New recurrence relationships between orthogonal polynomials which lead to new Lanczos-type algorithms

Lanczos methods for solving Ax = b consist in constructing a sequence of vectors (Xk),k = 1,... such that rk = b-AXk= Pk(A)r0, where Pk is the orthogonal polynomial of degree at most k with respect to the linear functional c defined as c(εi) = (y, Air0). Let P(1)k be the regular monic polynomial of degree k belonging to the family of formal orthogonal polynomials (FOP) with respect to c(1) defined as c(1)(εi) = c(εi+1). All Lanczos-type algorithms are characterized by the choice of one or two recurrence relationships, one for Pk and one for P(1)k. We shall study some new recurrence relations involving these two polynomials and their possible combinations to obtain new Lanczos-type algorithms. We will show that some recurrence relations exist, but cannot be used to derive Lanczos-type algorithms, while others do not exist at all

Numerical analysis of a hybrid air photovoltaic panel (PV)

During the photovoltaic conversion of solar panels, a significant amount of heat is generated, which causes an increase in the temperature of photovoltaic cells and decreases their efficiency and reliability. This negative effect of heat is caused by a part of the solar radiation that is not absorbed by the solar panels, which leads to heat and weakens its performance. Many efforts have been made to reduce this heating effect on the performance of the PV system, such as combining PV and thermal systems to form a hybrid PVT complex that produces both electricity and heat. Gambit and Fluent 6.3.26 software were used for geometry construction and numerical simulations. This work aims to improve the electrical performance of PV cells by enhancing the heat recovered from PVT panels. For this purpose, we performed a numerical simulation of three configurations (3) of PVT panels integrated with TFMS. We analyzed and compared a single air PVT module (without fins), an air PVT module with two fins, and an air PVT module with four fins. The obtained results represent the variations of the contours and the temperature profiles as well as the flow velocity as a function of the flow rates, and the results show that the use of air and the integration of fins has a significant effect on the cooling of the PVT panel elements and thus allowing to improve its performance

Three-dimensional analysis of flow characteristics in a heat exchanger equipped with a perforated heat sink

Finning or perforations are frequently used in heat exchange devices to increase the heat exchange between the contact surfaces and the surrounding fluid. Thus, the work undertaken in this paper is in the same context to search for a new design to improve the thermohydrodynamic performance of a heat exchanger.  In this context, the latter considered being equipped with a solid or perforated heat sink to identify the perforations' efficiency in optimizing the heat exchanger's performance. The thermohydrodynamic phenomenon governed by the partial differential equations system derived from the laws of conservation: continuity equation for mass, Navier-Stokes equations for momentum, and the energy equation. For the numerical solution, the finite volume method used, and the problem of pressure-velocity coupling intervening at the level of the Navier-Stokes equations solved using the SIMPLE algorithm. Calculations are made for a perforated deflector with different diameters and an unperforated deflector. For both cases, the inlet velocity was chosen in a range from 0.0018 to 0.009 m/s. The results are presented either as maps for the isothermal fields and velocity contours obtained for the meridian planes shown in the figures or as curves for the axial velocity and heat flow. Finally, a qualitative comparison of the different calculated results made, and it could deduce that a perforated deflector is much more efficient than a solid or solid deflector fixed at the same position. The increase in terms of transfers can go from 1.33% to 12.97%, and an excellent material reduction (from 2.32% to 55.85%) corresponds to a low flow resistance compared to the non-perforated case

Analysis of the surface state's influence on the thermohydraulic behavior of an incompressible fluid in convective laminar flow through a microchannel with corrugated surfaces

Le travail entrepris dans cet article présente une étude numérique thermo-énergétique de l'écoulement convectif laminaire dans un microcanal rectangulaire lisse ou la présence de discontinuités sur ses parois. Les ondulations présentent les discontinuités de la surface du mur. La paroi inférieure du microcanal portée à une température constante et uniforme. Le nombre de Reynolds utilisé, Re, a été choisi dans la gamme (50 à 350). La solution du système d'équations régissant le problème a été réalisée par un schéma de volumes finis associé à l'algorithme SIMPLE (Semi Implicit Method for Pressure Linked Equation) pour surmonter le problème de couplage pression-vitesse. L'étude s'est concentrée principalement sur les effets des deux paramètres pertinents : le nombre de Reynolds et la forme géométrique des microcanaux. Les deux champs de vitesse axiale et de température ont été analysés, et le nombre moyen de Nusselt, le coefficient de frottement et la quantité de chaleur évacuée. Les résultats montrent que la structure de l'écoulement est fortement perturbée par la présence de discontinuités sur les parois, et le nombre de Nusselt moyen augmente toujours la fonction du nombre de Reynolds pour les quatre cas étudiés, tandis que l'évolution du coefficient de frottement peut être croissante ou décroissant en fonction du nombre de Reynolds

Numerical Evaluation the Impact of the Inserts Shape on Thermo-Flow Behavior in a Heat Exchanger

The improvement of transfers in a heat exchanger can be achieved either by increasing its coolant thermal conductivity or by modifying its geometrical configuration. In this paper, we will be interested in the latter technique by choosing a three-dimensional configuration represented by a channel of rectangular section, on which solid fins of square, circular, or diamond section (vortex generator) have been transversally mounted, which are moreover adiabatic and non-rotating. A convective and forced airflow traverses the channel, and the study focused in principle on the effects of the shape of the fins on the structure of the flow and the rate of heat transfer. The problem is governed by the Navier-Stokes system, coupled with the energy equation de-scribing the thermal process. The resolution of the equation system governing the hydrodynamic phenomenon is performed numerically in three dimensions. To do this, the governing equations of the thermo-hydrodynamic phenomenon are discretized by a finite volume scheme. As for turbulence, it is modeled using the standard model k-ɛ, and the problem of pressure-velocity coupling is solved by the SIMPLE algorithm (Semi Implicit Method for Pressure Linked Equation). The computed results are presented as curves for the Nusselt number, friction factor, thermal enhancement factor, or amount of heat dissipated, and as a map for the contour of the axial velocity norm and the temperature field distribution

A game theory framework for clustering

The Game Theory-based Multi-Agent System (GTMAS) of Toreyen and Salhi, [10] and [12], implements a loosely coupled hybrid algorithm that may involve any number of algorithms suitable, a priori, for the solution of a given optimisation problem. The system allows the available algorithms to co-operate toward the solution of the problem in hand as well as compete for the computing facilities they require to run. This co-operative/competitive aspect is captured through the implementation of the Prisoners? Dilemma paradigm of game theory. Here, we apply GTMAS to the problem of clustering European Union (EU) economies, including Turkey, to find out whether the latter, based on a number of criteria, can fit in the EU and find out which countries, if any, it has strong similaries with. This clustering problem is first converted into an optimisation problem, namely the Travelling Salesman Problem (TSP) before being solved with GTMAS involving two players (agents) each implementing a standard combinatorial optimisation algorithm. Computational results are included

A New Lanczos-Type Algorithm for Systems of Linear Equations

Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal polynomials of low degree. In this paper, we consider a recurrence relation that has not been studied before and which involves a relatively higher degree polynomial. Interestingly, it leads to an algorithm that shows superior stability when compared to existing Lanczos-type algorithms. This new algorithm is derived and described. It is then compared to the best known algorithms of this type, namely A5/B10, A8/B10, as well as Arnoldi's algorithm, on a set of standard test problems. Numerical results are included

Theoretical study of the erbium-doped fiber laser passively mode-locked by nonlinear polarization rotation

We investigate theoretically the mode-locking properties of an erbium-doped birefringent fiber laser in a unidirectional cavity containing an optical isolator. The mode-locking is achieved through nonlinear polarization rotation. The approach is based on a master equation which takes explicitly into account the angles between the eigen axis of the fiber at each side of the polarizer. The stability conditions of both the stationary and localized solutions are determined. This allows to establish a stability diagram versus the angles which gives the domains where the laser operates in continuous, mode-locked or unstable regime. The model also allows to calculate the pulse duration together with the pulse energy as a function of the orientation of the eigen axis of the fiber with respect to the polarizer

A19/B6: A new Lanczos-type algorithm and its implementation

Lanczos-type algorithms are mostly derived using recurrence relationships between formal orthogonal polynomials. Various recurrence relations between these polynomials can be used for this purpose. In this paper, we discuss recurrence relations A 19 and B 6 for the choice Ui ( x ) = P(1)i(x), where Ui is an auxiliary family of polynomials of exact degree i. This leads to new Lanczos-type algorithm A19=B6 that shows superior stability when compared to existing algorithms of the same type. This new algorithm is derived and described here. Computational results obtained with it are compared to those of the most robust algorithms of this type namely A12, A new 12 A5=B10 and A8=B10 on the same test problems. These results are included