Constructal design of forced convection cooled microchannel heat sinks and heat exchangers

Heat transfer from arrays of circular and non-circular ducts subject to finite volume and constant pressure drop constraints is examined. It is shown that the optimal duct dimension is independent of the array structure and hence represents an optimal construction element. Solutions are presented for the optimal duct dimensions and maximum heat transfer per unit volume for the parallel plate channel, rectangular channel, elliptic duct, circular duct, polygonal ducts, and triangular ducts. Approximate analytical results show that the optimal shape is the isosceles right triangle and square duct due to their ability to provide the most efficient packing in a fixed volume. Whereas a more exact analysis reveals that the parallel plate channel array is in fact the superior system. An approximate relationship is developed which is very nearly a universal solution for any duct shape in terms of the Bejan number and duct aspect ratio. Finally, validation of the relationships is provided using exact results from the open literature.     

Gas slippage effect on the permeability of circular cylinders in a square array

The gas slippage phenomenon is usually observed when gas flow through porous media under low pressure, and has received an increasing attention for its importance in science and engineering. In the past decades, although many theoretical, numerical and experimental works have been done to predict the permeability of a square array of circular cylinders, little literature is available in studying the slippage effect on permeability. In this paper, the gas slippage effect on the permeability of circular cylinders in a square array is studied theoretically. The permeabilities at low and high solid fractions are derived with cell model and lubrication theory by coupling with a first-order slip boundary condition. The present results are finally validated through a comparison with some available results.     

Constructal conjugate cooling channels with internal heat generation

This paper presents a geometric optimisation of conjugate cooling channels in forced convection with internal heat generation. Two configurations were studied; circular channels and square channels. The configurations were optimised in such a way that the peak temperatures were minimised subject to the constraint of fixed total global volume. The fluid was forced through the cooling channels by the pressure difference across the channels. The structure has one degree of freedom as design variable: channel hydraulic diameter and once the optimal channel hydraulic diameter is found, optimal elemental volume and channel-to-channel spacing result. A gradient-based optimisation algorithm is applied in order to search for the best and optimal geometric configurations that improve thermal performance by minimising thermal resistance for a wide range of dimensionless pressure difference. This optimiser adequately handles the numerical objective function obtained from CFD simulations. The results obtained show the behaviour of the applied pressure difference on the optimised geometry. There are unique optimal design variables for a given pressure difference. The numerical results obtained are in agreement with the theoretical formulation using scale analysis and method of intersection of asymptotes.     

Constructal design of T–Y assembly of fins for an optimized heat removal

Constructal design has been applied to a large variety of problems in nature and engineering to optimize the architecture of animate and inanimate flow systems. This numerical work uses this method to seek for the best geometry of a T–Y assembly of fins, i.e., an assembly where there is a cavity between the two branches of the assembly of fins. The global thermal resistance of the assembly is minimized by geometric optimization subject to the following constraints: the total volume, the volume of fin-material, and the volume of the cavity. Parametric study was performed to show the behavior of the twice minimized global thermal resistance. The results show that smaller cavity volume and larger fins volume improve the performance of the assembly of fins. The twice minimized global thermal resistance of the assembly and its corresponding optimal configurations calculated for the studied parameters were correlated by power laws.     

Numerical Study of Forced Convection of Nanofluid Flow Over a Backward Facing Step With a Corrugated Bottom Wall in the Presence of Different Shaped Obstacles

In this paper, a numerical study of laminar forced convection of nanofluid flow over a backward facing step with a corrugated bottom wall in the presence of different shaped obstacles placed behind the step was performed. The bottom corrugated wall of the channel downstream of the step is isothermally heated and the other walls of the channel and obstacle surface are assumed to be adiabatic. The governing equations are solved with a finite-element method. The influences of the Reynolds number (between 10 and 200), solid volume fraction of the nanoparticle (between 0 and 0.05), and obstacle type (circular, square, and diamond shaped) on fluid flow and heat transfer are numerically investigated. It is observed that among different obstacles, the diamond shaped obstacle provides better local heat transfer enhancement characteristic in the vicinity of the step compared to the circular or square obstacle at high Reynolds number. Heat transfer enhancement of 6.66% is achieved in terms of maximum values with a diamond shaped obstacle compared to the no-obstacle case of the corrugated channel. Adding an obstacle deteriorates heat transfer in terms of average values for the backward facing step geometry with a corrugated wall. When the solid volume fraction of nanoparticle is increased, maximum and average heat transfer rate increase. Heat transfer enhancements of 7.45%, 7.42%, 6.94%, and 6.64% are obtained for the average values for circle, diamond, square, and no-obstacle cases, respectively, when solid volume fraction of 0.05 is compared to pure fluid.     

风电消纳下多型号制氢机组阵列优化调度研究

以风电消纳下多型号制氢机组阵列的优化调度为研究对象,首先研究碱式制氢机组的功率-效率特性。在此基础上,以经济收益最大化为目标,对机组出力进行双层优化。使用所提混合二进制萤火虫算法进行机组启停状态优化,粒子群算法进行考虑功率-效率特性的机组功率分配优化。最后对多种阵列方案的经济收益和风电消纳能力进行对比分析。实验结果证明所提算法的有效性和多型号制氢机组阵列方案的优越性。     

Numerical estimation of pressure drop and heat transfer characteristics in annular‐finned channel heat exchangers with different channel configurations

In this numerical investigation, three‐dimensional analysis has been used to study the effect of finned channels configuration of (circular, square, and triangular shape) and fin spacing with four rows in staggered arrangements. The finite volume method with k‐ ω turbulent model is applied to estimate the heat transfer and flow characteristics. The results illustrate that the development of the boundary layer between the fins surfaces is credited to the finned channels configuration, fin spacing, and Reynolds number. Moreover, the results of pressure drop and heat transfer with various channel configuration and different fin spacings (1.6, 2, and 4 mm) are presented and validated with the available correlations. The triangular‐finned channel with 1.6 mm fin spacing offered higher heat transfer enhancement followed by square‐ and circular‐finned channels. A considerable agreement was observed when the current findings and the existing correlations were compared, with a maximum deviation of 15% for all the cases.     

Closure of non-equilibrium volume-averaged energy equations in high-conductivity porous media

A formulation for closure of the volume-averaged energy equations under local thermal non-equilibrium conditions has been proposed, providing a general method for obtaining the relevant effective properties for high-conductivity porous materials. The method requires numerical solution of the flow field, as well as closure problems, over a representative volume of porous media. This study considers an array of highly conductive circular cylinders for which all relevant effective properties are obtained. Comparisons are made to results in literature for low Reynolds numbers, while results at higher Reynolds numbers are presented to provide insight into the effects of inertia on the effective properties.     

Numerical Evaluation of Flow and Heat Transfer in Plate-Pin Fin Heat Sinks with Various Pin Cross-Sections

A numerical investigation of the thermal and hydraulic performance of 20 different plate-pin fin heat sinks with various shapes of pin cross-sections (square, circular, elliptic, NACA profile, and dropform) and different ratios of pin widths to plate fin spacing (0.3, 0.4, 0.5, and 0.6) was performed. Finite volume method-based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based shear-stress-transport model was used to predict the turbulent flow and heat transfer through the heat sink channels. The present study provides original information about the performance of this new type of compound heat sink.     

3.5Mt/a重油催化裂化装置吸收稳定系统优化

大连石化生产丙烯流程中,3.5Mt/a催化裂化装置液化气中乙烷含量对气体分馏装置的操作产生直接影响。脱乙烷塔顶排出乙烷时,会造成丙烯的伴随排放,造成经济损失。利用大连石化OTS平台的Unisim Design流程模拟软件,对3.5Mt/a催化裂化装置吸收稳定系统进行建模,分析影响液化气中乙烷含量的主要影响因素,并依据流程模拟结果,对操作条件进行寻优,进而指导装置生产。本次寻优只针对液化气中乙烷含量对气体分馏装置的影响,其他优化不在本次研究范围内。通过对装置实际操作条件的优化,液化气中乙烷含量较优化前下降0.684%(体积分数),干气中丙烯含量下降0.102%(体积分数),从2010年5月开始,至当年11月,已产生直接经济效益960万元。通过流程模拟软件指导装置生产,进行操作寻优,投资少,回报率高,见效快,是企业精细化管理的一条新路。     

Constructal design of Y-shaped assembly of fins

This work relies on constructal design to perform the geometric optimization of the Y-shaped assembly of fins. It is shown numerically that the global thermal resistance of the Y-shaped assembly of fins can be minimized by geometric optimization subject to total volume and fin material constraints. A triple optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly, an internal optimal ratio of plate-fin thicknesses and an optimal angle between the tributary branches and the horizontal. Parametric study was performed to show the behavior of the minimized global thermal resistance. The results also show that the optimized Y-shaped structure performs better than the optimized T-shaped one.     

Analysis of design variables for water-gas-shift reactors by model-based optimization

This work analyzes the water-gas-shift reactor design as component of the CO clean-up system of the ethanol processor for H₂ production applied to PEM fuel cells. The WGS reactor constitutes the element of greater volume of the processor motivating its optimization. A model-based reactor optimization for different reactor configurations permits to obtain both designs for reducing volumes and optimal operating conditions. The heterogeneous model used allows computing the optimal reactor length and diameter, and the optimal catalyst particle diameter. The model computes the constraints required for catalyst, such as maximum and minimum operation temperature. The volume is sensitive to the CO outlet concentration. According to the required CO conversion it is necessary more than one reactor unit for the case study analyzed. When considering the insulating material, there exists an optimal thickness that affects the final volume and the design variables. These results are useful for estimating the minimum and relative sizes that allows conventional reactor technology.     

Magnetohydrodynamic Natural Convection in a Square Enclosure with Four Circular Cylinders Positioned at Different Rectangular Locations

We deploy a finite volume numerical computation to investigate the two-dimensional hydromagnetic natural convection in a cooled square enclosure in the presence of four inner heated circular cylinders with identical shape. The inner circular cylinders are placed in a rectangular array with equal distance away from each other within the enclosure and moving along the diagonals of the enclosure. All the walls of the enclosure are kept isothermal with temperatures less than that of the cylinders. A uniform magnetic field is applied along the horizontal direction normal to the vertical wall. All solid walls are assumed electrically insulated. Simulations are performed for a range of the controlling parameters such as the Rayleigh number 10³ to 10⁶, Hartmann number 0 to 50, and the dimensionless horizontal and vertical distance from the center of a cylinder to center of another cylinder 0.3 to 0.7. The study specifically aims to understand the effects of the location of the cylinders in the enclosure on the magnetoconvective transport, when they moved along the diagonals of the enclosure. It is observed that the unsteady behavior of the flow and thermal fields at relatively larger Rayleigh numbers and for some cylinder position are suppressed by imposition of the magnetic field. The heat transfer strongly depends on the position of the cylinders and the strength of the magnetic field. Hence, by controlling the position of the objects and the magnetic field strength, a significant control on the hydrodynamic and thermal transport can be achieved.     

Effect of optimal spinning reserve requirement on system pollution emission considering reserve supplying demand response in the electricity market

Pollution emission reduction is becoming an inevitable global goal. Incorporating pollution reduction goals into power system operation affects several different aspects, such as unit scheduling and system reliability. At the same time, changes in the energy scheduling change the required optimal reserve amount. Optimal spinning reserve scheduling also affects the energy market scheduling. Optimal reserve allocation changes the energy scheduling, which affect the amount of pollution emission. Therefore, incorporating pollution emission reduction and optimal spinning reserve scheduling cannot be studied separately. Analysis of the system effects of pollution reduction should be performed considering the ancillary service market, specificity the optimal spinning reserve scheduling. This problem is addressed in this paper by incorporating optimal spinning reserve scheduling in a combined environment economic dispatch (CEED) in one objective function. The framework of this paper enables the study of the effect of optimal reserve scheduling and emission reduction as well as an analysis of the system effects of pollution reduction. With the increased AMI and smart grid realization, the reserve supplying demand response (RSDR) is becoming an important player in the reserve market, and thus, these resources are also taken into account. In this paper, the objective function is social cost minimization, including the costs associated with energy provision, reserve procurement, expected interruptions and environmental pollution. A MIP-based optimization method is developed, which reduces the computational burden considerably while maintaining the ability to reach to the optimal solution. The IEEE RTS 1996 is used as a test case for numerical simulations, and the results are presented. The numerical results show that optimal reserve scheduling and RSDR utilization resources have a considerable impact on environmental–economic cost characteristics.     

A simple mathematical model for determining the equivalent permeability of fractured porous media

A simple mathematical model has been proposed so as to determine the equivalent permeability of fractured porous media. The model consists of square blocks placed in an array with vertical and horizontal fractures between the blocks. An analytical expression valid for all macroscopic flow directions has been derived for the equivalent permeability of the fractured porous media, assuming a horizontal flow through the blocks placed in a porous medium. The analytical expression agrees well with the existing equations and also with the microscopic numerical results carried out using a unit structure with periodic boundary conditions. The foregoing two-dimensional model has been extended to a three dimensional case in which the cubic rocks are arranged in a cubic array. The resulting three-dimensional analytical expression for the equivalent permeability is found to agree very well with both existing formula and microscopic numerical simulation.     

气体横掠单管强制对流换热的大涡模拟

应用大涡模拟与二价全展开ETC有限元离散格式相结合的方法对气体横掠单管强制对流换热进行了数值模拟,分别计算了气体横掠团管和方管时的温度场,得到了管壁平均换热系数,数值结果与实验关联式符合较好。同时还表明大涡模拟方法善于捕捉温度场以及流场涡系的时间演化过程,非常适合于具有大尺度涡的绕流运动温度场的分析。     

Shape factor and shape optimization for a periodic array of isothermal pipes

We address the problem of two-dimensional heat conduction in a solid slab embedded with a periodic array of isothermal pipes of general cross-section. The objective of this work is two-fold: to develop a numerical procedure through which we can obtain the shape factor associated with a given configuration and, to develop a numerical shape optimization algorithm through which we can compute shapes that extremize the transport rate. The shape factor is obtained by first transforming the periodic array of pipes into a periodic array of strips using the generalized Schwarz–Christoffel transformation and, subsequently, by developing an integral equation of the first kind for the temperature gradient using the boundary element method. The integral equation is solved both numerically and analytically/asymptotically with excellent agreement between the results. The shape optimization problems, which are formulated with respect to the parameters of the generalized Schwarz–Christoffel transformation, are solved numerically to compute the shape that maximizes the cross-sectional area and the shape that minimizes the perimeter of the cross-section, given the shape factor and the distance between two consecutive pipes. It is inferred that the problems are adjoint to the transport rate minimization and transport rate maximization problems, respectively. The optimal shapes are computed numerically and validated with available analytical and numerical results for a single pipe. Furthermore, motivated by the analytical result, we propose a parametric set of equations that describe well the optimal shapes. The versatility of the Laplace equation suggests that similar formulations have applications in continuum mechanics, electricity, hydraulics and drug reduction.     

Mixed convection heat transfer in a differentially heated square enclosure with a conductive rotating circular cylinder at different vertical locations

In this investigation, a numerical simulation using a finite volume scheme is carried out for a laminar steady mixed convection problem in a two-dimensional square enclosure of width and height (L), with a rotating circular cylinder of radius (R = 0.2 L) enclosed inside it. The solution is performed to analyze mixed convection in this enclosure where the left side wall is subjected to an isothermal temperature higher than the opposite right side wall. The upper and lower enclosure walls are considered adiabatic. The enclosure under study is filled with air with Prandtl number is taken as 0.71. Fluid flow and thermal fields and the average Nusselt number are presented for the Richardson numbers ranging as 0, 1, 5 and 10, while Reynolds number ranging as 50, 100, 200 and 300. The effects of various locations and solid-fluid thermal conductivity ratios on the heat transport process are studied in the present work. The results of the present investigation explain that increase in the Richardson and Reynolds numbers has a significant role on the flow and temperature fields and the rotating cylinder locations have an important effect in enhancing convection heat transfer in the square enclosure. The results explain also, that the average Nusselt number value increases as the Reynolds and Richardson numbers increase and the convection phenomenon is strongly affected by these parameters. The results showed a good agreement with further published works.     

A Numerical Study of Entropy Generation in the Entrance Region of Curved Pipes

In this study, developing incompressible viscous flow and heat transfer in curved pipes are studied numerically considering a constant heat flux at the wall to analyze the entropy generation. The governing equations including continuity, momentum and energy equations are solved using a second order finite difference method based on the projection algorithm. Entropy generation and thermodynamic optimization are investigated through the entrance region of the curved pipes with circular cross section by a general non-dimensional analysis both numerically and analytically. Optimal Reynolds number calculation based on the entropy generation minimization are carried out for two cases considering the two groups of non-dimensional parameters. The comparison of the numerical results in the entrance region with the analytical ones in the fully developed region indicates that both solutions predict nearly the same optimal Reynolds numbers.     

Magnetic field effects on natural convection around a horizontal circular cylinder inside a square enclosure filled with nanofluid

In this study, natural convection in a concentric annulus between a cold outer square and heated inner circular cylinders in presence of static radial magnetic field is investigated numerically using the lattice Boltzmann method. The inner and outer cylinders are maintained at constant uniform temperatures and it is assumed that all walls are insulating the magnetic field. The numerical investigation is carried out for different governing parameters namely; the Hartmann number, nanoparticles volume fraction and Rayleigh number. The effective thermal conductivity and viscosity of nanofluids are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. Also, the multi-distribution-function (MDF) model is used for simulating the effect of uniform magnetic field. The results reveal that the average Nusselt number is an increasing function of nanoparticle volume fraction as well as the Rayleigh number, while it is a decreasing function of the Hartmann number.