Mourad Magherbi

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.

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.

Effect of an External Oriented Magnetic Field on Entropy Generation in Natural Convection

The influence of an external oriented magnetic field on entropy generation in natural convection for air and liquid gallium is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on five parameters which are: the Prandtl number, the irreversibility coefficients, the inclination angle of the magnetic field, the thermal Grashof and the Hartmann numbers. Effects of these parameters on total and local irreversibilities as well as on heat transfer and fluid flow are studied. It was found that the magnetic field tends to decrease the convection currents, the heat transfer and entropy generation inside the enclosure. Influence of inclination angle of the magnetic field on local irreversibility is then studied.

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.

Entropy Generation at Natural Convection in an Inclined Rectangular Cavity

Natural convection in an inclined rectangular cavity filled with air is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls of the cavity are adiabatic. Entropy generation due to heat transfer and fluid friction has been determined in transient state for laminar natural convection by solving numerically: the continuity, momentum and energy equations, using a Control Volume Finite Element Method. The structure of the studied flows depends on four dimensionless parameters which are: the thermal Grashof number, the inclination angle, the irreversibility distribution ratio and the aspect ratio of the cavity. The obtained results show that entropy generation tends towards asymptotic values for lower thermal Grashof number values, whereas it takes an oscillative behavior for higher values of thermal Grashof number. Transient entropy generation increases towards a maximum value, then decreases asymptotically to a constant value that depends on aspect ratio of the enclosure. Entropy generation increases with the increase of thermal Grashof number, irreversibility distribution ratio and aspect ratio of the cavity. Bejan number is used to measure the predominance of either thermal or viscous irreversibility. At local level, irreversibility charts show that entropy generation is mainly localized on bottom corner of the left heated wall and upper corner of the right cooled wall.

Entropy Generation in Double-Diffusive Convection in a Square Porous Cavity using Darcy–Brinkman Formulation

The article reports a numerical study of entropy generation in double-diffusive convection through a square porous cavity saturated with a binary perfect gas mixture and submitted to horizontal thermal and concentration gradients. The analysis is performed using Darcy–Brinkman formulation with the Boussinesq approximation. The set of coupled equations of mass, momentum, energy and species conservation are solved using the control volume finite-element method. Effects of the Darcy number, the porosity and the thermal porous Rayleigh number on entropy generation are studied. It was found that entropy generation considerably depends on the Darcy number. Porosity induces the increase of entropy generation, especially at higher values of thermal porous Rayleigh number.

Analysis of the Magnetic Field Effect on Entropy Generation at Thermosolutal Convection in a Square Cavity

Thermosolutal convection in a square cavity filled with air and submitted to an inclined magnetic field is investigated numerically. The cavity is heated and cooled along the active walls with a mass gradient whereas the two other walls of the cavity are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined in transient state for laminar flow by solving numerically the continuity, momentum energy and mass balance equations, using a Control Volume Finite—Element Method. The structure of the studied flows depends on four dimensionless parameters which are the Grashof number, the buoyancy ratio, the Hartman number and the inclination angle. The results show that the magnetic field parameter has a retarding effect on the flow in the cavity and this lead to a decrease of entropy generation, Temperature and concentration decrease with increasing value of the magnetic field parameter.

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.

Effects of Radiation Heat Transfer on Entropy Generation at Thermosolutal Convection in a Square Cavity Subjected to a Magnetic Field

Thermosolutal convection in a square cavity filled with a binary perfect gas mixture and submitted to an oriented magnetic field taking into account the effect of radiation heat transfer is numerically investigated. The cavity is heated and cooled along the active walls whereas the two other walls are adiabatic and insulated. Entropy generation due to heat and mass transfer, fluid friction and magnetic effect has been determined for laminar flow by solving numerically: The continuity, momentum energy and mass balance equations, using a Control Volume Finite-Element Method. The structure of the studied flows depends on five dimensionless parameters which are: The Grashof number, the buoyancy ratio, the Hartman number, the inclination angle of the magnetic field and the radiation parameter.