Role of moving horizontal walls on entropy generation during mixed convection within entrapped triangular cavities

A comprehensive analysis based on the irreversibilities associated with the energy flow and entropy generation is highly essential for the optimization of thermal systems. Entropy generation during mixed convection process has been studied in entrapped triangular cavities for moving horizontal walls involving isothermally hot inclined walls and cold horizontal walls (case 1) or isothermally cold inclined walls and hot horizontal walls (case 2). Overall it is found that, Re = 100 may be preferred over Re → 0, Re = 1 and Re = 10 at Pr = 0.026 and 7.2, Gr = 10³ − 10⁵ within the cavities, irrespective of the cases. In addition to Re = 100, Re = 10 may be optimal for the upper cavity with case 1 and lower cavity with case 2 at Gr ≈ 10⁵ (higher Gr regime) and Pr = 7.2 based on moderate heat transfer rates.     

Role of various moving walls on entropy generation during mixed convection within entrapped porous triangular cavities

The aim of the present investigation is to analyze the effect of the motion of horizontal walls on the entropy generation and heat transfer rates in an entrapped triangular porous cavity during mixed convection. Two different thermal boundary conditions are considered as follows: (i) hot inclined walls and cold horizontal walls and (ii) cold inclined walls and hot horizontal walls. Overall, Re?=?100 may be recommended at Pr_m?=?0.026, 7.2, Gr?=?10⁵, and Da_m?=?10^?4 to 10^?2 within the upper and lower cavities for cases 1 and 2.     

Magnetohydrodynamic natural convection in trapezoidal cavities

A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra = 10⁵ and 10⁶ respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra = 10⁵ and 10⁶ respectively.     

Natural convection for hot materials confined within two entrapped porous trapezoidal cavities

This paper analyzes the detailed heat transfer and fluid flow within two entrapped porous trapezoidal cavities involving cold inclined walls and hot horizontal walls. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Darcy-modified Rayleigh number, aspect ratio of two entrapped trapezoidal cavities and thermal conductivity ratio between the middle horizontal wall and fluid medium. Heat transfer rates are estimated in terms of local and mean Nusselt numbers. Local Nusselt numbers with spatial distribution exhibit monotonic trend irrespective of all Rayleigh numbers for the upper trapezoidal whereas wavy distribution of local Nusselt number occur for the lower trapezoidal.     

Inhomogeneous flow model of natural convection,entropy generation,and heatlines visualization in wavy I-shaped enclosure with rectangular heater

The present investigation is on examination of the natural convection and entropy generation considering the heatlines visualization of nanofluid I-shaped enclosure with two corrugated walls considering inner rectangular heater of three different heights. The influence of Brownian motion along with thermophoresis had been implemented using Inhomogeneous two-phase model of nanofluid. The governing equations were solved numerically using COMSOL software. Influence of Rayleigh number $$, Buoyancy ratio number $$, Lewis number $$, heater length $$. The results indicate that the influence of Lewis number on heat transfer bettering is stronger at high Rayleigh number $$ while its impact is negligible at a lower value of Rayleigh number (conduction mode). In addition, the total entropy generation gets its highest value at Lewis number $$. Bejan number, fluid flow strength and heat rate increase as the rectangular heater height increases. Also, higher heat transfer augmentation is taken when the heater height is $$ while increasing the heater height to $$ leads to more total entropy generation. The impact of heater height on total entropy generation is highly affected by Rayleigh number as increasing the heater height from $$ into $$, total entropy generation increases by $$ at $$ while it increases by $$ at $$.     

Analysis of entropy generation during natural convection in porous enclosures with curved surfaces

The natural convection is analyzed via the entropy generation approach in the differentially heated, porous enclosures with curved (concave or convex) vertical walls. The numerical simulations have been carried out for various fluids (Prandtl number: Pr_m?=?0.015, 0.7, and 7.2) at various permeabilities (Darcy numbers: 10^?5?≤?Da_m?≤?10^?2) for a high value of Rayleigh number (Ra_m?=?10⁶). The finite element method is employed to solve the governing equations and that is further used to calculate the entropy generation and average Nusselt number. The detailed spatial distributions of S_θ and S_ψ are analyzed for all the wall curvatures. Overall, the case with the highly concave surfaces (case 3) is the optimal case at low Da_m, whereas the cases with the less convex surfaces (cases 1 and 2) are the most efficient cases at high Da_m.     

Numerical simulation of double-diffusive mixed convection and entropy generation in a lid-driven trapezoidal enclosure with a heat source

In this study, entropy generation of double-diffusive mixed convection is investigated inside a right-angled trapezoidal cavity with a partially heated and salted bottom wall. Similar to the approach that assigns color to streamlines, a new coloring scheme is employed to visualize heatlines and masslines in a more meaningful manner. In addition, various consequential parameters, namely the Lewis and Richardson numbers, the buoyancy ratio, the direction of lid movement, and the heat source location, have been analyzed. According to the results, as the Lewis number increases, the average Nusselt number declines, while the total entropy generation augments. Furthermore, for Le?=?0.1, the conduction mass transfer dominates the mass transfer field; hence, the masslines are virtually perpendicular to the isoconcentration lines.     

Entropy generation and natural convection in rectangular cavities

This work presents a numerical analysis of entropy generation in rectangular cavities that were submitted to the natural convection process. This natural convection process was caused by temperature differences between the vertical walls of the cavities. Momentum and energy equations were used to solve this problem. These equations were coupled by the Boussinesq approximation. Initially the cavities were submitted to uniform temperature and velocity fields. The hypothesis of perfect insulation was considered for the top and bottom walls of the cavity. Impermeability and non-slip condition in the boundary were assumed for every wall of the cavity. The numerical analysis is performed through a two-dimensional model with the Finite Volume method. The results of the entropy generation obtained to a square cavity were used to validate the numerical model and it presented good concordance with results from other authors. Additionally, an analysis of the entropy generation in rectangular cavities was performed with five aspect ratios, five Rayleigh numbers and four irreversibility coefficients. The results of this work indicate that: (a) the total entropy generation in steady state increases linearly in both cases, the aspect ratio and the irreversibility coefficient, and exponentially with the Rayleigh number; (b) the influence of the aspect ratio on Bejan number is proportional to Rayleigh number and inversely proportional to the irreversibility coefficient; (c) for the same aspect ratio, the entropy generation due to the viscous effects increases with the Rayleigh number and, for a certain Rayleigh number, the entropy generation due to the viscous effects also increases with the aspect ratio.     

Analysis of entropy generation during natural convection in tilted triangular enclosures with various base angles

ABSTRACT

This paper presents a study of entropy generation during natural convection in a triangular enclosure with various configurations (cases 1 and 2 symmetric about Y-axis, and case 3 symmetric about X-axis) for the linearly heated inclined walls. The detailed analysis and comparison for the various base angles (φ = 45° and 60°) of the triangular enclosures have been carried out for Pr = 0.015 ? 1,000 and Ra = 10³ ? 10⁵. The results show that, case 3 configuration with the tilt angle φ = 60° may be the optimal shape based on the minimum total entropy generation (S_total) with the high heat transfer rate at Ra = 10⁵, irrespective of Pr.     

Natural convection in divided trapezoidal cavities filled with fluid saturated porous media

A numerical work was performed to determine the heat transfer and fluid flow due to buoyancy forces in divided trapezoidal enclosures filled with fluid saturated porous media. In the present investigation, bottom wall was non-uniformly heated while two vertical walls were insulated and the top wall was maintained at constant cold temperature. The divider had constant thermal conductivity. Flow patterns and temperature distribution were obtained by solving numerically the governing equations, using Darcy's law. Results are presented for different values of the governing parameters, such as Rayleigh number for a porous medium, location of the partition, thickness of the partition and thermal conductivity ratio between solid and fluid media. It was observed that the conduction mode of heat transfer became dominant inside the cavity for higher thickness of the partition, low Rayleigh numbers, and low thermal conductivity ratio.     

Numerical investigation of several physical and geometric parameters in the natural convection into trapezoidal cavities

Natural convection in trapezoidal cavities, especially those with two internal baffles in conjunction with an insulated floor, inclined top surface, and isothermal left-heated and isothermal right-cooled vertical walls, has been investigated numerically using the Element based Finite Volume Method (EbFVM). In numerical simulations, the effect of three inclination angles of the upper surface as well as the effect of the Rayleigh number (Ra), the Prandtl number (Pr), and the baffle’s height (H_b) on the stream functions, temperature profiles, and local and average Nusselt numbers has been investigated. A parametric study was performed for a wide range of Ra numbers (10³ ? Ra ? 10⁶) H_b heights (H_b = H¹/3, 2H¹/3, and H¹), Pr numbers (Pr = 0.7, 10 and 130), and top angle (θ) ranges from 10 to 20. A correlation for the average Nusselt number in terms of Pr and Ra numbers, and the inclination of the upper surface of the cavity is proposed for each baffle height investigated.     

Natural convection and entropy generation in a square cavity

A natural convection in a square cavity finds considerable interest in thermal engineering applications. However, the use of entropy generation concept enables to identify the optimum conditions for its practical application. Consequently, in the present study, natural convection in a square cavity with differential top and bottom wall temperatures is investigated. A numerical scheme using the control volume approach is introduced when discretizing the governing flow and energy equations. The study is extended to include the analysis of the entropy in the cavity. It is found that the local rise of temperature occurs at the right bottom of the cavity due to vertical circulation developed in the cavity. The entropy generation amplifies when circulation along the x-axis increases and, the entropy generation becomes minimum for a particular Rayleigh number. © 1998 John Wiley & Sons, Ltd.     

Three-dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

The present article provides a three-dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (${10}^3\le \mathit{Ra}\le {10}^7$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from $\mathit{Ra}={10}^3$ to ${10}^7$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient $\mathit{\phi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number ($\mathit{Ra}={10}^3$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of $\mathit{Ra}={10}^4$ and ${10}^5$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large ($\mathit{Ra}{\ge 10}^6$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.     

Analysis of entropy generation for distributed heating in processing of materials by thermal convection

Analysis of entropy generation has been carried out for square cavities with distributed heated sources filled with various materials involving wide range of Pr(=0.015, 0.7, 10, 1000) during the conduction and convection regime within Ra(=10³ ? 10⁵). Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on elemental basis set via Galerkin finite element method. Local entropy maps are analyzed in detail for various cases and the dominance of thermal and frictional irreversibilities is studied via average Bejan number. The heat transfer irreversibility is found to dominate during conduction regime while the fluid friction irreversibility dominates the entropy generation in the convection regime, except for the low Pr fluid based on the heating configuration of the cavity. Further, the variation of total entropy generation has been observed to be similar for different heating configurations for higher Pr fluids (=10, 1000) whereas, the configuration of cavity has been found to have little effect on total entropy generation for fluids with Pr = 0.7 during both conduction and convection regimes. Thermal mixing and degree of temperature uniformity due to distributed heating in various cases are also reported and optimum cases for processing of various fluids are presented based on minimum entropy generation.