The present paper deals with the influence of the Lorentz force associated with an applied radial... more The present paper deals with the influence of the Lorentz force associated with an applied radial magnetic field on the axisymmetric stagnation flow impinging obliquely onto a uniformly rotating circular cylinder. It is found that the boundary layer flow is described by an exact solution of the Navier–Stokes equations when Hall effects are ignored. The stability of this basic solution is then considered in the framework of Görtler–Hammerlin assumption according to which linear disturbances inherit the underlying symmetry of the basic flow. The resulting eigenvalue problem is solved numerically by means of a pseudospectral method using Laguerre’s polynomials. The scheme is specifically designed to solve boundary layer equations. The numerical experiments indicate that the effect of cylinder rotation is to reduce the stability of the basic flow and most importantly the magnetic field acts to either increase or decrease it, depending on whether the rotation rate is smaller or greater t...
A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a c... more A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a cylinder. A simple second order explicit solution is obtained. It is shown that this solution is accurate even for high values of the Biot number in a region surrounding the center of the cylinder.
T HE use of simple mathematical formulations to solve the heat conduction problems is of great in... more T HE use of simple mathematical formulations to solve the heat conduction problems is of great interest for engineering calculations. Though the traditional analytical models are widely used because of their numerous industrial applications [1–4], they sometimes do not provide satisfaction for large values of Biot number. In addition, these models do not predict the temperature inside the solid (at the center, for example). In the case of spherical geometries, the analytical solution is expressed as an infinite series which necessitates the numerical solution of a characteristic equation for each value of theBiot number [5]. Moreover, this analytical method sometimes requires the calculation of several hundred terms in the series in order to reach the expected accuracy [6]. A perturbation method has been used in [7] to develop first-order models which can be viewed as improved lumped models for the slab, infinite cylinder, and spherical geometries. A second-order model has been examined in [8] for the slab and in [9] for the cylinder. The aim of this paper is to extend the ideas of [7–9] to the case of a sphere subjected to convection to a surrounding fluid. It is shown that this model gives accurate enough results even for an infinite Biot number. The validity of the model is discussed and the region of the sphere where it can be used is determined.
On presente une methode approchee de calcul des transferts radiatifs dans une enceinte contenant ... more On presente une methode approchee de calcul des transferts radiatifs dans une enceinte contenant un milieu transparent et maillee en elements finis. Le principe de la methode proposee consiste a ne considerer les echanges qu'entre chaque element du maillage et la surface complementaire qui lui est associee et a laquelle on lui attribue une temperature fictive.
Numerical Heat Transfer, Part A: Applications, 1995
This paper deals with the numerical solution of laminar natural convection in a trapezoidal enclo... more This paper deals with the numerical solution of laminar natural convection in a trapezoidal enclosure by a control volume based finite element method and the vorticity-stream function formulation. Steady state solutions have been obtained for aspect ratios of 3 and 6 and for Rayleigh numbers ranging from 10 to 2 × 10. Numerical results are presented for the flow patterns
International Journal of Heat and Mass Transfer, 1997
ABSTRACT This paper deals with the calculation of heat fluxes at singular boundaries. We show tha... more ABSTRACT This paper deals with the calculation of heat fluxes at singular boundaries. We show that accurate evaluation of these fluxes can be made by using a heat balance on boundary control volumes. Numerical examples in heat diffusion and natural convection problems are considered to assess the correctness of the proposed method. Finally, the region of influence of the singularity is discussed.
This paper is devoted to the presentation of a control volume based finite element method (CVFEM)... more This paper is devoted to the presentation of a control volume based finite element method (CVFEM). Its implementation is explicited for both Helmholtz and primitive variable formulations for planar and spatial problems. Application for solving acoustical eigenmode shows that the CVFEM is at least as accurate as the Galerkin FEM.
ABSTRACT We show in this paper that the Adomian decomposition method is closely related to a pert... more ABSTRACT We show in this paper that the Adomian decomposition method is closely related to a perturbation method used to deal with some heat conduction problems. Three examples demonstrate that the obtained series are strictly identical.
Numerical Heat Transfer, Part B: Fundamentals, 2006
A diffuse approximation-based collocation method is used to solve a two-dimensional heterogeneous... more A diffuse approximation-based collocation method is used to solve a two-dimensional heterogeneous heat conduction problem. It is shown that one has to take into account the neighbors of each neighbor of the calculation node in order to achieve sufficient accuracy in the case of strong heterogeneity.
Numerical Heat Transfer, Part B: Fundamentals, 2000
ABSTRACT The main objective of this article is to assess the performance of a meshless method cal... more ABSTRACT The main objective of this article is to assess the performance of a meshless method called the diffuse approximation method (DAM). This numerical method is presented for the calculation of two-dimensional, incompressible, laminar thermal flows. The two-dimensional natural-convection problems in a square cavity and in an eccentric annulus demonstrate the accuracy and capabilities of the proposed technique for high Rayleigh numbers.
The present paper deals with the influence of the Lorentz force associated with an applied radial... more The present paper deals with the influence of the Lorentz force associated with an applied radial magnetic field on the axisymmetric stagnation flow impinging obliquely onto a uniformly rotating circular cylinder. It is found that the boundary layer flow is described by an exact solution of the Navier–Stokes equations when Hall effects are ignored. The stability of this basic solution is then considered in the framework of Görtler–Hammerlin assumption according to which linear disturbances inherit the underlying symmetry of the basic flow. The resulting eigenvalue problem is solved numerically by means of a pseudospectral method using Laguerre’s polynomials. The scheme is specifically designed to solve boundary layer equations. The numerical experiments indicate that the effect of cylinder rotation is to reduce the stability of the basic flow and most importantly the magnetic field acts to either increase or decrease it, depending on whether the rotation rate is smaller or greater t...
A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a c... more A perturbation method is used to solve an unsteady one-dimensional heat conduction problem in a cylinder. A simple second order explicit solution is obtained. It is shown that this solution is accurate even for high values of the Biot number in a region surrounding the center of the cylinder.
T HE use of simple mathematical formulations to solve the heat conduction problems is of great in... more T HE use of simple mathematical formulations to solve the heat conduction problems is of great interest for engineering calculations. Though the traditional analytical models are widely used because of their numerous industrial applications [1–4], they sometimes do not provide satisfaction for large values of Biot number. In addition, these models do not predict the temperature inside the solid (at the center, for example). In the case of spherical geometries, the analytical solution is expressed as an infinite series which necessitates the numerical solution of a characteristic equation for each value of theBiot number [5]. Moreover, this analytical method sometimes requires the calculation of several hundred terms in the series in order to reach the expected accuracy [6]. A perturbation method has been used in [7] to develop first-order models which can be viewed as improved lumped models for the slab, infinite cylinder, and spherical geometries. A second-order model has been examined in [8] for the slab and in [9] for the cylinder. The aim of this paper is to extend the ideas of [7–9] to the case of a sphere subjected to convection to a surrounding fluid. It is shown that this model gives accurate enough results even for an infinite Biot number. The validity of the model is discussed and the region of the sphere where it can be used is determined.
On presente une methode approchee de calcul des transferts radiatifs dans une enceinte contenant ... more On presente une methode approchee de calcul des transferts radiatifs dans une enceinte contenant un milieu transparent et maillee en elements finis. Le principe de la methode proposee consiste a ne considerer les echanges qu'entre chaque element du maillage et la surface complementaire qui lui est associee et a laquelle on lui attribue une temperature fictive.
Numerical Heat Transfer, Part A: Applications, 1995
This paper deals with the numerical solution of laminar natural convection in a trapezoidal enclo... more This paper deals with the numerical solution of laminar natural convection in a trapezoidal enclosure by a control volume based finite element method and the vorticity-stream function formulation. Steady state solutions have been obtained for aspect ratios of 3 and 6 and for Rayleigh numbers ranging from 10 to 2 × 10. Numerical results are presented for the flow patterns
International Journal of Heat and Mass Transfer, 1997
ABSTRACT This paper deals with the calculation of heat fluxes at singular boundaries. We show tha... more ABSTRACT This paper deals with the calculation of heat fluxes at singular boundaries. We show that accurate evaluation of these fluxes can be made by using a heat balance on boundary control volumes. Numerical examples in heat diffusion and natural convection problems are considered to assess the correctness of the proposed method. Finally, the region of influence of the singularity is discussed.
This paper is devoted to the presentation of a control volume based finite element method (CVFEM)... more This paper is devoted to the presentation of a control volume based finite element method (CVFEM). Its implementation is explicited for both Helmholtz and primitive variable formulations for planar and spatial problems. Application for solving acoustical eigenmode shows that the CVFEM is at least as accurate as the Galerkin FEM.
ABSTRACT We show in this paper that the Adomian decomposition method is closely related to a pert... more ABSTRACT We show in this paper that the Adomian decomposition method is closely related to a perturbation method used to deal with some heat conduction problems. Three examples demonstrate that the obtained series are strictly identical.
Numerical Heat Transfer, Part B: Fundamentals, 2006
A diffuse approximation-based collocation method is used to solve a two-dimensional heterogeneous... more A diffuse approximation-based collocation method is used to solve a two-dimensional heterogeneous heat conduction problem. It is shown that one has to take into account the neighbors of each neighbor of the calculation node in order to achieve sufficient accuracy in the case of strong heterogeneity.
Numerical Heat Transfer, Part B: Fundamentals, 2000
ABSTRACT The main objective of this article is to assess the performance of a meshless method cal... more ABSTRACT The main objective of this article is to assess the performance of a meshless method called the diffuse approximation method (DAM). This numerical method is presented for the calculation of two-dimensional, incompressible, laminar thermal flows. The two-dimensional natural-convection problems in a square cavity and in an eccentric annulus demonstrate the accuracy and capabilities of the proposed technique for high Rayleigh numbers.
Uploads