Non-axisymmetric forced and free flow in a vertical circular duct

The fully developed laminar mixed convection in a vertical circular duct is studied analytically, with reference to non-axisymmetric boundary conditions such that the fluid temperature does not change along the axial direction. The Boussinesq approximation is applied by taking the average temperature in a duct section as the reference fluid temperature. The dimensionless momentum and energy balance equations are solved by employing Fourier series expansions of the temperature and the velocity fields. The solution shows that the temperature field is not influenced by the velocity distribution and that the Fanning friction factor is not affected by buoyancy. On the other hand, the velocity field is strongly influenced by the buoyancy forces and may display flow reversal phenomena. Two special cases are studied in detail: a duct with a sinusoidal wall temperature distribution; a duct subjected to an external convection heat transfer with two environments having different reference temperatures.     

Entropy generation through hexagonal cross‐sectional duct for constant wall temperature in laminar flow

Second law analysis of heat transfer in laminar flow for hexagonal cross‐section duct was analysed analytically. Geometrical effect of hexagonal duct was considered. The variation of total entropy generation was studied along the duct length. As a working fluid water and unused engine oil were used to compare the effect of fluid in the duct. Results were compared with circular cross‐section duct. It is found that the non‐dimensional entropy generation in a hexagonal cross‐section duct can be as high as a factor of four than that for a circular duct. Further, the unused engine oil gives up to about ten times lower non‐dimensional entropy generation values than that of water but needs about ten times more pumping power to heat transfer ratio. Copyright © 2004 John Wiley & Sons, Ltd.     

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.     

Combined forced and free flow in a vertical circular duct subjected to non-axisymmetric wall heating conditions

The fully developed mixed convection flow in a vertical circular duct is investigated analytically, under the assumption of laminar parallel flow. A wall heat flux uniform in the axial direction and dependent on the angular coordinate is considered. As a consequence, the fluid temperature is three dimensional, since it changes in the radial, axial and angular directions. An analytical method based on Fourier series expansions of temperature and velocity fields is adopted to determine the velocity and the temperature distributions as well as the friction factor and the average Nusselt number. The general solution, expressed in terms of Bessel functions, is applied to study a case that has a special importance in technical applications: a duct whose wall is half subject to a uniform heat flux and half adiabatic. The positive and negative threshold values of the ratio between the Grashof number Gr and the Reynolds number Re for the onset of the flow reversal phenomenon are determined. A comparison between the average Nusselt number for the considered non-axisymmetric case and that for the case of a duct subject to a uniform wall heat flux is performed.     

On the performance and entropy generation of the double-pass solar air heater with longitudinal fins

The performance and entropy generation of the double-pass flat plate solar air heater with longitudinal fins are studied numerically. The mathematical models described the heat transfer characteristics of the double-pass flat plate solar air heater derived from the conservation equations of energy. The predictions are done at air mass flow rate ranging between 0.02 and 0.1 kg/s. The effects of the inlet condition of working fluid and dimension of the solar air heater on the heat transfer characteristics, performance, and entropy generation are considered.     

Second law analysis of fully developed laminar flow for rectangular ducts with semicircular ends

Second law analysis is performed analytically for rectangular ducts with semicircular ends in laminar flow. Two different situations are considered for the analysis. In the first case, boundaries of duct are considered in constant wall temperature. In the second case, constant wall heat flux boundary conditions applied. Entropy generation is obtained for various cross sectional areas, various wall heat flux and Reynolds numbers. It is found that with the increasing aspect ratio (β) values for both constant wall temperature (CWT) and constant heat flux (CHF) total entropy generation increases, however, required pumping power also increases.     

Entropy generation and mechanical efficiency in laminar peristaltic flow through an elliptical duct

Heat transfer analysis coupled with peristaltic transport is important in many real-world application areas varying from microchannels to spacecrafts. Power production, chemical, and food industries, electronics, and environmental engineering are some examples of applications. In thermal devices, the overall performance of a heat exchanger depends on heat exchanger efficiency and entropy generation. The main purpose of this paper is to study a mathematical model coupling the peristaltic pumping with the heat transfer phenomenon for an incompressible Newtonian fluid in an elliptical tube. The Navier–Stokes and energy equations have been analytically solved for long wavelength, small Reynolds, and small Peclet numbers approximations. Exact expressions of velocity profile and temperature distribution have been found in the wave frame analysis. The impacts of pertinent parameters on the physical quantities of the problem have been analyzed with the help of graphs. We concluded that the geometrical parameters (occlusion, aspect ratio) enhance the pressure rise and the mechanical efficiency. It should be noted that the best way for minimizing entropy generation is decreasing occlusion, aspect ratio, flow rate, or Brinkman number.     

Performance optimisation of laminar fully developed flow through square ducts with rounded corners

A study on combined first and second law based optimisation of thermal-hydraulic performance of laminar fully developed flow through square ducts with rounded corners has been presented in this paper. The objective functions have been considered according to suggestions of Webb and Bergles [7]. Four specific geometric constraints have been imposed on the shape of the ducts and these ducts have also been subjected to three different thermal and (or) hydraulic constraints. Two different thermal boundary conditions have been considered and the correlations for friction factor and Nusselt numbers have been adopted from the study of Ray and Misra [21]. The results obtained from the present study clearly show that the optimal duct geometry strongly depends on geometric and thermal-hydraulic constraints, as well as, the objective functions and hence, no general comment can be made with respect to the superiority of a particular geometry of the ducts. Nevertheless, the present study also shows that although entropy generation minimisation may be considered to be an important tool, one requires being careful in using it for thermal-hydraulic optimisation since it may lead to contradictory results for some of the performance evaluation criteria.     

A numerical study on developing laminar forced convection and entropy generation in half- and double-sine ducts

In the present paper, the developing laminar forced convection and entropy generation in both double- and half-sine ducts are investigated with numerical methods. The studied cases cover Re ranging from 86 to 2000. The duct aspect ratio (Λ/a) and the external heat flux (q^*) are varied as Λ/a=2, 4 and 8, and the values of q^* are varied as 0.0405, 0.0811 and 0.1622, respectively. The comparisons of the flow features, including the distributions of axial velocity, temperature, Nusselt number and the local entropy generation, in the double- and half-sine ducts are provided in detail in the paper. Particularly, the optimal analysis of the two-type ducts based on the minimal entropy generation principle is the major concern. Through the evaluations of the overall entropy generation in the whole flow domain, the optimal option between the double- and half-sine duct is found to be dependent on the duct aspect-ratio, external heat flux and Re. Among all the cases studied, the half-sine duct with Λ/a=2 is found to have the minimal entropy generation, and therefore is concluded as the optimal option for achieving the least irreversibility and best exergy utilization in the thermal system.     

Numerical analysis of entropy generation in mixed-convection MHD flow in vertical channel

A numerical analysis is performed of the entropy generation within a combined forced and free convective magnetohydrodynamic (MHD) flow in a parallel-plate vertical channel. The MHD flow is assumed to be steady state, laminar and fully developed. The analysis takes account of the effects of both Joule heating and viscous dissipation. The nonlinear governing equations for the velocity and temperature fields are solved using the differential transformation method (D.T.M.). It is shown that the numerical results are in good agreement with the analytical solutions. The numerical values of the velocity and temperature are used to derive the corresponding entropy generation number (N_s) and Bejan number (B_e) within the vertical channel under asymmetric heating conditions. The results show that the minimum entropy generation number and the maximum Bejan number occur near the centerline of the channel. Overall, the results confirm that the differential transformation method provides an accurate and computationally-efficient means of analyzing the nonlinear governing equations of the velocity and temperature fields for MHD flow.     

弯曲管内的泰勒-迪安流动的数值模拟

流过横截面为正方形的弯曲管内的泰勒-迪安流,除了外墙以外的其它墙壁随着弯曲管中心轴旋转,沿着管的轴向具有压力梯度.数值计算使用光谱分析法.内圆筒旋转的流动和由于压力的流动的综合作用所产生的流动,在较宽的角速度和压力梯度范围内进行了计算.获得了断面二次流动类型的变化的情况.并对得到的解进行了线性稳定性分析.     

Entropy generation analysis of nanofluid flow in a circular tube subjected to constant wall temperature

Due to their improved thermal conductivity, nanofluids have the potential to be used as heat transfer fluids in thermal systems. However adding particles into nanofluids will increase the viscosity of the fluid flow. This demonstrates that there is a trade-off between heat transfer enhancement and viscosity. It might not be ideal to achieve a heat transfer enhancement along with a relatively high pumping power. This study presents an analytical investigation on the entropy generation of a nanofluid flow through a circular tube with a constant wall temperature. Nanofluid thermo-physical properties are obtained from literature or calculated from suitable correlations. The present study focuses on water based alumina and titanium dioxide nanofluids. Outcome of the analysis shows that titanium dioxide nanofluids offer lower total dimensionless entropy generation compared to that of alumina nanofluids. Addition of 4% titanium dioxide nanoparticles reduces the total dimensionless entropy generation by 9.7% as compared to only 6.4% reduction observed when using alumina. It is also noted that dimension configurations of the circular tube play a significant role in determining the entropy generation.     

Viscous dissipation effect on entropy generation in curved square microchannels

The viscous dissipation effect on the thermodynamic performance of the curved square microchannels in laminar flow is numerically investigated. The classical Navier-Stokes equations are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the heat transfer entropy generation number and frictional entropy generation number augment relatively under viscous dissipation effect for the case of fluid heated, and the opposite results can be found for the case of fluid cooled. The heat transfer entropy generation number increases with Reynolds number at large Reynolds number region under viscous dissipation effect when ethylene glycol is heated. The total entropy generation number extremum exists for aniline, and the extremum happens earlier when aniline is heated than when aniline is cooled. The smaller the curvature radius is, the earlier the extremum appears. The extremum does not occur for ethylene glycol due to the predomination of frictional entropy generation in the total entropy generation.     

Numerical analysis of entropy generation through non-grey gas radiation in a cylindrical annulus

This study is devoted to analyze the radiative heat transfer of non-grey gas confined in a cylindrical annulus with isothermal walls. The radiative heat transfer equation is resolved through the Ray Tracing method, which is associated to the statistical narrow bands correlated–k (SNBcK) model to compute the medium radiative properties. Special focus is given on the components of radiative entropy generation and its dependency on geometrical and thermodynamic parameters. The results show that entropy generation is greatly affected by gas and wall temperatures. Moreover, the dominance between wall radiative entropy generation and the volumetric one depends mainly on differences between gas and wall temperatures.     

Numerical and entropy studies of hydrogen-fuelled micro-combustors with different geometric shaped ribs

Micro-combustor design plays an important role in determining the performances of Micro Thermo-Photovoltaic (MTPV) systems. In this work, 3D numerical simulations are conducted on a hydrogen-fuelled micro-combustor with two ribs to achieve a more uniform but higher wall temperature. The effects of: 1) the shape of the ribs, 2) the axial location, 3) the height, 4) the inlet velocity and 5) the equivalence ratio are evaluated. The numerical model is built with a standard k-ε turbulence model and EDC chemical reaction model (eddy dissipation concept). These models are validated before being applied to study 3 different ribs with a cross-sectional view of: 1) rectangular, 2) Ո-shaped and 3) Ս-shaped (defined basing on the bottom rib). It is found that the combustor with 2 ribs performs generally better than that of a single-rib one under the same flow conditions. The optimum design is found to be the Ս-shaped ribs, since the mean temperature of the outer wall is increased by 25.4 K in comparison with other designs. In addition, the mean temperature is observed to increase with increased inlet velocity. However, it decreases slightly with increased rib height. Further analysis is conducted on entropy production due to chemical reactions and heat transfer processes. It is found that the chemical reaction and the conduction heat transfer contribute 70% and 15% of the total entropy generation respectively. Furthermore, the thermodynamic 2^nd-law efficiency remains in the range of 46%–51%, as the equivalence ratio varies from 0.8 to 1.2. This study provides physical insights on the optimum design of a hydrogen-fuelled micro-combustor.     

Numerical investigation on developing laminar forced convection and entropy generation in a wavy channel

The present paper investigates the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The effects of aspect ratio (W/H) and Reynolds number (Re) on entropy generation are the major concerns. The studied cases cover W/H = 1, 2 and 4, and Re range from 100 to 400. The flow features, including secondary flow motion and temperature distribution as well as the detailed distributions of local entropy generation due to frictional and heat transfer irreversibilities are reported. Through the evaluations of entropy generation in the whole flow field, the case of W/H = 1 is found to have the minimal entropy generation among all of the analyzed cases. Besides, the higher Re is found to be beneficial for obtaining the lower values of the total resultant entropy generation in the flow field. Accordingly, the case with W/H = 1 and higher Re is suggested to be used under the current flow conditions, so that the irreversibility resulted from the developing laminar forced convection in the wavy channel could be least and the best exergy utilization could be achieved.     

Heat transfer and entropy generation for forced convection through a microduct of rectangular cross-section: Effects of velocity slip,temperature jump,and duct geometry

This work presents numerical solutions for fully developed velocity, temperature, and entropy generation distribution due to forced convection in microelectromechanical systems (MEMS) in the Slip-flow regime, for which the Knudsen number lies within the range 0.001 < Kn < 0.1. Invoking the temperature jump equation, the H1 boundary condition is investigated. It was observed that some of the previous reports in the literature can be misleading and lead to erroneous results specially when it comes to Second Law (of Thermodynamics) aspects of the problem. The results can be generalized to the macroscale counterparts by letting Kn = 0.     

Fully developed mixed convection and flow reversal in a vertical rectangular duct with uniform wall heat flux

Combined forced and free flow in a vertical rectangular duct is investigated for laminar and fully developed regime. The velocity field, the temperature field, the friction factor and the Nusselt number are evaluated analytically by employing finite Fourier transforms. The thermal boundary condition considered is an axially uniform wall heat flux and a peripherally uniform wall temperature, i.e. an H1 boundary condition. The necessary and sufficient condition for the onset of flow reversal is determined either in the case of upward flow in a cooled duct or in the case of downward flow in a heated duct. The special case of free convection, i.e. the case of a purely buoyancy-driven flow, is discussed. The occurrence of effects of pre-heating or pre-cooling in the fluid is analysed. It is pointed out that although these effects occur in rectangular ducts, they are not present either in circular ducts or in parallel-plate channels.     

Exergetic performance comparison of air and hydrogen gas flowing through the annular curved duct

The main objective of this study is to parametrically compare the exergetic performance of air and hydrogen gas flow through the curved annular duct. For this purpose, it is assumed that, i) air and hydrogen are considered to be ideal gas, ii) the flow of these gases is steady state and laminar fully developed, ii) these gases have constant physical properties, iii) the channel inner and outer walls are exposed to constant wall boundary condition. Moreover, the following important parameters are taken into consideration: i) aspect ratio (four different values which are 5.50, 3.80, 2.90 and 2.36), ii) environment temperature (ranging from ?30 to 30 with 10 °C intervals), iii) Dean number (varying between 24 and 208), and iv) operating pressure (=1 atm). Considering these parameters, exergy destruction and exergy efficiencies are calculated for each aspect ratio. Consequently, exergetic efficiency rises with the increase of Dean number, inner wall temperature, aspect ratio and the decrease of dead state temperature. Also, it is noticed that the gas specie highly affects the volumetric entropy generation rate, exergy destruction rate and exergy efficiency.