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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 aims to develop a multidomain boundary element method (BEM) for modeling 2D complex turbulent thermal flow using low Reynolds two‐equation turbulence models.

The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as a subdomain technique. The resulting system matrix is an overdetermined, sparse block banded and solved using a fast iterative linear least squares solver.

The simulation of a turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model. A grid consisting of over 100,000 elements could be solved in the order of a few minutes using a 3.0 Ghz P4 and 1 GB memory indicating good efficiency.

The paper shows, for the first time, that the BEM is applicable to thermal flows using k‐ε.

This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.

The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.

The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non‐Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non‐linear terms is converted into equivalent boundary integrals by the multi‐domain dual reciprocity method (MD‐DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for the approximation of field variables. The iterative numerical formulation is achieved by viewing the material as divided into small elements and on each of them the integral representation formulae for the velocity and temperature are applied and discretised using linear boundary elements. The final system of non‐linear algebraic equations is solved by a modified Newton's method. The numerical examples include non‐Newtonian problems with viscous dissipation, temperature‐dependent viscosity and natural convection due to bouyancy forces.

The purpose of this paper is to examine numerically the three natural convection of air induced by temperature difference between a cold outer cubic enclosure and a hot inner cylinder. Simulations have been carried out for Rayleigh numbers ranging from 103 to 107 and titled angle of the enclosure from 0° to 90°. The developed mathematical model is governed by the coupled equations of continuity, momentum and energy, and is solved by finite volume method. The effects of cylinder inclination and Rayleigh number on fluid flow and heat transfer are presented. The distribution of isocontours of temperature and isosurfaces of velocity eventually reaches a steady state in the range of Rayleigh numbers between 103 and 107 for titled inclination of 90°; however, for the remaining inclinations, Rayleigh number must be in the range 103-106 to avoid unsteady state, which is manifested by the division of the area containing the maximum local heat transfer rate into three parts for a Rayleigh number equal to 107 and an inclination of 90°. We mention that instability study is not included in the present paper, which is solely devoted to three-dimensional calculations. Results also indicate that optimal average heat transfer rate is obtained for both high Rayleigh number of 106 and high inclination of 90° for the two cases of the inner cylinder and cubical enclosure.

The manuscript deals with prediction of the three-dimensional natural convection phenomena in a cubical cavity induced by an isothermal cylinder at the center with different inclinations by simulating the flow using highly numerical methods such as finite volume method.

It is found that the local Nusselt number through active walls for titled inclination set at 90°, the symmetry of the flow is conserved and the area containing the maximum heat transfer is divided into three smaller areas situated near the upper portion of the wall, taking the maximum value. That may be due to the preparation of local occurrence of instabilities and bifurcation phenomena that appear for Ra > 107, which is not included in the present paper to save journal space. It was found also that an optimal heat transfer appears when the cylinder orientation becomes vertical (a = 90°). For this inclination, buoyancy forces act upward, corresponding to an aiding situation. In addition, heat transfer rate is increasing with Rayleigh numbers, so correlations of average Nusselt through the cubical cavity and the cylinder are established as function of two parameters (Ra, a). Comparisons of the numerical results with those obtained from all correlations show good agreements.

To the author’s knowledge, studies have thus far adressed three-dimensional cuboids enclosures induced by an inner shape which the location is changed. However, no study has examined three-dimensional natural convection between the inner isothermal cylinder and outer cooled cubical enclosure when the outer enclosure is tilted.

Vorticity formulations for the incompressible Navier‐Stokes equations have certain advantages over primitive‐variable formulations including the fact that the number of equations to be solved is reduced through the elimination of the pressure variable, identical satisfaction of the incompressibility constraint and the continuity equation, and an implicitly higher‐order approximation of the velocity components. For the most part, vorticity methods have been used to solve exterior isothermal problems. In this research, a vorticity formulation is used to study the natural convection flows in differentially‐heated enclosures. The numerical algorithm is divided into three steps: two kinematic steps and one kinetic step. The kinematics are governed by the generalized Helmholtz decomposition (GHD) which is solved using a boundary element method (BEM) whereas the kinetics are governed by the vorticity equation which is solved using a finite element method (FEM). In the first kinematic step, vortex sheet strengths are determined from a novel Galerkin implementation of the GHD. These vortex sheet strengths are used to determine Neumann boundary conditions for the vorticity equation. (The thermal boundary conditions are already known.) In the second kinematic step, the interior velocity field is determined using the regular (non‐Galerkin) form of the GHD. This step, in a sense, linearizes the convective acceleration terms in both the vorticity and energy equations. In the third kinetic step, the coupled vorticity and energy equations are solved using a Galerkin FEM to determine the updated values of the vorticity and thermal fields. Two benchmark problems are considered to show the robustness and versatility of this formulation including natural convection in an 8×1 differentially‐heated enclosure at a near critical Rayleigh number.

The purpose of the paper is to study the steady and periodic solution of a lid‐driven cavity flow problem with the gradual increase of Reynolds number (Re) up to 10,000.

The problem is solved by unsteady stream function‐vorticity formulation using the clustered grids. The alternating direction implicit (ADI) method and the central difference scheme have been used for discretization of the governing equations. Total vorticity error and the total kinetic energy have been considered for ensuring the state of flow condition. The midplane velocity distribution and the top wall vortex distribution are compared with the results of other authors and found to show good agreement.

Kinetic energy variation with time is studied for large time computation. Below 7,500, it becomes constant signifying the flow to be in steady‐state. At Re=10,000, the fluid flow has an oscillating nature. The dimensionless period of oscillation is found to be 1.63. It is demonstrated that the present computation is able to capture the periodic solution after the bifurcation very accurately.

The findings will be useful in conducting a steady and periodic solution of variety of fluid flows or thermally‐driven fluid flows.

The purpose of this study is to quantify the free convective heat transfer around a vertical cylindrical electronic component equipped with vertical fins representing an antenna, contained in a closed cavity maintained isothermal. Its cooling is provided via a water-based copper nanofluid whose volume fraction varies between 0% and 10%. Its effective viscosity and thermal conductivity are determined with the Brinkman and Maxwell models.

The governing equation system has been solved by means of the volume control method based on the SIMPLE algorithm.

A Nusselt-Rayleigh correlation valid in the 3.32 × 10⁵ – 6.74 × 10⁷ Rayleigh number range is proposed. It allows the thermal sizing of the considered system used in high power electronics to ensure their correct operation in the worst conditions.

The proposed correlations are original and unpublished.

The main purpose of this work is to arrive at a three-dimensional (3D) numerical solution on mixed convection in a cubic cavity with a longitudinally located triangular fin in different sides.

The 3D governing equations are solved via finite volume technique by writing a code in FORTRAN platform. The governing parameters are chosen as Richardson number, 0.01 ≤ Ri ≤ 10 and thermal conductivity ratio 0.01 ≤ Rc ≤ 100 for fixed parameters of Pr = 0.7 and Re = 100. Two cases are considered for a lid-driven wall from left to right (V+) and right to left (V−).

It is observed that entropy generation due to heat transfer becomes dominant onto entropy generation because of fluid friction. The most important parameter is the direction of the moving lid, and lower values are obtained when the lid moves from right to left.

The main originality of this work is to arrive at a solution of a 3D problem of mixed convection and entropy generation for lid-driven cavity with conductive triangular fin attachments.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.