Hamou Sadat

A new meshless approach for three dimensional fluid flow and related heat transfer problems

Abstract The mathematical formulation, basic concept and numerical implementation of a meshless method for solving three dimensional fluid flow and related heat transfer problems are presented in this paper. A second order moving least squares approximation is used for the spatial discretization together with an implicit scheme for time marching. The vorticity and vector potential formulation of Navier–Stokes equations is employed to avoid the difficulties associated with pressure–velocity coupling. Two three-dimensional examples of natural convection in a differentially heated cubic cavity and in the annular space between a sphere and a cube are considered and steady-state solutions are obtained for Rayleigh numbers in the range of 10 3 –10 6 . Results show the flexibility of the method and demonstrate its accuracy.

Meshless method for solving coupled radiative and conductive heat transfer in complex multi-dimensional geometries

A meshless method DAM is employed to solve the coupled radiative and conductive heat transfer problem in a semi-transparent medium enclosed in complex 2D and 3D geometries. The meshless method for radiative transfer is based on the even parity formulation of the discrete ordinates method. Cases of combined conduction–radiation are presented and the results are compared with other benchmark approximate solutions.

Meshless Method for Solving Transient Radiative and Conductive Heat Transfer in Two-Dimensional Complex Geometries

A diffuse approximation meshless method (DAM) is employed to solve the transient radiative and conductive heat transfer problem in a semitransparent medium enclosed in 2-D complex geometries. The computational spatial domain is discretized by a set of nodes scattered in the domain and boundary without information on the relationship between them. The meshless method for radiative transfer equation is based on the even-parity formulation of the discrete ordinates method without any form of upwinding. Results of dimensionless temperature distribution at different dimensionless times are obtained and validated with other benchmark approximate solutions in order to illustrate the performance of the proposed method.

First-Order and Second-Order Meshless Formulations of the Radiative Transfer Equation: A Comparative Study

In this article we compare the first- and second-order formulations of the radiative transfer equation (RTE) by using a diffuse approximation meshless (DAM) method. These formulations include the first-order radiative transfer equation (FORTE), the second-order radiative transfer equation (SORTE), and the even parity method. All of them are solved without upwinding treatment. In order to investigate the accuracy and cost, different radiative transfer problems in complex 2-D and 3-D geometries are considered. Prediction results obtained by the proposed methods are compared with other references in order to illustrate the performance of different formulations and of the meshless method.

Oblique axisymmetric stagnation flows in magnetohydrodynamics

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 Gortler–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 than some critical value...

Meshless method for solving coupled radiative and conductive heat transfer in refractive index medium

A diffuse approximation meshless method (DAM) is employed as a means of solving the coupled radiative and conductive heat transfer problems in semi-transparent refractive index media contained in 1D and 2D geometries. The meshless approach for radiative transfer is based on the discrete ordinates equation. Cases of combined conduction- radiation are presented, including plane parallel slab, square enclosure, and semicircular enclosure with an inner circle. The influence of the refractive index on the temperature distributions and heat fluxes is investigated. Results obtained using the proposed meshless method are compared with those reported in the literature to demonstrate the flexibility and accuracy of the method.

Restitution of the Temperature Field Inside a Cylinder of Semitransparent Dense Medium From Directional Intensity Data

The purpose of this paper is to obtain the temperature field inside a cylinder filled in with a dense nonscattering semitransparent medium from directional intensity data by solving the inverse radiative transfer equation. This equation is solved in a first approach with the help of a discrete scheme, and the solution is then exactly obtained by separating the physical set on two disjoint domains on which a Laplace transform is applied, followed by the resolution of a first kind Fredholm equation.

Linear stability of a nonorthogonal axisymmetric stagnation flow on a rotating cylinder

The present analysis deals with the onset of instability in an axisymmetric stagnation flow obliquely impinging on a uniformly rotating circular cylinder. The basic flow is described by an exact solution of the Navier-Stokes equations, discovered by Weidmann and Putkaradze [Eur. J. Mech. B/Fluids 22, 123 (2003)]. An eigenvalue problem for the linear stability is formulated, regardless of the free stream obliqueness, and then solved numerically by means of a collocation method using Laguerre’s polynomials. It is established that the basic stagnation flow is stable for sufficiently high Reynolds numbers. This is in conformity with the unconditional linear stability of two-dimensional Hiemenz stagnation flow. Instability occurs for Reynolds numbers smaller than some threshold value that increases with the rotation rate of the cylinder. At criticality, the flow undergoes a Hopf bifurcation, leading then to an oscillatory secondary motion.

Simulations of coupled radiative and convective heat transfer in 2D and 3D semitransparent medium by the moving least square method

ABSTRACT The aim of the paper is to use the moving least square meshless method to study the coupled problem between radiation and natural convection in semitransparent medium of 2D and 3D geometries. The flow is incompressible, laminar, and governed in the vorticity-stream function formulation (2D) and vorticity-vector potential formulation (3D) of Navier–Stokes equations. We use the discrete ordinate method to solve the radiative transfer equation. We study the influence of optical thickness, albedo, heat source, and geometry shape to the flow patterns and temperature distributions. The examples (square, cylindrical ring, and cubic) are taken to compare to the references to check the performance of the proposed method. The results show that the moving least square meshless method is capable to deal with the coupled radiation and natural convection with stability and accuracy.

On the Boundary Intensities in a Plane Parallel Slab With Linearly Varying Refractive Index

An exact expression of the outgoing boundary intensities in the case of a gray semi-transparent medium confined in a plane parallel slab with a refractive index linearly depending on the position is proposed. It is shown that directly using the diffuse reflection law gives in a much easier way exactly the same result as the one obtained with the pseudo-source method.