H. Abbassi

Entropy generation at the onset of natural convection

The entropy generation due to heat transfer and friction has been determined in transient state for laminar natural convection by solving numerically the mass, momentum and energy balance equations, using a control volume finite-element method. The variations of the total entropy generation as function of time for Rayleigh number and irreversibility distribution ratio set at 103⩽Ra⩽105 and 10−4⩽ϕ⩽10−1 were investigated. The evolution of the maximum of entropy generation with the Rayleigh number is studied. The effect of the irreversibility distribution ratio on the maximum entropy generation and the entropy generation in steady state are analyzed. The irreversibility maps for Rayleigh number set at 103⩽Ra⩽105 and irreversibility distribution ratio ϕ=10−4 are plotted.

Two-dimensional laminar fluid flow and heat transfer in a channel with a built-in heated square cylinder

A numerical investigation was conducted to analyze the unsteady flow field and heat transfer characteristics in a horizontal channel with a built-in heated square cylinder. Hydrodynamic behavior and heat transfer results are obtained by the solution of the complete Navier–Stokes and energy equations using a control volume finite element method (CVFEM) adapted to the staggered grid. The Computation was made for two channel blockage ratios (β=1/4 and 1/8), different Reynolds and Richardson numbers ranging from 62 to 200 and from 0 to 0.1 respectively at Pr=0.71. The flow is found to be unstable when the Richardson number crosses the critical value of 0.13. The results are presented to show the effects of the blockage ratio, the Reynolds and the Richardson numbers on the flow pattern and the heat transfer from the square cylinder. Heat transfer correlation are obtained through forced and mixed convection.

Numerical investigation of forced convection in a plane channel with a built-in triangular prism

Abstract Structure of laminar flow and heat transfer, in a two-dimensional horizontal channel differentially heated, with a built-in triangular prism is investigated from the numerical solutions of complete Navier–Stokes and energy equations. The numerical scheme is based on Control Volume Finite-Element Method with the SIMPLER algorithm for pressure-velocity coupling. Many standard test flows are successfully simulated. Results are obtained for Reynolds number ranging from 20 to 250 at Pr= 0.71 with constant physical properties. The flow is especially studied in details for two Reynolds numbers, Re= 30 as a sample of the symmetric flow, and Re= 100 as a sample for the periodic flow. Results are presented to show how the presence of such bluff body affects the flow pattern and the heat transfer from the hot bottom plate to the flow in both cases, symmetric and periodic flows.

SECOND LAW ANALYSIS IN CONVECTIVE HEAT AND MASS TRANSFER

This paper reports the numerical determination of the entropy generation due to heat transfer, mass transfer and fluid friction in steady state for laminar double diffusive convection, in an inclined enclosure with heat and mass diffusive walls, by solving numerically the mass, momentum, species conservation and energy balance equations, using a Control Volume Finite-Element Method. The influences of the inclination angle, the thermal Grashof number and the buoyancy ratio on total entropy generation were investigated. The irreversibilities localization due to heat transfer, mass transfer and fluid friction is discussed for three inclination angles at a fixed thermal Grashof number.

MIXED CONVECTION IN A PLANE CHANNEL WITH A BUILT-IN TRIANGULAR PRISM

The superposition of Von Karman street and convective cells in a horizontal plane channel containing a triangular prism and heated from below constitute the principal subject of this numerical investigation. The numerical scheme is based on the control volume finite element method (CVFEM) adapted to the standard staggered grid with the SIM PLER algorithm for pressure-velocity coupling and an Alternating Direction Implicit (ADI) scheme for the time integration. Many standard test flows are simulated successfully. Results are obtained for a Grashof number ranging from 0 to 1.5 10 4 at Pr 0.71 and Re 100 with constant physical properties. At the outlet of the computational domain a convective boundary condition (CBC) is used. Results are presented to show the effect of development of convective cells on the flow pattern and on the Strouhal number. Regarding the heat transfer rate, we focus on the effect of the presence of the triangular prism on the heat flux transferred from the hot wall to the flow.The superposition of Von Karman street and convective cells in a horizontal plane channel containing a triangular prism and heated from below constitute the principal subject of this numerical investigation. The numerical scheme is based on the control volume finite element method (CVFEM) adapted to the standard staggered grid with the SIM PLER algorithm for pressure-velocity coupling and an Alternating Direction Implicit (ADI) scheme for the time integration. Many standard test flows are simulated successfully. Results are obtained for a Grashof number ranging from 0 to 1.5 10 4 at Pr 0.71 and Re 100 with constant physical properties. At the outlet of the computational domain a convective boundary condition (CBC) is used. Results are presented to show the effect of development of convective cells on the flow pattern and on the Strouhal number. Regarding the heat transfer rate, we focus on the effect of the presence of the triangular prism on the heat flux transferred from the hot wall to the flow.

Entropy generation in Poiseuille–Benard channel flow

The issue of entropy generation in Poiseuille–Benard channel flow is analyzed by solving numerically the mass, momentum and energy equations with the use of the classic Boussinesq incompressible approximation. The numerical scheme is based on Control Volume Finite Element Method with the SIMPLER algorithm for pressure–velocity coupling. Results are obtained for Rayleigh numbers Ra and irreversibility φ ranging from 103 to 5×104 and from 10−4 to 10 respectively. Variations of entropy generation and the Bejan number as a function of Ra and φ are studied. The limit value φl for which entropy generation due to heat transfer is equal to entropy due to fluid friction is evaluated. It has been found that φl is a decreasing function of the Rayleigh number Ra. φl varies from 0.0015 to 0.096 when Ra decrease from 5×104 to 103. Stream lines and entropy generation maps are plotted at six times over one period at Ra =104 and φ=10−3. It has been found that the maximum entropy generation is localized at areas where heat exchanged between the walls and the flow is maximum. No significant entropy production is seen in the main flow.

Numerical Investigation of Forced Convection in a Horizontal Channel With a Built-In Triangular Prism

Structure of laminar flow and heat transfer, in a two-dimensional horizontal channel differentially heated, with a builtin triangular prism is investigated from the numerical solutions of complete Navier–Stokes and energy equations. The numerical scheme is based on Control Volume Finite-Element Method with the SIMPLER algorithm for pressure-velocity coupling. Many standard test flows are successfully simulated. Results are obtained for Reynolds number ranging from 20 to 250 at Pr =0.71 with constant physical properties. The flow is especially studied in details for two Reynolds numbers, Re =30 as a sample of the symmetric flow, and Re =100 as a sample for the periodic flow. Results are presented to show how the presence of such bluff body affects the flow pattern and the heat transfer from the hot bottom plate to the flow in both cases, symmetric and periodic flows.  2001 Editions scientifiques et medicales Elsevier SAS laminar flow / periodic / obstacle / heat transfer / shedding / vortices / forced convection Resume—La convection forcee d’air dans un canal plan differentiellement chauffe et contenant un obstacle ayant la forme d’un prisme triangulaire est etudiee numeriquement. Les equations de conservation sont resolues pour une geometrie bidimensionnelle par une methode de volumes finis a maillage non structure en conservant la vitesse et la pression comme variables dynamiques du probleme. Plusieurs tests de validations du code de calcul ont ete realises avec succes. Les resultats sont obtenus pour Reynolds allant de 20 a 250 pour Pr =0,71. L’ecoulement est particulierement etudie en details pour Re =30 et Re =100 comme etant deux echantillons respectifs de l’ecoulement symetrique et de l’ecoulement periodique. L’objectif de ce travail est l’etude de l’effet de l’obstacle sur la structure de l’ecoulement et sur les transferts thermiques.  2001 Editions scientifiques et medicales Elsevier SAS ecoulement laminaire / periodique / obstacle / transfert thermique / detachement / tourbillons / convection forcee

Influence of Dufour effect on entropy generation in double diffusive convection

The influence of Dufour effect on entropy generation in double diffusive convection is numerically investigated in this paper. The dimensionless total entropy generation is evaluated as a function of: the buoyancy ratio N, a parameter characterising the solutal buoyancy forces by report to the thermal ones; the Dufour parameter KF, a parameter characterising the influence of the diffusion-thermo effect; the thermal Grashof number. More details of the investigation is focused for the special case when N = −1.

Entropy generation in double diffusive convection in presence of the Soret effect

Influence of the Soret effect on entropy generation in a square cavity filled with a binary gas mixture in double diffusive convection is numerically studied. It was found that entropy generation increases with the increase of thermal diffusion and buoyancy ratios for fixed thermal Grashof number. Total irreversibility takes a minimum value at a special buoyancy ratio ranging between 1 and 0. Soret effect causes the increase of total irreversibility by more than 50% at higher values of thermal Grashof number and buoyancy ratio. More details of the irreversibilities localisation are discussed.

A comparison between linear and exponential schemes in control volume finite element method

In this paper, we present a comparison of linear and exponential interpolation functions for control volume finite element method. The exponential interpolation function is expressed in the elemental local coordinate system whereas the classic linear interpolation function is expressed in the global coordinate system. The comparison is achieved in the case of the Green‐Taylor vortex, a flow from which we know the analytical solution. Firstly, the two functions are applied to a triangular element of the domain to compare the results given by each interpolation function to the exact value. Secondly, these two functions are compared when used to solve the discretized equations over the entire domain.