Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions

Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10^?5–10^?3 and at a representative high Rayleigh number, Ra = 5 × 10⁵. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, thermal mixing, and temperature uniformity.     

Effects of Thermal Boundary Conditions on Entropy Generation during Natural Convection

A comprehensive numerical study on entropy generation during natural convection is studied in a square cavity subjected to a wide variety of thermal boundary conditions. Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on the elemental basis set via the Galerkin finite element method. The thermal and fluid irreversibilities during the conduction and convection dominant regimes are analyzed in detail for various fluids (Pr = 0.026,988.24) within Ra = 10³–10⁵. Further, the effect of Ra on the total entropy generation and average Bejan number is discussed. It is observed that thermal boundary conditions significantly affect the thermal mixing, temperature uniformity, and the entropy generation in the cavity. A case where the bottom wall is hot isothermal with linearly cooled side walls and adiabatic top wall is found to result in high thermal mixing and a higher degree of temperature uniformity with minimum total entropy generation.     

Entropy Generation Minimization Versus Thermal Mixing Due to Natural Convection in Differentially and Discretely Heated Square Cavities

Uniform temperature distribution is a key parameter in many thermal processing applications. A considerable amount of additional energy is used to enhance the fluid mixing in order to maintain the temperature uniformity, but that affects the overall efficiency of the process. In this article, an alternate approach is proposed for maintaining uniform temperature via various distributed/discrete heating strategies while maintaining the minimal entropy generation. The system of laminar natural convection in differentially and discretely heated square cavities filled with various materials (molten metals, air, aqueous solutions, oils) is considered, and finite element simulations are performed for a range of Rayleigh numbers (Ra = 10³–10⁵). Entropy generation is evaluated using finite-element basis sets for the first time in this work, and the derivatives at particular nodes are estimated based on the functions within adjacent elements. Analysis of entropy generation in each case is carried out and a detailed investigation of entropy production due to local heat transfer and fluid friction irreversibilities is presented. It is found that a high thermal mixing may not be the optimal situation for achieving uniform temperature distribution based on entropy production. A greater degree of temperature uniformity with moderate thermal mixing may correspond to minimum entropy generation with distributed heating. Further, based on entropy generation minimization approach, it has been thermodynamically established that the distributed heating methodology with multiple heat sources may be the energy efficient strategy for attaining adequate uniform temperature distribution with minimum entropy generation.     

Role of Entropy Generation On Thermal Management During Natural Convection in a Tilted Square Cavity with Isothermal and Non-Isothermal Hot Walls

Entropy generation during natural convection within tilted square cavity inclined with different angles (? = 30°and 75°) for various thermal boundary conditions (case 1: isothermal heating and case 2: non-isothermal heating) has been studied. Simulations are carried out over a range of parameters: Rayleigh number (10³ ≤ Ra ≤ 10⁵) and Prandtl numbers (Pr = 0.025 and 998.24). The numerical results are presented in terms of isotherms (θ), streamlines (ψ), entropy generation due to heat transfer (S _θ ) and fluid friction (S _ψ ). Heating strategy is energy efficient for case 2 (non-isothermal heating) due to its less total entropy generation with reasonable heat transfer rate, irrespective of Pr.     

Analysis of Particle Dispersion and Entropy Generation in Turbulent Mixed Convection of CuO-Water Nanofluid

In the present study, turbulent mixed convection of CuO-water nanofluid is investigated in a vertical duct. In order to simulate the nanofluid flow, the fluid phase is considered as continuous whilst the discrete particles are dispersed through it. The dispersion of CuO nanoparticles at different Reynolds numbers is studied to predict the effective mechanisms concerning nanoparticles dispersion. Results show that in the turbulent fully developed region of the duct, the effect of thermophoresis is more important than Brownian motion and the dispersion of particles is higher in the duct core region. However, in the entrance region, the particles are dispersed almost uniformly. Also, increasing the nanoparticles volume fraction augments the root mean square of turbulent velocity fluctuations and this enhances the convective heat transfer as compared with the laminar flow. Moreover, increasing the nanoparticle volume fraction decreases the thermal entropy generation and increases the frictional entropy generation and due to the dominance of thermal entropy generation, the total entropy generation therefore reduces.     

Effect of Undulations on the Natural Convection Heat Transfer and Entropy Generation Inside a Porous Right-Angled Triangular Enclosure

In the present study, natural convection in a two-dimensional porous right-angled triangular enclosure with one wavy wall is studied numerically. Three cases with one, two, and three undulations on the left wall are studied in this analysis. The stream function-vorticity equations are solved using finite-difference technique and a structured nonorthogonal body-fitted mesh is used for computations. The effect of Rayleigh number (Ra = 10³–10⁶), Darcy number (Da = 10^?4–10^?2) and undulations on the heat transfer, fluid flow, and entropy generation is investigated. It is found that average Nusselt number increases with Darcy number and number of undulations present on the left wall at fixed Darcy number.     

燃煤锅炉吹灰过程的熵产分析

电站燃煤锅炉运行中对受热面进行吹灰,要经历一系列不可逆过程,出现各种熵产,从热力学第二定律出发,分析电站锅炉吹灰过程的熵产,建立了吹灰蒸汽减压熵产、吹灰蒸汽混合熵产、吹灰蒸汽传热熵产、吹灰蒸汽排烟熵产以及吹灰器电机熵产的计算模型.利用某台燃煤锅炉的现场数据进行了实例计算,结果表明:同一个受热面吹灰所产牛的各种熵产在数值...     

Numerical Study on Mixed Convection Heat Transfer in Inclined Triangular Cavities

This article presents a parametric study on flow behavior and heat transfer in an inclined triangular cavity subjected to a moving lid and temperature differential. The systematic study considers three physical parameters (inclination angle, Reynolds number, and Grashof number) and explores the influence of these parameters on flow pattern and heat transfer characteristics. A series of computations were performed for the inclination angle (θ) ranging from 0° to 360° (in increments of 45°), Reynolds number (Re) from 100 to 1,500, and Grashof number (Gr) from 10⁵ to 10⁷. The numerical results show that there are three kinds of flow regime in a triangular cavity inclined from 0° to 360°: buoyancy-dominant, inertia-dominant, and intermediate transition (mixed convection flow). It is interesting that the case with Re = 100, Gr = 10⁷, and θ = 0° exhibits five circulation cells and induces excellent thermal performance, corresponding to wavy profiles in local Nusselt number and local friction factor. The study also reveals that the good thermal performance within a local region can generate higher friction force on the neighboring boundary and this friction force may reduce the strength of the vortex.     

Entropy Analysis of a Coupled‐Convection Flow through a Vertical Channel Partially Filled by a Porous Medium with Injection/Suction and Slip Boundary Conditions

Flow fields, thermal fields, and entropy generation have been investigated for fully developed mixed convection flow between two vertical porous plates. The vertical channel is partially filled by a porous medium, and channel walls are subjected to a constant injection velocity at the left wall and constant suction velocity at the right wall. The viscous dissipation effects and velocity slip for the longitudinal component of the velocity at the channel walls are also taken into account. The momentum and energy equations for the mixed convection problem in the vertical channel are solved by means of the perturbation series method, by taking perturbation parameter proportional to the Brinkman number. For the present problem, numerical solution is also obtained and compared with the analytical solution. The effects of various pertinent parameters on the velocity distribution, temperature distribution, entropy generation rate, and Bejan number are investigated and discussed graphically.     

Entropy Generation due to Combined Natural Convection and Thermal Radiation within a Rectangular Enclosure

ABSTRACT

The present work investigates entropy production due to coupled natural convection/radiation heat transfer phenomenon in an inclined rectangular enclosure, isothermally heated from the bottom side and isothermally cooled from the other sides. The discrete-ordinate method is used in modeling the radiative transport equation while the statistical narrow band correlated-k model is adopted to deduce the radiative properties of the medium. The influence of pertinent parameters such as aspect ratio, inclination angle and walls emissivities on entropy generation is studied. It is found that the volumetric entropy generation is reduced when increasing the inclination angle of the enclosure. Moreover, it is shown that the minimum entropy production due to radiation heat transfer in participating media occurs at aspect ratio equal to unity.     

Natural Convection Heat Transfer and Entropy Generation in a Porous Trapezoidal Enclosure Saturated with Power-Law Non-Newtonian Fluids

Abstract

In the present study, natural convection heat transfer and its associated entropy generation in a porous trapezoidal enclosure saturated with a power-law non-Newtonian fluid has been numerically investigated. Horizontal walls of the enclosure are assumed to be adiabatic while the side walls are considered to be kept at a constant temperature. A continuum-based approach is adapted here to model the fluid flow through porous media and the Darcy’s law is modified to account for non-Newtonian rheological behavior of the fluid. The obtained governing equations are discretized using the finite volume method and a detailed parametric study is undertaken to account for the effects of various relevant parameters of the problem on the heat transfer and entropy generation rates. It was shown that the impact of the power-law index on both entropy generation and heat transfer significantly intensifies in a convection-dominated flow regime inside the enclosure, especially for a shear thinning liquid. Moreover, heat transfer rate and entropy generation increase as the sidewall angle is elevated.     

Non-Darcy Mixed Convection in a Porous Square Enclosure Under Suction/Injection Effects with a Non-Isothermal Vertical Wall

The influence of suction/injection at bottom/top or top/bottom walls on non-Darcy mixed convection flow with a sinusoidally varying temperature on the left vertical wall in a two-dimensional square porous enclosure is analyzed. The Forchheimer extended Darcy model is considered for flow equations. The fully developed equations are nondimensionalized, and then solved numerically by the Galerkin finite element method. A parametric study is carried out and the results are obtained for various values of the parameters such as the Grashof number (Gr*), Rayleigh number (Ra), suction/injection velocity (a), suction/injection window width (D/H), and amplitude (λ) of the sinusoidally varying temperature profile. The computed flow and temperature fields are visualized through streamlines, isotherms, and loal/global cumulative heat flux plots.     

Numerical Investigation of the Entropy Generation Due to Natural Convection in a Partially Heated Square Cavity Filled With Nanofluids

A comprehensive numerical investigation has been carried out on the heat transfer performance and entropy generation within a rectangular cavity containing nanofluid. The cavity consists of two heat sources located on the bottom and a side wall. The effects of influential parameters including type and concentration of nanoparticles, radius of corner, width and thickness of heaters, heater distance from corners and aspect ratio of the enclosure were studied. The results showed that the Nusselt number enhanced by increasing the aspect ratio of the cavity, the distance of heaters from the corners, and concentration of nanoparticle and applying Cu as nanoparticle while it reduced by increasing the radius of the corner and the width and thickness of the heat sources. The entropy generation was found to be profoundly minimized by lowering the Rayleigh number. In addition, the entropy generation was attenuated by increasing the Eckert number, corner radius, the distance from the corner and concentration of nanoparticles and using Al₂O₃ as nanoparticle. On the other hand, increasing the aspect ratio of the cavity, width and thickness of the heaters augmented the entropy generation. Interestingly, the entropy generation of the system was lowered by just increasing the distance of one heater from the corner, whereas increasing the thickness and width of one heater resulted in larger entropy generation. This study provides valuable insight into the change in the amount of heat transfer and entropy by altering the geometry as well as fluid properties.     

Soret Effect on Double-Diffusive Convection in a Square Porous Cavity Heated and Salted from Below

This article presents a numerical study of the Soret effect on double diffusion in a two-dimensional square cavity filled with a saturated Darcy porous medium. The horizontal walls of the cavity are subject to different but uniform temperatures and concentrations such that the medium is heated and salted from below. The left and right vertical walls are adiabatic and impermeable. Combined effects of the buoyancy ratio N (?1.5 < N < 4.4) and the Soret parameter M (?60.5 < M < 155) on the fluid flow and heat and mass transfer characteristics corresponding to monocellular, bicellular, and tricellular modes are studied for R _T  = 200 and Le = 10. It is found that the thresholds of N marking the transitions towards the oscillatory regime strongly depend on the Soret parameter M. The thermodiffusion phenomenon considerably affects the heat transfer; the Nusselt number increases with M in the case of the tricellular flow, but it goes through a maximum in the case of monocellular and bicellular flows.     

Radiation Effect on Mixed Convection over an Isothermal Wedge in Porous Media: The Entire Regime

A straightforward heat exchanger thermal model is presented and verified experimentally. It may be used to predict the performance of a coil that has condensation occurring on the gas side. Experimentally determined heat and mass transfer coefficients are employed in the model Sample data are presented for a wide range of surface wetting conditions. Partially wet heat exchangers are analyzed by employing an area weighting scheme to the dry and wet portions of the coil with moderate success. It is shown that employing a heat / mass transfer analogy in predicting the performance of a condensing heal exchanger may lead to a considerably undersized coil design.     

Mixed Convection in Lid-Driven Trapezoidal Cavities with an Aiding or Opposing Side Wall

Mixed convection heat transfer and fluid flow fields inside a lid-driven trapezoidal cavity were studied numerically. The cavity horizontal walls were thermally insulated while the inclined side walls were maintained isothermally at different temperatures. Forced convection was induced by moving the hotter right inclined side wall. The problem is formulated using the stream function–vorticity procedure. Together with the established boundary conditions on the right moving wall, the problem is solved by the finite difference method. The Richardson number Ri (0.01–10) and inclination angle of the side walls Φ (66–80°) were considered as pertinent parameters and investigated in two lid-driven cases: aiding and opposing directions. The results show that the behavior of Nusselt number is different from Richardson number depending on the direction of the lid. The inclination angle of the side walls was found to have a significant effect on Nusselt number when Ri was relatively low (≤1); otherwise, a negligible effect of Φ on Nusselt number was recorded.     

部分填充多孔介质圆管中强迫对流传热与熵产的理论研究

为确定部分填充多孔介质圆管内传热最优的填充方式,对部分填充多孔介质圆管中的强迫对流传热开展研究。在圆管的外表面施加恒定热流,假设管内的流动和传热均处于充分发展段,分别采用达西-布林克曼模型和局部非热平衡模型描述管内流动与传热,获得管内速度场、温度分布、努塞尔数和熵产的解析解,重点讨论达西数、应力跳跃系数等相关参数对圆管中流动与综合换热性能的影响。结果表明:随着填充比的变化,部分填充多孔介质圆管中努塞尔数和熵产分别存在最大值和最小值。     

Effect of Various Thermal Boundary Conditions on Natural Convection in a Trapezoidal Cavity with Linearly Heated Side Wall(s)

A penalty finite-element-based study has been carried out for natural-convection flow in a trapezoidal cavity with uniformly heated bottom wall and linearly heated and/or cooled vertical wall(s) in the presence of an insulated top wall. For linearly heated side walls, symmetry in flow patterns is observed, whereas secondary circulation is observed for the linearly heated left wall and cooled right wall. The local Nusselt number indicates reversal of heat flow at the side walls or the left wall. The average Nusselt number versus Rayleigh number illustrates that the overall heat transfer rate at the bottom wall is larger for the linearly heated left wall and cooled right wall.     

Thermal Response of Saturated Porous Spherical Body Containing a Cavity under Several Boundary Conditions

A semi-analytical solution for the saturated porous spherical body containing a hollow space is discussed under several boundary conditions, including pervious surface versus impervious surface, boundary surface subjected to a variable temperature loading versus adiabatic surface, boundary surface subjected to a variable mechanical loading versus fixed displacement surface, and combined boundary conditions. Methods for determining the integration constants of the analytical expressions are derived. Numerical analyses are compared to demonstrate the thermal effects on the evolution of temperature, pore pressure, radial displacement, radial and tangential stresses in and around the geometry of the hollow spherical body subjected to thermal or mechanical perturbations.