Optimal Porosity in an Air Heater Conduit Filled with a Porous Matrix

In the present study, flow and forced convective heat transfer in an air heater conduit filled with a porous matrix with a uniform constant solar heat flux has been investigated analytically, based on minimal entropy generation principle. While trying to decrease entropy generation due to heat transfer, pressure loss entropy generation increases, which indicates that an optimal porosity value exists. The influence of Reynolds number, fluid properties, constant uniform heat flux, flow, and geometry of the system on the optimum matrix porosity has been investigated. It was revealed that optimum matrix porosity values increase as Reynolds number increases. In the range of the present study, a correlation predicting optimal matrix porosity was proposed using least squares analysis.     

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.     

Numerical Investigation of the Magnetic Field Effects on the Entropy Generation and Heat Transfer in a Nanofluid Filled Cavity with Natural Convection

This paper presents a numerical investigation of the entropy generation and heat transfer in a ferrofluid (water and 4% Fe₃O₄ nanoparticles) filled cavity with natural convection using a two phase mixture model and control volume technique. The effect of applying a nonuniform magnetic field on the entropy generation and heat transfer in the cavity and also the interaction of magnetic force and the buoyancy force are investigated. Based on the obtained results, applying a magnetic field will enhance the heat transfer mechanism. Furthermore, by applying the nonuniform magnetic field on the ferrofluid filled cavity with natural convection, the total entropy generation is decreased considerably at higher Rayleigh numbers. Therefore, applying a magnetic field can be considered as a suitable method for entropy generation minimization in order to have high efficiency in the system.     

Forced convection and entropy generation inside a channel with a heat‐generating porous block

The flow pattern and heat transfer in a composite system containing a porous region has received considerable attention due to its importance in many engineering applications. In this study a thermal lattice Boltzmann model with nine velocities, D2Q9, is employed to investigate the fluid flow, heat transfer, and entropy generation inside a channel with a heat‐generating porous block. The effects of the porous block's length, porosity, and the Reynolds number, overflow pattern, heat transfer, and entropy generation were studied. The mentioned parameters have different effects on heat transfer and conjugate phenomena. By increasing the block length, Reynolds number, and porosity the dimensionless entropy generation will reduce. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21017     

Entropy analysis in MHD Couette flow of chemically reacting viscoelastic fluid past a deformable porous channel

Here, an investigation of MHD Couette flow of a chemically reacting viscoelastic fluid past a deformable porous layer with entropy generation using Walters liquid model has been considered. A binary, homogeneous, and isotropic mixture of fluid and solid phases in the porous medium is considered. The impact of heat source parameter and Soret effect are taken into account. The governing equations are solved analytically to obtain the expressions for solid displacement, fluid velocity, temperature, and concentration. The impact of relevant parameters on the flow system, temperature, concentration, mass transfer flux, entropy generation number, and Bejan number are discussed graphically. It is observed that solid displacement enhances due to the growth of drag and viscoelastic parameter, while it reduces due to rising volume fraction parameter. Fluid velocity rises when the volume fraction parameter increases. Rising Brinkmann number enhances the temperature, while Brinkmann number and Soret number reduces the species concentration. The irreversibility of heat transfer dominates the flow near the channel plates, while the effect of fluid friction irreversibility can be observed within the channel centerline region.     

Entropy Generation Analysis of the MHD Flow of Couple Stress Fluid between Two Concentric Rotating Cylinders with Porous Lining

An attempt has been made to study the entropy generation analysis of couple stress fluid flow in an annulus between two concentric rotating vertical cylinders. There is a porous lining attached to the inside of an outer cylinder. The flow is under the influence of a radial magnetic field. The flow in the annular gap is caused by rotation of the cylinders. The Stokes couple stress flow model is employed. The flow in the porous sleeve is governed by Darcy's law. The velocity, temperature, entropy generation number, Bejan number, wall shear stress and heat transfer rate at the inner and outer cylinders are obtained numerically by employing a finite difference scheme with vanishing of couple stresses on the boundary. The effect of relevant parameters on the flow and entropy generation rate are discussed and depicted through graphs.     

Numerical investigation of porous rib arrangement on heat transfer and entropy generation of nanofluid flow in an annulus using a two-phase mixture model

The effect of porous rib arrays on the heat transfer and entropy generation of laminar nanofluid flow inside annuli is studied numerically, using a two-phase mixture model for nanofluid flow simulation. Porous media, nanoparticles, and vortex formation are simultaneously affecting the characteristics of the system. Results showed that the permeability and height of porous ribs have significant effects on the thermal performance of system. Vortex zones also affect the trend of variation of entropy and performance numbers, and local optimums exist for these two parameters. The role of nanofluid in heat transfer enhancement in recirculating zones is more significant for higher volume fractions.     

Entropy generation in conduits filled with porous medium totally and partially

Exergy or entropy generation analysis as a tool of applied thermodynamics is becoming standard practice for optimizing energy conversion systems and in identifying the deficiency of a component in a system. Porous media is used to enhance heat transfer in heat exchangers (HE). Also, porous layer adjusted to the inner surface simulates the fouling effect in heat exchangers. Optimizing the heat exchanger inserted with porous media and understanding the fouling effect on the rate of heat transfer and fluid flow is crucial for HE design and operations, which motivate the present work. The present work mainly investigates entropy generation due to flow in a pipe fully or partially filled with porous medium. The pipe is assumed to be isothermal. The porous layer is inserted at the core of the pipe or attached on the inner surface of the pipe. Forced, laminar flow is assumed. The effects of porous layer thickness and permeability of layer on the rate of entropy generation were investigated. Developing and fully developed flow conditions are considered in the analysis.     

Effects of the inclination angle on natural convection heat transfer and entropy generation in a square porous enclosure

ABSTRACT

In this paper, we analyze numerically the effects of the inclination angle on natural convection heat transfer and entropy generation characteristics in a two-dimensional square enclosure saturated with a porous medium. There is a significant alteration in Nusselt number with the orientation of the enclosure at higher values of Rayleigh number. It reveals that the variation of entropy generation rate with the inclination angle is significant for higher values of Darcy number. The dominant source of irreversibility is due to heat transfer at low values of Darcy number, whereas entropy generation due to fluid flow dominates over that due to heat transfer for larger values of Darcy number.     

Entropy generation in a porous channel with hydromagnetic effect

An analytical work has been performed to study the First and Second Laws (of thermodynamics) characteristics of flow and heat transfer inside a vertical channel made of two parallel plates embedded in a porous medium and under the action of transverse magnetic field. Combined free and forced convection inside the channel is considered. Flow is assumed to be steady, laminar, fully developed of electrically conducting and heat-generating/absorbing fluid. Both vertical walls are kept isothermal at the same or different temperatures. Governing equations in Cartesian coordinate are simplified and solved analytically to develop expressions for velocity and temperature, entropy generation number and irreversibility distribution ratio. Velocity, temperature and entropy generation profiles are presented graphically.     

Entropy generation and pumping power in a turbulent fluid flow through a smooth pipe subjected to constant heat flux

In a heat exchange process, heat transfer and pumping power requirements are the two main considerations. Efforts made to increase heat transfer in a fluid flow usually cause increase in the pumping power requirement. In an effort to avoid inefficient utilization of energy through excessive entropy generation, a thermodynamic analysis of turbulent fluid flow through a smooth duct subjected to constant heat flux has been made in this study. The temperature dependence of the viscosity was taken into consideration in determining the heat transfer coefficient and friction factor. It was shown that the viscosity variation has a considerable effect on both the entropy generation and the pumping power. Pumping power to heat transfer ratio and the entropy generation per unit heat transfer can become very large especially for low heat flux conditions.     

Numerical investigation of nonuniform transverse magnetic field effects on the flow and heat transfer of magnetic nanofluid in a sintered porous channel

In this paper, fluid flow and convective heat transfer of a ferrofluid (water and 4 vol% Fe₃O₄) in sintered Aluminum porous channel, which is subjected to a nonuniform transverse magnetic field have been studied. The numerical simulations supposed an ordinary cubic and staggered arrangement organized by uniformly sized particles with a small contact area for the porous media and constant heat flux at the surface of the microchannel. A wire, in which the electric current passes creates a nonuniform magnetic field, which is perpendicular to the flow direction. To do this simulation, the control volume technique and the two‐phase mixture model have been employed. The results show that the obtained local heat transfer coefficient on the channel surface increased with increasing mass flow rate and decreased slightly along the axial direction. Moreover, exerting the above‐mentioned magnetic field increases the Nusselt number that enhances the heat transfer rate while it has no effect on the pressure drop along the channel.     

Entropy Generation of Natural Convection Heat Transfer in a Square Cavity Using Al2O3–Water Nanofluid

Entropy generation of an Al₂O₃–water nanofluid due to heat transfer and fluid friction irreversibility has been investigated in a square cavity subject to different side‐wall temperatures using a nanofluid for natural convection flow. This study has been carried out for the pertinent parameters in the following ranges: Rayleigh number between 10⁴ and 10⁷ and volume fraction between 0 and 0.05. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation, average entropy generation, and average Bejan number are determined. The results are compared for a pure fluid and a nanofluid. It is totally found that the heat transfer, and entropy generation of the nanofluid is more than the pure fluid and minimum entropy generation and Nusselt number occur in the pure fluid at any Rayleigh number. Results depict that the addition of nanoparticles to the pure fluid has more effect on the entropy generation as the Rayleigh number goes up.     

Second law analysis of pseudo-plastic nanofluid stream past a stretching sheet with a sliding consequence

The entropy generation (second law of thermodynamics) analysis of gyrotactic microorganism flow of power-law nanofluid with slip effects and combined effect of heat and mass transfer past a stretching sheet has been studied. The flow is maintained with Lorentz force and thermal radiation. The governing nonlinear partial differential equations are transformed into ordinary differential equations using similarity transformations. The impact of different physical parameters, such as convective bouncy parameter, power-law parameter, Brownian motion parameter, thermophoresis parameter, and slip parameter for velocity and temperature on the entropy generation number (Ns) are plotted graphically with the help of MATLAB built in bvp4c solver technique. Further, the uniqueness of this study is to find out the ratios of various irreversibilities due to thermal and mass diffusions, momentum diffusion, and microorganism over the total entropy generation rate. Our results showed that the power-law parameter and Brownian motion parameter influenced entropy generation positively. The slip parameter for velocity and temperature and the thermophoresis parameter helps to reduce the entropy production.     

Generation of entropy during forced convection of heat in nanofluid stagnation-point flows over a cylinder embedded in porous media

Thermodynamics and heat transfer of an impinging nanofluid flow upon a cylinder with constant surface temperature and embedded in porous media are investigated. Numerical solutions reveal the flow velocity and temperature fields as well as the Nusselt number. These are then used to calculate the rate of entropy generation within the system by viscous and heat transfer irreversibilities. It is demonstrated that changes in the concentration of nanoparticles modify the thermal and hydrodynamic boundary layers and hence can alter the Nusselt number and entropy generation considerably. However, the shear stress on the surface of the cylinder is observed to be less affected by the variations in the concentration of nanoparticles. Further, the Reynolds number and non-uniform transpiration are shown to affect the Nusselt number and entropy generation. It is argued that the influences of Reynolds number on the boundary layer thickness can majorly modify the irreversibility and Bejan number.     

Flow and heat transfer analysis of MHD third-grade fluid flow through a vertical microchannel subjected to entropy generation

This paper analyses the generation of entropy in an electrically conducting third-grade fluid through a vertical channel considering the variable thermal conductivity. Aspects of radiation, viscous dissipation, porous medium, Joule heating, convective boundary condition, and heat generation are studied. Nonlinear systems of ordinary differential equations are obtained via applying suitable dimensionless variables. After that, the system is solved with the aid of using the Runge–Kutta–Fehlberg method. The numerical solutions are used to characterize the irreversibility and irreversibility ratio. It is established that the entropy is enhanced with accelerating estimations of the third-grade material parameter, Brinkman number, magnetism, Biot number, porous parameter, and the impact is decelerated with elevating values of the radiation. The rate of heat transfer is higher for the Brinkman number, and a similar impact on drag force is noticed for magnetic and Grashof numbers. All the parameters on flow, temperature, fluid irreversibility and irreversibility ratio are discussed through graphical illustration.     

S型流道冷板的流体域熵产分析及流道优化

粘性流体在流动和传热过程中,由于粘性耗散和热传导的存在造成能量损失。为分析流体流动和传热过程的能量损失并得到冷板的最优流道形式,本文以某电子器件用S型流道液冷冷板为分析对象,通过数值模拟,得到S型流道液冷冷板的流体域熵产率随工质流量的变化规律,对流体域充分发展的直段和弯段内熵产率大小进行了比较,并在固定流量下,分析了熵产率大小沿工质流动方向上的变化情况。提出冷板流道优化方案,并从换热表现、压头损失和总能量损失三方面对不同流道形式的冷板进行了综合评价和比较,得到了冷板流道的最优形式,为工程实际提供参考。     

Local entropy generation for saturated two-phase flow

This paper addresses the estimation of local entropy generation rate for diabatic saturated two-phase flow of a pure fluid. Two different approaches have been adopted for this thermodynamic characterization: the separated flow model using the classical vapor flow quality, and the mixture model, using the thermodynamic vapor quality. Based on these two models, two distinct expressions for the local entropy generation have been proposed. The analysis explicitly shows the contribution of heat transfer and pressure drop respectively to the local entropy generation. The contribution due to phase-change process is also determined using the mixture model. The developed formulation is applied to analyze the thermodynamic performance of enhanced heat transfer tubes under different conditions. It is shown that enhanced tubes may be a relevant solution for reducing entropy generation at low mass velocities whereas smooth tubes remain the best solution at higher ones.     

Entropy generation during the quasi-steady burning of spherical fuel particles

Entropy generation during the quasi-steady combustion of spherical liquid fuel particles has been presented in detail. The effects of freestream velocity, particle diameter, ambient temperature and gravity, on the entropy generation rate, have been discussed in detail. In the range of sub-critical freestream velocity, where an envelope flame is present, the entropy generation rate presents a minimum value. At a critical velocity, where the flame transition occurs, the entropy generation rate reaches a maximum value. Flame transition significantly affects the entropy generation rate, which suffers a sharp decrease in its value after the transition. Heat transfer and chemical reaction contribute almost equally to the total entropy generation rate. When normal gravity is considered in an upward flow configuration, there is an increase in the entropy generation rate as compared to the zero gravity case. The effect of gravity poses a complex variation pattern in the entropy generation rate, for a downward flow configuration. The entropy generation rate decreases with increasing ambient temperature. The entropy generation rate increases with the particle diameter. A correlation has been presented for the non-dimensional entropy generation number as a function of Froude number.     

传热强化管管内熵产分析与热力性能评价

根据热力学第二定律,对传热强化管管内热力过程进行熵产分析,建立了基于流动与传热过程熵增原理的管内传热熵产方程,导出恒热流和恒壁温2种常见工况下的无因次熵产数表达式.在不同雷诺数和进口温差条件下,对2种螺旋槽管和光管进行恒壁温工况的熵产分析和热力性能评价,分析了传热和流动摩阻引起的熵产变化规律及2种不可逆损失占总熵产的份额.结果表明,熵产分析可用于评价传热强化管的综合热力性能,确定合理的运行工况、结构参数及强化换热形式,为强化管的应用评估及优化设计提供参考.