Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

Heat transfer and second law analyses of forced convection in a channel partially filled by porous media and featuring internal heat sources

This paper provides a comprehensive study on the heat transfer and entropy generation rates in a channel partially filled with a porous medium and under constant wall heat flux. The porous inserts are attached to the walls of the channel and the system features internal heat sources due to exothermic or endothermic physical or physicochemical processes. Darcy-Brinkman model is used for modelling the transport of momentum and an analytical study on the basis of LTNE (local thermal non-equilibrium) condition is conducted. Further analysis through considering the simplifying, LTE (local thermal equilibrium) model is also presented. Analytical solutions are, first, developed for the velocity and temperature fields. These are subsequently incorporated into the fundamental equations of entropy generation and both local and total entropy generation rates are investigated for a number of cases. It is argued that, comparing with LTE, the LTNE approach yields more accurate results on the temperature distribution within the system and therefore reveals more realistic Nusselt number and entropy generation rates. In keeping with the previous investigations, bifurcation phenomena are observed in the temperature field and rates of entropy generation. It is, further, demonstrated that partial filling of the channel leads to a substantial reduction of the total entropy generation. The results also show that the exothermicity or endothermicity characteristics of the system have significant impacts on the temperature fields, Nusselt number and entropy generation rates

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition: an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers

Analytical investigation of heat transfer enhancement in a channel partially filled with a porous material under local thermal non-equilibrium condition: Effects of different thermal boundary conditions at the porous-fluid interface

Enhancement of forced convective heat transfer is analytically investigated in a channel partially filled with a porous medium under local thermal non-equilibrium (LTNE) condition. Thermally and hydrodynamically fully developed conditions are considered. The flow inside the porous material is modelled by the Darcy–Brinkman–Forchheimer equation. The thermal boundary conditions at the interface between the porous medium and the clear region are described by two different models. For each interface model exact solutions are developed for the solid and fluid temperature fields. The Nusselt number (Nu) associated with each interface model is derived in terms of the porous insert normalised thickness (S) and other pertinent parameters such as thermal conductivity ratio (k), Biot number (Bi), and Darcy number (Da). The differences between the two interface models in predicting the temperature fields of the solid and fluid phases and validity of the Local Thermal Equilibrium (LTE) assumption are examined. Subsequently, for each model the values of S, Bi, k and Da at which LTE holds are determined. Further, the maximum values of S up to that the two models predict LTE condition are found as a function of Bi, k and Da. For each model and for different pertinent parameters the optimum value of S, which maximises the Nu number, is then found. The results show that, in general, the obtained Nu numbers can be strongly dependent upon the applied interface model. For large values of k and Bi, there are significant disparities between the Nu numbers predicted by the two models. Nonetheless, for most values of k and Bi, and under different values of Da numbers both models predict similar trends of variation of Nu number versus S. The Nu number and pressure drop ratio are then used to determine the Heat Transfer Performance (HTP). It is found that for S < 0.9, HTP is independent of Da number and the model used at the porous-fluid interface. For S > 0.9, reduction of Da results in smaller values of HTP and signifies the difference between the values of HTP predicted by the two interface models

Porous materials in building energy technologies—a review of the applications, modelling and experiments

Improving energy efficiency in buildings is central to achieving the goals set by Paris agreement in 2015, as it reduces the energy consumption and consequently the emission of greenhouse gases without jeopardising human comfort. The literature includes a large number of articles on energy performance of the residential and commercial buildings. Many researchers have examined porous materials as affordable and promising means of improving the energy efficiency of buildings. Further, some of the natural media involved in building energy technologies are porous. However, currently, there is no review article exclusively focused on the porous media pertinent to the building energy technologies. Accordingly, this article performs a review of literature on the applications, modelling and experimental studies about the materials containing macro, micro, and nano-porous media and their advantages and limitations in different building energy technologies. These include roof cooling, ground-source heat pumps and heat exchangers, insulations, and thermal energy storage systems. The progress made and the remaining challenges in each technology are discussed and some conclusions and suggestions are made for the future research

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

Non-equilibrium thermodynamic analysis of double diffusive, nanofluid forced convection in microreactors with radiation effects

This paper presents a theoretical investigation of the second law performance of double diffusive forced convection in microreactors with the inclusion of nanofluid and radiation effects. The investigated microreactors consist of a single microchannel, fully filled by a porous medium. The transport of heat and mass are analysed by including the thick walls and a first order, catalytic chemical reaction on the internal surfaces of the microchannel. Two sets of thermal boundary conditions are considered on the external surfaces of the microchannel; (1) constant temperature and (2) constant heat flux boundary condition on the lower wall and convective boundary condition on the upper wall. The local thermal non-equilibrium approach is taken to thermally analyse the porous section of the system. The mass dispersion equation is coupled with the transport of heat in the nanofluid flow through consideration of Soret effect. The problem is analytically solved and illustrations of the temperature fields, Nusselt number, total entropy generation rate and performance evaluation criterion (PEC) are provided. It is shown that the radiation effect tends to modify the thermal behaviour within the porous section of the system. The radiation parameter also reduces the overall temperature of the system. It is further demonstrated that, expectedly, the nanoparticles reduce the temperature of the system and increase the Nusselt number. The total entropy generation rate and consequently PEC shows a strong relation with radiation parameter and volumetric concentration of nanoparticles

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

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

RIBBONS: Rapid Inpainting Based on Browsing of Neighborhood Statistics

Image inpainting refers to filling missing places in images using neighboring pixels. It also has many applications in different tasks of image processing. Most of these applications enhance the image quality by significant unwanted changes or even elimination of some existing pixels. These changes require considerable computational complexities which in turn results in remarkable processing time. In this paper we propose a fast inpainting algorithm called RIBBONS based on selection of patches around each missing pixel. This would accelerate the execution speed and the capability of online frame inpainting in video. The applied cost-function is a combination of statistical and spatial features in all neighboring pixels. We evaluate some candidate patches using the proposed cost function and minimize it to achieve the final patch. Experimental results show the higher speed of 'Ribbons' in comparison with previous methods while being comparable in terms of PSNR and SSIM for the images in MISC dataset