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External natural convection is rarely studied by numerical simulation in the literature due to the fact that flow of interest takes place in an unbounded domain and that if a limited computational domain is used the corresponding outer boundary conditions are unknown. In this study, we propose outer boundary conditions for a limited computational domain and make the corresponding numerical implementation in the scope of a projection method combining spectral methods and domain decomposition techniques. Numerical simulations are performed for both steady natural convection about an isothermal cylinder and transient natural convection around a line‐source. An experiment is also realized in water using particle image velocimetry and thermocouples to make a comparison during transients of external natural convection around a platinum wire heated by Joule effect. Good agreement, observed between numerical simulations and experiments, validated the outer boundary conditions proposed and their numerical implementation. It is also shown that, if one tolerates prediction error, numerical results obtained remain at least reasonable in a region near the line‐source during the entire transients. We thus paved the way for numerical simulation of external natural convection although further studies remain to be done for higher heating power (higher Rayleigh number).

The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique magnetic field. The momentum equations include the magnetic effect, and the induced magnetic field due to the motion of the electrically conducting fluid is neglected. Quadratic triangular elements are used to ensure accurate approximation for second order derivatives of stream function appearing in the vorticity equation.

Governing equations in terms of stream function and vorticity are solved by FEM using quadratic triangular elements. Vorticity boundary conditions are obtained through Taylor series expansion of stream function equation by using more interior stream function values to improve the accuracy. Isothermally heated or cooled and/or adiabatic conditions for the temperature are imposed. Results are obtained for Rayleigh number values and Hartmann number values up to 1000000 and 100, respectively.

It is observed that streamlines form a thin boundary layer close to the heated walls as Ha increases. The same effect is seen in the vorticity contours, and isotherms are not affected much. As Ra increases streamlines are deformed moving from the heated walls through cooled walls. Vorticity starts to develop boundary layers close to heated and adjacent walls. Isotherms are pushed towards the sinusoidally heated wall whereas in the case of linearly heated left and bottom walls they expand towards cooled part of the cavity as Ra increases.

The application of FEM with quadratic elements for solving natural convection flow problem under the effect of a magnetic field is new in the sense that the results are obtained for large values of Rayleigh and Hartmann numbers.

The purpose of this paper is to present a numerical solution for the problem of steady laminar flow and heat transfer characteristics of viscous incompressible fluid.

For this purpose a two dimensional code has been developed to simulate the natural convection heat transfer along a vertical cylinder, for four different geometries: from vertical cylinder in infinite medium; from a vertical flat plate in an infinite medium; from an open assembly of a finite vertical cylinder; and from an open rectangular pitch assembly of cylinders.

The effects of various parameters of interest have been discussed through simulations. The Nusselt numbers of constant wall temperature and constant heat flux cylinders calculated numerically and compared with Lee et al. and Heckel et al., respectively, and are found within reasonable agreement. For large radius, a vertical cylinder has been treated as a vertical flat plate, so that the curvature effects become negligible. For the case of vertical flat plate, Nusselt number has been compared with analytical relation for the local Nusselt number given by Jaluria.

The natural convection has been studied for four different geometries: the flow regime in all the case studies has been assumed to be Laminar.

Computer code developed for current study can be applied to many other geometries to simulate natural convection heat transfer.

The purpose of this paper is to study the effects of finite wall thickness on the natural convection and entropy generation in a square cavity filled with Al₂O₃–water nanofluid in the presence of bottom heat source.

The moving isothermal heater was placed on the bottom solid wall. The vertical walls (left and right walls) were fully maintained at low temperatures. The rest of the bottom solid wall along with the top horizontal wall was kept adiabatic. The boundaries of the domain are assumed to be impermeable; the fluid within the cavity is a water-based nanofluid having Al₂O₃ nanoparticles. The Boussinesq approximation is applicable. The dimensionless governing equations subject to the selected boundary conditions are solved using the finite difference method. The current proposed numerical method is proven excellent through comparisons with the existing experimental and numerical published studies.

Numerical results were demonstrated graphically in several forms including streamlines, isotherms and local entropy generation, as well as the local and average Nusselt numbers. The results reveal that the thermal conductivity and thickness of the solid wall are important control parameters for optimization of heat transfer and Bejan number within the partially heated square cavity.

According to the past research studies mentioned above and to the best of the authors’ knowledge, the gap regarding the problem with entropy generation analysis and natural convection in partially heated square cavity has yet to be filled. Because of this, this study aims to investigate the entropy generation analysis as well as the natural convection in nanofluid-filled square cavity which was heated partially. A square cavity with an isothermal heater located on the bottom solid horizontal wall of the cavity and partly cold sidewalls are essential problems in thermal processing applications. Hence, the authors believe that this present work will be a valuable contribution in improving the thermal performance.

In general, the bifurcation phenomenon of the natural convection has largely been studied. But the bifurcation of natural convection under magnetic conditions has not been studied as per the authors’ knowledge. This paper aims to investigate the changes in bifurcation phenomenon by the self-induced circular magnetic field.

The authors numerically solved the natural convection in an annulus. The SIMPLE algorithm was adopted for pressure-momenturm coupling. The Boussinesq approximation was used for numerical modeling of natural convection. Finally, the Lorentz force effect by the magnetic field was considered through the source terms in the momentum conservation equation.

It was determined that the heat-transfer rate changes by 17% owing to the applied magnetic effect, and the range of the Rayleigh number for flow bifurcation is changed by the magnetic effect. Moreover, under the strong magnetic condition, the flow bifurcation continues even at very high Ra. Previously, flow bifurcation has been understood as a flow instability phenomena, and the Lorentz force was regarded as a flow-damping effect; however, in this study, it was found that the magnetic field can boost the flow instability and induce flow bifurcation even in the Rayleigh number region where the bifurcation does not appear.

This paper is dealing with the bifurcation phenomenon in MHD natural convection problems. In the past, the electromagnetic forces were regarded as always acting to damp out the existing flows; herewith, the authors first investigated that the magnetic effect can boost the bifurcation of a kind of flow instability phenomenon.

The effect of the tube wall heat conduction on the natural convection in a tilted long cylindrical envelope with constant, but different temperature of the two ends and an adiabatic outer surface was numerically investigated. The envelope is supposed to be a simplified model for the pulse tube in a pulse tube refrigerator when the pulse tube is positioned at different orientations. It is found that the cylindrical envelope lateral wall heat conduction can enhance the heat transfer from the hot end to the cold end, not only because of the increase in pure heat conduction in the wall, but more importantly, also the intensification of the natural convection within the enclosure. This enhancement is resulted from the big temperature difference between the tube wall and the adjacent fluid near the hot and cold ends. Adoption of low thermal conductivity tube can effectively reduce such additional heat transfers from hot to cold end, thus reducing the loss of cooling capacity for the pulse tube refrigerator.

The purpose of this paper is to study problem of conjugate MHD natural convection of Al₂O₃-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model numerically.

An isothermal heater is placed on the left wall of the square cavity, while the right wall is maintained at a constant cold temperature. The horizontal top and bottom walls are kept adiabatic. The boundaries of the annulus are assumed to be impermeable, the fluid within the cavity is a water-based nanofluid having Al₂O₃ nanoparticles. The Boussinesq approximation is applicable. The governing equations subject to the boundary conditions are solved using the finite difference method.

Numerical results are presented graphically in the form of streamlines, isotherms and nanoparticles distributions as well as the local and average Nusselt numbers. The results show that the effect of the nanoparticles addition on the average Nusselt number is essential for low Rayleigh, high Hartmann and high values of length ratio when attenuated the convective flow.

According to exist studies and to the authors’ best knowledge, so far, there have been no studies of conjugate natural convection of Al₂O₃-water nanofluid in a square cavity with a conductive inner block using Buongiorno’s two-phase model with the effect of the magnetic field. Thus, the authors believe that this work is new and valuable. The aim of this study is to investigate the MHD natural convection of Al₂O₃-water nanofluid in a square cavity with conductive inner block using Buongiorno’s two-phase model.

The purpose of this paper is to apply the lattice Boltzmann method (LBM) with multiple distribution functions model, to simulate transient natural convection of air in a two-dimensional square cavity in the presence of a magnetic quadrupole field, under non-gravitational as well as gravitational conditions.

The density-temperature double distribution functions and D2Q9 model of LBM for the momentum and temperature equations are currently employed. Detailed transient structures of the flow and isotherms at unsteady state are obtained and compared for a range of magnetic force numbers from 1 to 100. Characteristics of the natural convection at initial moment, quasi-steady state and steady state are presented in present work.

At initial time, effects of the magnetic field and gravity are both relatively limited, but the effects become efficient as time evolves. Bi-cellular flow structures are obtained under non-gravitational condition, while the flow presents a single vortex structure at first under gravitational condition, and then emerges a bi-cellular structure with the increase of magnetic field force number. The average Nusselt number generally increases with the augment of magnetic field intensity.

This paper will be useful in the researches on crystal material and protein growth, oxygen concentration sensor, enhancement or suppression of the heat transfer in micro-electronics and micro-processing technology, etc.

The current study extended the application of LBM on the transient natural convective problem of paramagnetic fluids in the presence of an inhomogeneous magnetic field.

A numerical method for the solution of the Navier‐Stokes equations is developed using an integral representation of the conservation equations. The velocity‐vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary‐domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. The boundary‐domain integral formulation is developed and tested for natural convection flows in closed cavities with complex geometries.

This paper describes the solution of a steady‐state natural convection problem in porous media by the radial basis function collocation method (RBFCM). This mesh‐free (polygon‐free) numerical method is for a coupled set of mass, momentum, and energy equations in two dimensions structured by the Hardy's multiquadrics with different shape parameter and different order of polynomial augmentation. The solution is formulated in primitive variables and involves iterative treatment of coupled pressure, velocity, pressure correction, velocity correction, and energy equations. Numerical examples include convergence studies with different collocation point density and arrangements for a two‐dimensional differentially heated rectangular cavity problem at filtration Rayleigh numbers Ra*=25, 50 and 100, and aspect ratios A=1/2, 1, and 2. The solution is assessed by comparison with reference results of the fine‐mesh finite volume method in terms of mid‐plane velocity components, mid‐plane and insulated surface temperatures, streamfunction minimum, and Nusselt number.