Jen Yang
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Inclination Angle ◽  
Heat Transfer Performance ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Internal Heat ◽  
Transfer Performance ◽  
Maximum Heat ◽  
Inclined Enclosure

ABSTRACT Simulations are performed to examine magnetohydrodynamic convection of an Ag–water nanofluid within an inclined enclosure containing a center heater oriented in different directions. In performing the analysis, the left and right vertical walls are assumed to be isothermally cooled, while the bottom wall is isothermally heated and the top wall is adiabatic. The governing equations are solved numerically using the finite-volume method. The simulations focus on the effects of the Rayleigh number (Ra = 104, 105 and 106), Hartmann number (Ha = 0, 25 and 50), inclination angle (γ = 0°, 45°, 90° and 135°), orientation of heater (horizontal or vertical) and internal heat generation (S = 0, 10 and 20) on the convective heat transfer performance within the enclosure. The results show that the heat transfer performance is dominated by the inclination angle of the enclosure and the Hartmann number. In particular, the heat transfer rate reduces as inclination angle and Hartmann number increase. The maximum heat transfer performance is obtained with a vertical center heater, an inclination angle of γ = 45° and a Rayleigh number of Ra = 106. It is additionally shown that the heat transfer performance improves with an increasing volume fraction of nanoparticles.

scholarly journals Hydromagnetic natural convection from a horizontal porous annulus with heat generation or absorption

2020 ◽  
Vol 307 ◽  
pp. 01005
Author(s):  
Jabrane Belabid ◽  
Soufiane Belhouideg
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Heat Generation ◽  
Inclination Angle ◽  
Hartmann Number ◽  
Saturated Porous Medium ◽  
Darcy Law ◽  
Cylindrical Annulus ◽  
Field Inclination

The problem of unsteady laminar, two-dimensional hydromagnetic natural convection heat transfer in a concentric horizontal cylindrical annulus filled with a fluid-saturated porous medium in the presence of a transverse magnetic field and fluid heal generation effects is studied numerically. It is assumed that the inner and outer walls of the cylindrical annulus are maintained at uniform and constant temperatures Ti and To respectively. The model consists of the heat equation and the equations of motion under the Darcy law. The derived problem with the stream function-temperature formulation is solved numerically using the alternating direction implicit method. This investigation concerns the effect of magnetic field inclination angle, Hartmann number and heat generation on the heat transfer and the flow pattern. The obtained numerical results are presented graphically in terms of streamlines and isotherms. It was found that the heat transfer mechanisms and the flow characteristics depend strongly on the magnetic field inclination angle, Hartmann number and heat generation..

scholarly journals CuO–Water Nanofluid Magnetohydrodynamic Natural Convection inside a Sinusoidal Annulus in Presence of Melting Heat Transfer

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
M. Sheikholeslami ◽  
R. Ellahi ◽  
C. Fetecau
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Limiting Case ◽  
Good Agreement ◽  
Melting Parameter

Impact of nanofluid natural convection due to magnetic field in existence of melting heat transfer is simulated using CVFEM in this research. KKL model is taken into account to obtain properties of CuO–H2O nanofluid. Roles of melting parameter (δ), CuO–H2O volume fraction (ϕ), Hartmann number (Ha), and Rayleigh (Ra) number are depicted in outputs. Results depict that temperature gradient improves with rise of Rayleigh number and melting parameter. Nusselt number detracts with rise of Ha. At the end, a comparison as a limiting case of the considered problem with the existing studies is made and found in good agreement.

The Effect of Temperature Dependent Electrical Conductivity on the MHD Natural Convection of Al2O3–Water Nanofluid in a Rectangular Enclosure

2014 ◽  
Author(s):  
Ali Mohammad Asadian ◽  
Omid Abouali ◽  
Mahmoud Yaghoubi ◽  
Goodarz Ahmadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Electrical Conductivity ◽  
Natural Convection ◽  
Effect Of Temperature ◽  
Fluid Viscosity ◽  
Heat Transfer Characteristics ◽  
Volume Fractions ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

The present paper is concerned with the study of flow and heat transfer characteristics in the steady state free convective flow of Al2O3-waternanofluids in a square enclosure in the presence of magnetic field. Attention is given to the temperature variation of the electrical conductivity and its effect on the electromagnetic force induced by the motion of the nanofluid. A new experimental correlation recently presented in the literature was used for this aim. In all the earlier studies in this area the electrical conductivity variation of nanofluid with temperature was neglected. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature and this variation is modeled using the available experimental correlations. The governing differential equations are solved numerically using finite element method. The features of fluid flow and heat transfer characteristics are analyzed for various strengths of the magnetic field and different nanoparticle volume fractions. The results show that when the inclusion of the variation of the electrical conductivity with temperature in the numerical model noticeably affects the natural convection heat transfer in the studied rectangular cavity. The variations of Nusselt number for natural convection of Al2O3-water nanofluid with nanoparticle volume fractions are presented at various Rayleigh and Hartmann numbers.

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