Entropy generation in hydrodynamic slip flow over a vertical plate with convective boundary

The present article aims to report the effects of hydrodynamic slip on entropy generation in the boundary layer flow over a vertical surface with convective boundary condition. Suitable similarity transformations are used to transform the fundamental equations of hydrodynamic and thermal boundary layer flow into ordinary differential equations. The governing equations are then solved numerically using the shooting method and the velocity and the temperature profiles are obtained for various values of parameters involved in the governing equations. The expressions for the entropy generation number and the Bejan number are presented and the results are discussed graphically and quantitatively for the slip parameter, the local Grashof number, the Prandtl number, the local convective heat transfer parameter, the group parameter and the local Reynolds number. It is observed that due to the presence of slip, entropy production in a thermal system can be controlled and reduced.     

Numerical investigation of buoyancy effects on hydromagnetic unsteady flow through a porous channel with suction/injection

The paper focus on first and second laws analysis for flow and heat transfer inside a vertical channel made of two uniformly porous parallel plates with suction/injection under the combined action of buoyancy force, transverse magnetic field and constant pressure gradient. Both vertical walls are kept isothermal at the same temperatures and the flow of the conducting fluid is assumed to be unsteady with variable viscosity. The nonlinear governing equations in Cartesian coordinate are obtained and solved numerically using semi-implicit finite difference techniques to develop expressions for velocity and temperature profiles. The entropy generation number, irreversibility distribution ratio and Bejan number are presented graphically and discussed quantitatively for various values of the embedded parameters.     

Thermodynamic second law analysis for a gravity-driven variable viscosity liquid film along an inclined heated plate with convective cooling

The inherent irreversibility and thermal stability in a gravity-driven temperature-dependent variable viscosity thin liquid film along an inclined heated plate with convective cooling is investigated. In this study, both the isothermal and isoflux heating of the plate are considered. The free surface of the liquid film is assumed to exchange heat with the surroundings following Newton’s cooling law and the fluid viscosity model varies as an inverse linear function of the temperature. Analytical solutions are constructed for the governing boundaryvalue problem, and important properties of velocity and temperature fields such as thermal stability criterion are obtained. Expressions for volumetric entropy generation numbers, irreversibility distribution ratio, and the Bejan number in the flow field are also obtained and discussed quantitatively.     

Numerical analysis of entropy generation in concentric curved annular ducts

The entropy generation has been numerically investigated in concentric curved annular square ducts under constant wall temperature boundary condition. The problem has been assumed to be steady, hydrodynamically and thermally fully developed and incompressible laminar flow with constant physical properties. The solutions of discretized equations for continuity, momentum and energy have been obtained by using an elliptic Fortran Program based on the SIMPLE algorithm. Solutions have been achieved for i) Dean numbers ranging from 3.6 to 207.1, ii) Annulus dimension ratios of 5.5, 3.8, 2.9 and 2.36, and iii) Prandtl number of 0.7. In this regard, local entropy generation as well as overall entropy generation in the whole flow field has been analyzed in detail. Moreover, the effects of Dean number and annulus dimension ratio on entropy generation arising from the friction and heat transfer have been investigated. Accordingly, it is concluded that the effect of volumetric entropy generation that is a result of fluid frictional irreversibility can be neglected as compared with volumetric entropy generation due to heat transfer irreversibility. As Dean number increases, the distribution of volumetric entropy generation coming out from the heat transfer irreversibility is formed by the temperature field, which is depending on the curvature.     

Numerical study of natural convection and entropy generation of Cu-water nanofluid around an obstacle in a cavity

In this work, natural convection and entropy generation in a square cavity with an obstacle filled with Cu-water nanofluid is numerically studied. Horizontal walls of the cavity are adiabatic and vertical walls are maintained at a different constant temperature. The study has been done for the Rayleigh numbers between 10³ and 10⁶, the obstacle dimensions (W/L) of 0.1?C0.5 and for base fluid as well as nanofluid. It is found that, using the nanofluid overall leads to increase the flow strength, Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. It is observed that by increasing the obstacle dimensions, the entropy generation increases and the Bejan number decreases, but the effect of the obstacle dimensions on Nusselt number depends on Rayleigh number. For the present thermal system, the increasing Nusselt number compared to increasing entropy generation due to increase obstacle dimensions is significant at low Rayleigh numbers.     

Aspect ratio effects of an adiabatic rectangular obstacle on natural convection and entropy generation of a nanofluid in an enclosure

In the present study, aspect ratio (AR) effects of a centered adiabatic rectangular obstacle numerically investigated on natural convection and entropy generation in a differentially heated enclosure filled with either water or nanofluid (Cu-water). The governing equations are solved numerically with finite volume method using the SIMPLER algorithm. The study has been done for Rayleigh numbers between 10³ and 10⁶, the aspect ratio of 1/3, 1/2, 1, 2 and 3 and for base fluid as well as nanofluid. It is found that, using the nanofluid leads to increase the flow strength, average Nusselt number and entropy generation and decrease the Bejan number especially at high Rayleigh numbers. At low Rayleigh numbers entropy generation is very low. By increasing Rayleigh number, entropy generation and Bejan number increases. It is observed that the viscose entropy generation is more considerable than the thermal entropy generation and has dominant role in total entropy generation. The maximum entropy generation occurs at AR = 1/3 and 3 and the minimum entropy generation occurs at AR = 1 and 1/2. It is observed that the effect of AR on Nusselt number, entropy generation and Bejan number depends on Rayleigh number.     

Numerical investigation on developing laminar forced convective heat transfer and entropy generation in an annular helicoidal tube

In this study, numerical investigations are conducted for forced convective heat transfer in an annular helicoidal tube under uniform wall temperature condition for laminar flow including developing region. The numerical computations reveal the developments and distributions of heat transfer and flow fields in the annular helicoidal tube when the outer tube wall is heated and the inner tube wall is insulated. The effects of Reynolds number, curvature ratio, and coil pitch on the circumferential average friction factor and Nusselt number at different axial locations, and the non-dimensional entropy generation number of laminar convection in an annular helicoidal tube are investigated. In addition, the differences of flow and heat transfer characteristics between the annular helicoidal tube and circular helicoidal tube are also described.     

Analytic heat and mass transfer of the mixed hydrodynamic/thermal slip MHD viscous flow over a stretching sheet

In this paper, the heat and mass transfer characteristics of the magnetohydrodynamic (MHD) viscous flow over a permeable stretching surface is solved analytically. The flow considered is under both the hydrodynamic and thermal slip conditions. The magnetohydrodynamic flow and heat transfer of an electrically conducting fluid, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation is studied. The solution is expressed in a closed form equation and is an exact solution of the full governing Navier-Stokes and energy equations. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with those existing in the literature. The effects of various physical parameters, such as magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail. Results show that there is only one physical solution for any combination of the slip together with all the parameters. The velocity/shear stress profiles and the temperature/heat transfer profiles are greatly influenced by these parameters.     

Heat transfer characteristics and entropy generation for wing-shaped-tubes with longitudinal external fins in cross-flow

A numerical study is conducted to clarify heat transfer characteristics, effectiveness and entropy generation for a bundle of wingshaped-tubes attached to Longitudinal fins (LF) at downstream side. The air-side Rea ranged from 1.8 x 10³ to 9.7 x 10³. The fin height (h_f) and fin thickness (δ) have been changed as: (2 mm ≤ h_f ≤ 12 mm) and (1.5 mm ≤ δ ≤ 3.5 mm). The analysis of entropy generation is based on the principle of minimizing the rate of total entropy generation that includes the generation of entropy due to heat transfer and friction losses. The temperature field around the wing-shaped-tubes with (LF) is predicted using commercial CFD FLUENT 6.3.26 software package. Correlations of Nu_a, St_a, and Bejan number (Be), as well as the irreversibility distribution ratio (Φ) in terms of Re_a and design parameters for the studied bundle are presented. Results indicated that, installing fins with heights from 2 to 12 mm results in an increase in Nua from 11 to 36% comparing with that of wing-shaped tubes without fins (NOF). The highest and lowest values of effectiveness (ε) at every value of the considered Re_a range are occurred at h_f = 6 mm and (NOF), respectively. The wing-shaped-tubes heat exchanger with h_f = 6 mm has the highest values of (ε), efficiency index (η) and area goodness factor (G _a) and also the lowest values of Φ and hence the best performance comparing with other arrangements. The minimum values of Φ are occurred at h_f = 6 mm. (Be) decreases with increasing Re_a for all studied h_f. The heat transfer irreversibility predominates for (1800 ≤ Re_a ≤ 4200) while the opposite is true for (6950 < Re_a ≤ 9700). δ has negligible effect on Nu_a and heat transfer irreversibility. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.

     

Experimental study on the effects of the number of heat exchanger modules on thermal characteristics in a premixed combustion system

The effects of the number of heat exchanger modules on thermal characteristics were experimentally studied in a premixed combustion system with a cross-flow staggered-tube heat exchanger. The various heat exchanger modules, from 4 to 8, combined with a premixed burner were tested to investigate the performance of the heat exchanger through the surface area of the heat exchanger at various equivalence ratios. Additionally, the performance of the heat exchanger was analyzed by applying entropy generation theory to the heat exchanger system. As a result, although the heat transfer rate increases with the increase of the equivalence ratio, the NO_x and CO concentrations also increase due to the increasing flame temperature. In addition, the entropy generation increases with an increase of the equivalence ratio. Furthermore, the heat transfer rate and the effectiveness are increased with the increase of the number of the heat exchanger modules. Also, the effectiveness is sharply increased when the number of the heat exchanger modules is increased from 4 to 5. Consequently, the optimal operating conditions regarding pollutant emission, effectiveness and entropy generation in this experimental range are 0.85 for the equivalence ratio and 8 for the number of heat exchanger modules.     

An analytical investigation into the Nusselt number and entropy generation rate of film condensation on a horizontal plate

This study investigates the heat transfer characteristics and entropy generation rate of a condensate film formed on a horizontal plate with suction at the wall. Applying the minimum mechanical energy principle, the dimensionless liquid film thickness along the plate is found to vary as a function of the Rayleigh number, the Jakob number, the Prandtl number and the suction parameter. The governing differential equation of the condensate thickness is solved numerically by using a finite-difference shooting method. Closed-form analytical expressions are derived for the Nusselt number and the dimensionless overall entropy generation number. When there is no suction at the wall, the results obtained from the analytical expression for the Nusselt number are found to be in good agreement with those presented in the literature. This paper was recommended for publication in revised form by Associate Editor Dae Hee Lee Tong-Bou Chang received the Ph.D. degree in Mechanical En-gineering from National Cheng Kung University, Tainan, Taiwan, in 1997. From 1997 to 2001, he was a researcher at Yuloon-Motor Group (Taiwan), whose job function includes design and characterization of the thermal and fluid flow systems for vehicle. Since 2002, he has been as a Professor at the Department of Mechanical Engineering, Southern Taiwan University. His current research interests include heat transfer with phase change, energy-system optimization, heat and mass transfer in porous medium, enhancement heat transfer and high performance heat exchangers.     

带有方形肋及双倾斜肋片的细通道内流动、传热和熵产分析

为了探究带有方形肋及双倾斜肋片细通道的流动换热及熵产特性,设计了2种带有方形肋及双倾斜肋片的组合细通道(MCDS-L, MCDS-R),然后采用数值模拟的方法分析其流动特性、传热特性和熵产特性,并将其分析结果同2种方形肋细通道(MCS-L, MCS-R)和一种双倾斜肋片细通道(MCD)进行对比。结果表明,在所研究的雷诺数范围内,组合通道的摩擦阻力系数基本一致且均高于其他3组通道(MCS-L, MCS-R, MCD) 。此外,组合通道的努塞尔数均高于其他3组通道,而熵产增大数均低于其他3组通道。其中,MCDS-L通道的努塞尔数最大,熵产增大数最低。表明MCDS-L通道的换热效果最佳,能量的综合利用程度最高。研究成果为微细通道热沉的设计提供参考。     

非均匀加热条件下微矩形槽道内的滑移流动换热特性

利用正交函数法对定热流密度加热、壁面温度在周向可任意变化条件下,气体在微矩形槽道内的热充分发展滑移流动的换热特性进行理论分析,获得相应条件下的Nu数计算方法及换热特性,并与大尺度槽道的换热特性进行比较,探讨了Kn数、槽道高宽比及不同加热条件对微矩形槽道内滑移流动换热性能的影响。结果表明,在任何加热条件下,微矩形槽道内的平均Nu数均低于相同加热条件下大尺度矩形槽道中的Nu数,且随Kn数的增加而减小。高宽比越小,平均Nu数下降越大。在相同的高宽比和Kn数下,单边加热条件下的换热性能相比相同加热条件的常规大槽道内的换热性能下降最小。     

Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip

The boundary layer heat transfer and entropy generation of a nanofluid over an isothermal linear stretching sheet with heat generation/ absorption have been analyzed. In the nanofluid model, the development of nanoparticles concentration gradient due to slip mechanisms, the effects of Brownian motion and thermophoresis, is taken into account. The dependency of the local Nusselt number and entropy generation number on the non-dimensional parameters is numerically investigated. The results show that the increase of heat generation parameter, Brownian motion parameter, or thermophoresis parameter decreases the entropy generation number in the vicinity of the sheet.     

微管道换热器多孔介质模型分析及应用

将微管道换热器抽象成多孔介质模型,由Brinkman-extended Darcy方程出发,分别按照双方程模型和单方程模型进行求解,以得到微管道内流体的速度场和温度场分布,并对单方程模型和双方程模型的解析解进行了对比,讨论了微管道高宽比和有效导热系数比对流动与传热的影响。证明了由基于多孔介质双方程、单方程模型所得的解析解均可用于预测微管道换热器中的容积平均速度与温度分布。利用基于多孔介质双方程模型还可得出微管道换热器的总热阻和优化设计结构,结合硅衬底上的多路感应耦合等离子体刻蚀工艺加工出了经结构优化的硅制微管道换热器。在满足局部热平衡条件下,基于多孔介质单方程模型更适用于实际工程计算,不必经由预先的试验确定换热系数。     

Numerical analysis of entropy generation in nanofluid flow over a transparent plate in porous medium in presence of solar radiation,viscous dissipation and variable magnetic field

The entropy generation of magneto-hydrodynamic mixed convection flow of nanofluid over a nonlinear stretching inclined transparent plate embedded in a porous medium due to solar radiation is investigated numerically. The nanofluid is made of Cu nanoparticles with water as the base fluid. The two-dimensional governing equations, in presence of the effects of viscous dissipation, variable magnetic field and solar radiation are transformed by similarity method to two coupled nonlinear ODEs and then solved using the numerical implicit Keller-Box method. The effects of various parameters such as nanoparticle volume fraction, magnetic parameter, porosity, effective extinction coefficient of porous medium, diameter of porous medium solid particles and Eckert, Brinkman and Hartman numbers is investigated on velocity, temperature and entropy generation number profiles. The results reveal that near to the plate surface the increase of nanoparticle volume fraction, porosity and porous medium geometric parameter cause the entropy generation number to increase, but far enough from the plate surface the increase of nanoparticle volume fraction, porosity and porous medium geometric parameter cause the entropy generation number to decrease. Also the entropy generation number increases with the increase of Brinkman number and Hartman number, and this increase is dominant near the plate surface. Closer to the plate surface the reduction of Eckert number causes the increase of entropy generation number, but the entropy generation number increases with the increase of Reynolds number.     

The forced convection flow over a flat plate with finite length with a constant convective boundary condition

The flow of a fluid past a flat plate of finite length and infinite width (two-dimensional flow) is considered. The plate is heated by convection from a fluid with constant temperature T _f with a constant heat transfer coefficient h _f . In all previous works, the problem was considered using boundary layer theory whereas, in the present work, the solution is based on the full Navier-Stokes equations. The problem is investigated numerically with a finite volume method using the commercial code ANSYS FLUENT. The governing parameters are the Reynolds number, the new heat transfer parameter, and the Prandtl number. In addition, the influence of these three parameters on the temperature field is investigated. It is found that high Reynolds and high Prandtl numbers the wall temperature increases along the plate. They reach a maximum near the trailing edge then decrease. The same occurs as the heat transfer parameter increases. When the Reynolds and Prandtl numbers are low, the plate temperature tends to become symmetric, with a maximum at the middle of the plate. The temperature profiles become thicker as the Reynolds number and the Prandtl number is reduced while the temperature profiles become thicker as the heat transfer parameter increases.     

微型制冷系统的熵产模型及分析

介绍了微型制冷系统的研制及熵产模型,分析了随着制冷系统尺寸的减小系统中各个部件熵产率的变化情况.制冷系统尺寸减小以后,压缩机内的熵产率及系统内不可逆热传导引起的熵产率增加;而换热器内由温差引起的熵产率减小,由摩擦引起的熵产率增加.对于微型制冷系统,提高微型压缩机的加工精度及减少系统内部热漏是系统成功运转的关键.     

飞机环境控制系统热交换器优化研究

一种以热力学第二定律为基础的熵产分析方法,应用于飞机环境控制系统的部件级优化设计.在给出的设计条件下,通过分析空气在环控系统中的流动过程,得出系统熵产与给定初始条件的函数关系,结合热交换器设计计算过程,得到热交换器热边流动长度、冷边流动长度和高度之间比例关系对整个系统熵产的影响,并应用该分析方法对某型飞机环控系统进行了优化计算验证.分析结果对飞机环境控制系统的优化设计具有一定指导作用.     

Influence of chemical reaction and viscous dissipation on MHD mixed convection flow

This paper investigates the effect of chemical reaction and viscous dissipation on MHD mixed convective heat and mass transfer flow of a viscous, incompressible, electrically conducting second grade fluid past a semi-infinite stretching sheet in the presence of thermal diffusion and thermal radiation with Rosseland approximation. The governing boundary layer equations are written into a dimensionless form by similarity transformations. Numerical results for the dimensionless velocity, temperature, concentration profiles as well as for the skin friction coefficient, Nusselt number and Sherwood number are obtained and displayed through graphs and tables for pertinent parameters to show interesting aspects of the solution.