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An analysis of thermodynamic irreversible principle (TPI), through determination of entropy generation rate, during double-diffusive convection in an octagonal shape, filled with saturated fluid in a porous enclosure, is numerically investigated in this work, by studying the influence of thermodiffusion effect on entropy generation variations. According to the fluid flow evolution under consideration, the influence of mass flux due to temperature gradient is incorporated into the governing equations of the problem, which are solved numerically, using the COMSOL software. Appropriated thermal and solutal Dirichlet boundary conditions are used under the Boussinesq approximation. For the porous medium, the Darcy–Brinkman model is assumed in coupling with energy and mass transfer balance equations. The flow model is described in terms of mass flux due to temperature gradient, buoyancy ratio, thermal Rayleigh number and porosity of the medium. Results of the variations of heat transfer and entropy generation in the studied enclosure are graphically illustrated and are basically discussed, through various physical aspects of the problem. The numerical computations are presented for various values of thermal Rayleigh number (RaT), thermal diffusion parameter (Kt), Darcy number (Da), buoyancy ratio (N) and porosity of the medium (ε). In addition, the total entropy generation due to thermal, species and mixed diffusion gradients; Darcy–Brinkman dissipation; and fluid friction are studied and discussed. It is found that the entropy generation increases strongly when passing from the cooperative case of buoyancy forces to the opposite case. A similar behaviour is obtained with increasing the thermal diffusion ratio, at a constant buoyancy ratio. Also, an accentuated increase in entropy generation is observed when the Darcy number exceeds the value 10−6. Moreover, the results show that the augmentation of the thermodiffusion effect induces an increase in total entropy generation, at fixed value of the porosity. [ABSTRACT FROM AUTHOR]

The paper provides a numerical investigation of the entropy generation analysis due to mixed convection with viscous dissipation effect of a laminar viscous and incompressible fluid, flowing in an inclined channel filled with a saturated porous medium. The Darcy-Brinkman model is employed. The Navier-Stokes and energy equations are solved by classic Boussinesq incompressible approximation. A special attention is given to the study of the influence of the channel inclination angle on the transient and the steady-state entropy generation. The fluctuations of the transient total entropy generation are investigated when the inclination angle is varied from $$0^{\circ }$$ to $$180^{\circ }$$ . Moreover, the entropy generation and the Bejan number were studied as a function of the inclination angle of the channel, in the steady state of mixed convection. It was found that the total entropy generation is maximum at inclination angle close to $$70^{\circ }$$ and minimum at $$0^{\circ }$$ and $$180^{\circ }$$ . [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The influence of Prandtl number on entropy generation in natural convection under an external uniform magnetic field for different electrically conducting fluids, from liquid metal to liquid passing through gas, in square cavity is numerically studied in steady-unsteady states by solving the mass, the momentum and the energy conservation equations. Entropy generation depends on three parameters which are: the Prandtl, the Hartmann and the thermal Grashof 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. The effect of Prandtl number tends to increase the heat transfer, on the other hand tends to decrease the entropy generation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper numerically investigates the effect of an externally evanescent magnetic field on total entropy generation in a fluid enclosed in a square cavity by using a control volume finite element method to solve the conservation equations at Prandtl number of 0·71. The values of relaxation time of the magnetic field are chosen, so that the Lorentz force acts only in the transient state of entropy generation in natural convection. The total entropy generation was calculated for, fixed value of irreversibility distribution ratio, different relaxation time varying from 0 to 1/5 and Grashof number varying from 104 to 105. The effects of the Hartman number and the magnetic field inclination angle on the evolution of total entropy generation throughout the transient regime were investigated. Results show that the application of evanescent magnetic field not only suppresses the fluctuation of the total entropy generation in the transient state, but also reduces the gap for magnetic field relaxation time less than 1/10. [ABSTRACT FROM AUTHOR]

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. [Copyright &y& Elsevier]