Challenges and progress on the modelling of entropy generation in porous media: a review

Depending upon the ultimate design, the use of porous media in thermal and chemical systems can provide significant operational advantages, including helping to maintain a uniform temperature distribution, increasing the heat transfer rate, controlling reaction rates, and improving heat flux absorption. For this reason, numerous experimental and numerical investigations have been performed on thermal and chemical systems that utilize various types of porous materials. Recently, previous thermal analyses of porous materials embedded in channels or cavities have been re-evaluated using a local thermal non-equilibrium (LTNE) modelling technique. Consequently, the second law analyses of these systems using the LTNE method have been a point of focus in a number of more recent investigations. This has resulted in a series of investigations in various porous systems, and comparisons of the results obtained from traditional local thermal equilibrium (LTE) and the more recent LTNE modelling approach. Moreover, the rapid development and deployment of micro-manufacturing techniques have resulted in an increase in manufacturing flexibility that has made the use of these materials much easier for many micro-thermal and chemical system applications, including emerging energy-related fields such as micro-reactors, micro-combustors, solar thermal collectors and many others. The result is a renewed interest in the thermal performance and the exergetic analysis of these porous thermochemical systems. This current investigation reviews the recent developments of the second law investigations and analyses in thermal and chemical problems in porous media. The effects of various parameters on the entropy generation in these systems are discussed, with particular attention given to the influence of local thermodynamic equilibrium and non-equilibrium upon the second law performance of these systems. This discussion is then followed by a review of the mathematical methods that have been used for simulations. Finally, conclusions and recommendations regarding the unexplored systems and the areas in the greatest need of further investigations are summarized

A thermodynamic analysis of forced convection through porous media using pore scale modeling

The flow thorough porous media is analyzed from a thermodynamic perspective, with a particular focus on the entropy generation inside the porous media, using a pore scale modeling approach. A single representative elementary volume was utilized to reduce the CPU time. Periodic boundary conditions were employed for the vertical boundaries, by re-injecting the velocity and temperature profiles from the outlet to the inlet and iterating. The entropy generation was determined for both circular and square cross-sectional configurations, and the effects of different Reynolds numbers, assuming Darcy and Forchheimer regimes, were also taken into account. Three porosities were evaluated and discussed for each cross-sectional configuration, and streamlines, isothermal lines and the local entropy generation rate contours were determined and compared. The local entropy generation rate contours indicated that the highest entropy generation regions were close to the inlet for low Reynolds flows and near the central cylinder for high Reynolds flows. Increasing Reynolds number from 100 to 200 reveals disturbances in the dimensionless volume averaged entropy generation rate trend that may be due to a change in the fluid flow regime. According to Bejan number evaluation for both cross-section configurations, it is demonstrated that is mainly provoked by the heat transfer irreversibility. A performance evaluation criterion parameter was calculated for different case-studies. By this parameter, conditions for obtaining the least entropy generation and the highest Nusselt number could be achieved simultaneously. Indeed, this parameter utilizes both the first and the second laws of thermodynamics to present the best case-study. According to the performance evaluation criterion, it is indicated that the square cross-section configuration with o=0.64 exhibits better thermal performance for low Reynolds number flows. A comparison between the equal porosity cases for two different cross-sectional configurations indicated that the square cross-section demonstrated a higher performance evaluation criterion than the circular cross-section, for a variety of different Reynolds numbers

Generation of entropy and forced convection of heat in a conduit partially filled with porous media- Local thermal non-equilibrium and exothermicity effects applied thermal engineering

The performance of a two-dimensional, axisymmetric channel with porous inserts attached to the walls is analyzed from the perspective of the first and second laws of thermodynamics. In this analysis, the flow is assumed to be fully developed with a constant heat flux imposed on the external surfaces of the walls, while heat could be internally generated by the fluid and solid phases. Using a Darcy-Brinkman model of momentum transport along with a two-equation thermal energy model, a convective model was developed to describe the thermal boundary conditions on the porous-fluid interface. The so-called Model A was employed on the walls of the channel and semi-analytical solutions were developed for the hydrodynamic, temperature, entropy generation fields and the Nusselt number, and an extensive parametric study was subsequently, conducted. The results indicated that the inclusion of exothermicity leads to significant modifications in the thermal and entropic behaviour of the system. In particular, through comparison with the recent literature, it was demonstrated that exothermicity can significantly impact the influence of the porous-fluid interface model upon the generation of both the local and total entropy within the system