Effects of uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity

2017 ◽  
Vol 27 (2) ◽  
pp. 334-357 ◽  
Author(s):  
T. Javed ◽  
Z. Mehmood ◽  
M.A. Siddiqui ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Absorption Coefficient ◽  
Uniform Magnetic Field ◽  
Left Wall ◽  
Content Type ◽  
Nusselt Numbers

Purpose The purpose of this paper is to perform a numerical study for heat transfer through natural convection in the presence of a constant magnetic field in an incompressible steady nanofluid flow inside an isosceles triangular cavity. Design/methodology/approach For this flow problem, the left wall of the cavity subjected to uniform/nonuniform heat was considered, while right and bottom walls of the cavity were kept cold. The obtained equations were solved by using the Galerkin weighted residual technique. Results are computed for a wide range of parameters including Rayleigh number (Ra) (10^3 < Ra < 10^7), Hartman number (Ha) (0 < Ha < 60), and heat-generation/-absorption coefficient (q) (−10 < q < 10), while, Prandtl number (Pr) was kept fixed at 6.2. These computed results are presented in terms of stream functions, isotherms, Nusselt numbers and average Nusselt numbers through figures. Findings It is observed that, in case of uniform heating of the side wall, the strength of stream lines’ circulations increases with an increase in Ra and decreases with an increase in Ha. Similarly, by increasing heat-absorption coefficient q, an increase in the circulation strength is noted and the circulation cell moves towards the left wall in the presence of a heat sink (q < 0) and moves to the cold right wall in the presence of a heat source (q > 0). In the case of nonuniformly heated left wall in the presence of a heat source (q > 0), a higher-temperature gradient is observed in the cavity and isotherms are clustered to the left wall in the lower portion and to right wall in the upper portion; these appear to be straight and parallel to the x-axis near the bottom wall. On the other hand, the heat transfer rate along all the walls of the cavity is observed to be higher for smaller values of q. Whereas, Nusselt number along the bottom wall (Nu-B) increases with an increase in the values of x, while, that along the left wall (Nu-L) first increases and then decreases. But Nusselt number along the right wall (Nu-R) is found to be qualitatively opposite to Nu-L with an increase in distance x. Whereas, average Nusselt number increases with an increase in Rayleigh number Ra and heat-generation/-absorption coefficient q. Research limitations/implications The problem is formulated for an incompressible flow; viscous dissipation has been neglected, negligible induced magnetic field has been considered and local thermal equilibrium has been considered. Originality/value Results presented in this paper are original and new for the effects of a uniform magnetic field on the natural convection of Cu–water nanofluid in a triangular cavity. Hence, this study is important for researchers working in the area of heat transfer in cavity flows involving the nanofluid to become familiar with the flow behavior and properties.

MHD natural convection and entropy analysis of a nanofluid inside T-shaped baffled enclosure

2018 ◽  
Vol 28 (12) ◽  
pp. 2916-2941 ◽  
Author(s):  
Taher Armaghani ◽  
A. Kasaeipoor ◽  
Mohsen Izadi ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Entropy Generation ◽  
Hartmann Number ◽  
Content Type ◽  
Thermal Indexes ◽  
The Impact

Purpose The purpose of this paper is to numerically study MHD natural convection and entropy generation of Al2O3-water alumina nanofluid inside of T-shaped baffled cavity which is subjected to a magnetic field. Design/methodology/approach Effect of various geometrical, fluid and flow factors such as aspect ratio of enclosure and baffle length, Rayleigh and Hartmann number of nanofluid have been considered in detail. The hydrodynamics and thermal indexes of nanofluid have been described using streamlines, isotherms and isentropic lines. Findings It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. It is found that by enhancing Hartmann number, symmetrical streamlines gradually lose symmetry and their values decline. The interesting finding is an increase in the impact of Hartmann number on heat transfer indexes with augmenting Rayleigh number. However, with augmenting Rayleigh number and, thus, strengthening the buoyant forces, the efficacy of Hartmann number one, an index indicating the simultaneous impact of natural heat transfer to entropy generation increases. It is clearly seen that the efficacy of nanofluid on increased Nusselt number enhances with increasing aspect ratio of the enclosure. Based on the results, the Nusselt number generally enhances with the larger baffle length in the enclosure. Finally, with larger Hartmann number and lesser Nusselt one, entropy production is reduced. Originality/value The authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

Heat Transfer by Natural Convection From an Array of Short, Wall-Attached Horizontal Cylinders

1982 ◽  
Vol 104 (1) ◽  
pp. 125-131 ◽  
Author(s):  
E. M. Sparrow ◽  
D. S. Cook ◽  
G. M. Chrysler
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Plate ◽  
Diameter Ratio ◽  
Nusselt Numbers ◽  
Cylinder Length ◽  
Horizontal Cylinders ◽  
Length To Diameter Ratio

Per-cylinder natural convection Nusselt numbers were measured for an in-line array of short horizontal cylinders that were affixed to a convectively participating vertical plate. The effect of cylinder length-to-diameter ratio, intercylinder spacing, position at which the cylinder is attached to the vertical plate, and Rayleigh number were investigated. The experiments were performed in air. It was found that the extent to which a given cylinder in the array was affected by cylinders situated below it depended on the Rayleigh number, with enhanced heat transfer coefficients being more likely at higher Rayleigh numbers. Greater enhancement occurred at larger intercylinder spacings. The qualitative characteristics of the Nusselt number results were insensitive to the cylinder length-to-diameter ratio, but the longer cylinders exhibited higher values of the Nusselt number. For the most part, the Nusselt numbers for the wall-attached horizontal cylinders fell below those for the classical horizontal cylinder of infinite length.

MHD natural convection in a square porous cavity filled with a water-based magnetic fluid in the presence of geothermal viscosity

2018 ◽  
Vol 28 (9) ◽  
pp. 2111-2131 ◽  
Author(s):  
Mikhail A. Sheremet ◽  
Marina S. Astanina ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Natural Convection ◽  
Magnetic Fluid ◽  
Convective Flow ◽  
Uniform Magnetic Field ◽  
Vertical Wall ◽  
Content Type ◽  
Porous Cavity ◽  
Water Based

Purpose The purpose of this paper is a numerical analysis of natural convection in a square porous cavity filled with a water-based magnetic fluid of geothermal viscosity under the effect of inclined uniform magnetic field. Design/methodology/approach The domain of interest includes the square porous cavity filled with a water-based magnetic fluid (W40). Horizontal walls are supposed to be adiabatic, while right vertical wall is kept at constant low temperature and left vertical wall is kept at constant high temperature. An inclined uniform magnetic field affects the fluid flow and heat transfer inside the cavity. The viscosity of the working fluid is proportional to the linearly decreasing function of depth (vertical coordinate) and inversely proportional to the linear function of temperature. It is assumed in the analysis that the flow is laminar. The fluid is Newtonian and the Boussinesq approximation is valid. The governing equations have been discretized using the finite difference method with the uniform grid. Simulations have been carried out for different values of the Rayleigh number, Hartmann number, Darcy number, magnetic field inclination angle and viscosity variation parameters. Findings It has been revealed that an increase in the viscosity parameters leads to the heat transfer enhancement and convective flow intensification. At the same time, this intensification is more essential for high values of the Rayleigh number. Originality/value The originality of this work is to analyze MHD natural convection in a square porous cavity filled with a water-based magnetic fluid of geothermal viscosity. The results would benefit scientists and engineers to become familiar with the analysis of convective heat and mass transfer in nanofluids, and the way to predict the properties of nanofluid convective flow in advanced technical systems, in industrial sectors including transportation, power generation, chemical sectors and electronics.

Natural convection of a hybrid nanofluid subjected to non-uniform magnetic field within porous medium including circular heater

2019 ◽  
Vol 29 (4) ◽  
pp. 1211-1231 ◽  
Author(s):  
Mohsen Izadi ◽  
Nemat M. Maleki ◽  
Ioan Pop ◽  
S.A.M. Mehryan
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Hybrid Nanofluid ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Content Type ◽  
Porosity Coefficient

PurposeThis paper aims to numerically investigate the natural convection heat transfer of a hybrid nanofluid into a porous cavity exposed to a variable magnetic field.Design/methodology/approachThe non-linear elliptical governing equations have been solved numerically using control volume based finite element method. The effects of different governing parameters including Rayleigh number (Ra= 103− 106), Hartman number (Ha= 0 − 50), volume fraction of nanoparticles (φ= 0 − 0.02), curvature of horizontal isolated wall (a= 0.85 − 1.15), porosity coefficient (ε= 0.1 − 0.9) and Darcy number (Da= 10−5− 10−1) have been studied.FindingsThe results indicate that at low Darcy numbers close to 0, the average Nusselt numberNuaenhances as porosity coefficient increases. Fora= 1 anda= 1.15 in comparison witha= 0.85, the stretching of the isothermal lines is maintained from the left side to the right side and vice versa, which indicates increased natural convection heat transfer for this configuration of the top and bottom walls. In addition, at higher Rayleigh numbers, by increasing the Hartmann number, a significant decrease is observed in the Nusselt number, which can be attributed to the decreased power of the flow.Originality/valueThe authors believe that all the results, both numerical and asymptotic, are original and have not been published elsewhere.

MHD heat transfer and entropy generation in inclined trapezoidal cavity filled with nanofluid

2017 ◽  
Vol 27 (10) ◽  
pp. 2174-2202 ◽  
Author(s):  
Kamel Milani Shirvan ◽  
Soroush Mirzakhanlari ◽  
Hakan F. Öztop ◽  
Mojtaba Mamourian ◽  
Khaled Al-Salem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Sensitivity Analysis ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Entropy Generation ◽  
Inclination Angle ◽  
Effective Parameters ◽  
Content Type ◽  
The Mean

Purpose The main purpose of this paper is to define 2D numerical study and a sensitivity analysis of natural convection heat transfer and entropy generation of Al2O3-water nanofluid in a trapezoidal cavity, with considering of the presence of a constant axial magnetic field. Design/methodology/approach The effects of the three effective parameters, the Rayleigh number, Hartmann number (Ha) and also inclination angle on the heat transfer performance and entropy generation, are investigated using a finite volume approach. The sensitivity analysis of the effective parameters is done utilizing the response surface methodology. Findings The results obtained showed that the mean Nusselt number and total entropy generation increase with the Rayleigh number. Also, increasing the inclination angle reduces the mean Nusselt number (regardless of the magnetic field). In addition, it is found that the mean Nusselt number increases until Ha = 10 and then decreases by increasing of Ha number, regardless of the inclination angle. The sensitivity of the mean Nusselt number to the Ha number and inclination angle α is negative. It is concluded that to maximize the mean Nusselt number and minimize the entropy generation, simultaneously, the Ha and inclination angle must be 50° and 0°, respectively. Originality/value There is no published research in the literature about sensitivity analysis of magneto-hydrodynamic heat transfer and entropy generation in inclined trapezoidal cavity filled with nanofluid.

Effects of magnetic field on the liquid gallium thermosyphon fluid flow; a numerical study

2019 ◽  
Vol 30 (2) ◽  
pp. 681-703
Author(s):  
Hamid Teimouri ◽  
Amin Behzadmehr
Keyword(s):  
Magnetic Field ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Liquid Gallium ◽  
Two Dimensional ◽  
Left Wall ◽  
Content Type ◽  
Wide Range

Purpose This paper aims to numerically study the laminar natural convection in a thermosyphon filled with liquid gallium exposed to a constant magnetic field. The left wall of the thermosyphon is at an uniformed hot temperature, whereas the right wall is at a uniform cold temperature. The top and bottom walls are considered to be adiabatic. All walls are electrically insulated. The effects of Hartmann number, in a wide range of Rayleigh number and aspect ratio combinations, on the natural convection throughout the thermosyphon, are investigated and discussed. Furthermore, different forces that influence the natural flow structure are studied. Design/methodology/approach A Fortran code is developed based on the finite volume method to solve the two-dimensional unsteady governing equations. Findings Imposing a magnetic field improves the stability of the fluid flow and thus reduces the Nusselt number. For a given Hartmann and Rayleigh number, there is an optimum aspect ratio for which the average velocity becomes maximum. Research limitations/implications This paper is a two-dimensional investigation. Originality/value To the best of the authors’ knowledge, the effect of the magnetic field on natural convection of liquid gallium in the considered thermosyphon has not been studied numerically in detail. The results of this paper would be helpful in considering the application of the low Prandtl number’s liquid metals in thermosyphon MHD generators and certain cooling devices.

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.

Laminar Natural Convection in a Discretely Heated Cavity: II—Comparisons of Experimental and Theoretical Results

1995 ◽  
Vol 117 (4) ◽  
pp. 910-917 ◽  
Author(s):  
T. J. Heindel ◽  
F. P. Incropera ◽  
S. Ramadhyani
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Nusselt Numbers ◽  
Numerical Predictions ◽  
Number Flow ◽  
Experimental Geometry

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

scholarly journals Natural convection in a differentially heated enclosure with triangular roof

1970 ◽  
Vol 39 (1) ◽  
pp. 1-7 ◽  
Author(s):  
Sumon Saha ◽  
Noman Hasan ◽  
Chowdhury Md Feroz
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Convection Heat Transfer ◽  
Element Analysis ◽  
Left Wall ◽  
Square Enclosure

A numerical study has been carried out for laminar natural convection heat transfer within a two-dimensional modified square enclosure having a triangular roof. The vertical sidewalls are differentially heated considering a constant flux heat source strip is flush mounted with the left wall. The opposite wall is considered isothermal having a temperature of the surrounding fluid. The rest of the walls are adiabatic. Air is considered as the fluid inside the enclosure. The solution has been carried out on the basis of finite element analysis by a non-linear parametric solver to examine the heat transfer and fluid flow characteristics. Different heights of the triangular roof have been considered for the present analysis. Fluid flow fields and isotherm patterns and the average Nusselt number are presented for the Rayleigh numbers ranging from 103 to 106 in order to show the effects of these governing parameters. The average Nusselt number computed for the case of isoflux heating is also compared with the case of isothermal heating as available in the literature. The outcome of the present investigation shows that the convective phenomenon is greatly influenced by the inclined roof height. Keywords: Natural convection, triangular roof, Rayleigh number, isoflux heating. Doi:10.3329/jme.v39i1.1826 Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 1-7

Natural convection in differentially heated enclosures subjected to variable temperature boundaries

2019 ◽  
Vol 29 (11) ◽  
pp. 4130-4141 ◽  
Author(s):  
Abdulmajeed Mohamad ◽  
Mikhail A. Sheremet ◽  
Jan Taler ◽  
Paweł Ocłoń
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Uniform Heating ◽  
Content Type ◽  
Left Hand ◽  
Heating And Cooling ◽  
Right Hand ◽  
The Right

Purpose Natural convection in differentially heated enclosures has been extensively investigated due to its importance in many industrial applications and has been used as a benchmark solution for testing numerical schemes. However, most of the published works considered uniform heating and cooling of the vertical boundaries. This paper aims to examine non-uniform heating and cooling of the mentioned boundaries. The mentioned case is very common in many electronic cooling devices, thermal storage systems, energy managements in buildings, material processing, etc. Design/methodology/approach Four cases are considered, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature is kept at a constant, cold temperature. In the second case, the left-hand wall’s temperature linearly increases along the wall, while the right-hand wall’s temperature is kept a constant, cold temperature. The third case, the left-hand wall’s temperature linearly decreases along the wall, while the right-hand wall’s temperature linearly increases along the wall. In the fourth case, the left-hand and the right-hand walls’ temperatures decrease along the wall, symmetry condition. Hence, four scenarios of natural convection in enclosures were covered. Findings It has been found that the average Nusselt number of the mentioned cases is less than the average Nusselt number of the uniformly heated and cooled enclosure, which reflects the physics of the problem. The work quantifies the deficiency in the rate of the heat transfer. Interestingly one of the mentioned cases showed two counter-rotating horizontal circulations. Such a flow structure can be considered for passively, highly controlled mechanism for species mixing processes application. Originality/value Previous works assumed that the vertical boundary is subjected to a constant temperature or to a sinusoidal varying temperature. The subject of the work is to examine the effect of non-uniformly heating and/or cooling vertical boundaries on the rate of heat transfer and flow structure for natural convection in a square enclosure. The temperature either linearly increases or decreases along the vertical coordinate at the boundary. Four scenarios are explored.

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