Genetic algorithm optimization for finned channel performance

Compared to a smooth channel,a finned channel provides a higher heat transfer coefficient;increasing the fin height enhances the heat transfer.However,this heat transfer enhancement is associated with an increase in the pressure drop.This leads to an increased pumping power requirement so that one may seek an optimum design for such systems.The main goal of this paper is to define the exact location and size of fins in such a way that a minimal pressure drop coincides with an optimal heat transfer based on the genetic algorithm.Each fin arrangement is considered a solution to the problem (an individual for genetic algorithm).An initial population is generated randomly at the first step.Then the algorithm has been searched among these solutions and made new solutions iteratively by its functions to find an optimum design as reported in this article.     

Thermodynamic optimization of finned crossflow heat exchangers for aircraft environmental control systems

This paper shows that the main geometric features of a flow component can be deduced from the thermodynamic optimization of the global performance of the largest flow system that incorporates the component. This approach represents a departure from the usual approach, where a flow component is optimized in isolation. The example chosen is the counterflow heat exchanger of the environmental control system (ECS) used on modern aircraft. The heat exchanger is fitted with a diffuser and a nozzle for the ram air, and the ECS runs on the boot strap air cycle, employing an additional compressor and turbine. Two heat transfer surface types are considered, finned and smooth parallel plates. Numerical results are reported for the external geometric aspect ratios of the heat exchanger, and for the plate-to-plate spacing of the smooth-plates model. It is shown that the optimized geometry for the core with finned surfaces is nearly the same as the optimized geometry for the core with smooth plates. Several of the optimized geometric features are robust with respect to changes in external parameters that vary from one application to the next. The method illustrated in this paper – the thermodynamic (constructal) optimization of flow geometry – is applicable to any system that runs on the basis of a limited amount of fuel (exergy) installed onboard, e.g., automobiles, ships, portable tools.     

Interaction of surface radiation with conjugate mixed convection from a vertical channel with multiple discrete heat sources

Important results of a numerical study performed on combined conduction–mixed convection–surface radiation from a vertical channel equipped with three identical flush-mounted discrete heat sources in its left wall are provided here. The channel has walls of identical height with the spacing varied by varying its aspect ratio (AR). The cooling medium is air that is considered to be radiatively transparent. The heat generated in the channel gets conducted along its walls before getting dissipated by mixed convection and radiation. The governing equations for fluid flow and heat transfer are considered without boundary layer approximations and are transformed into vorticity–stream function form and are later normalized. The resulting equations are solved, along with relevant boundary conditions, making use of the finite volume method. The computer code written for the purpose is validated both for fluid flow and heat transfer results with those available in the literature. Detailed parametric studies have been performed and the effects of modified Richardson number, surface emissivity, thermal conductivity and AR on various pertinent results have been looked into. The significance of radiation in various regimes of mixed convection has been elucidated. The relative contributions of mixed convection and radiation in carrying the mandated cooling load have been thoroughly explored.     

Multi-objective optimization of the sandwich panels with prismatic cores using genetic algorithms

In the present study, a new type of sandwich panels with prismatic cores, which are capable of load bearing as well as cooling, is optimized to have minimum weight and maximum heat transfer performance. In order to simultaneously minimize the total weight and maximize the heat transfer performance, a multi-objective optimization approach has been developed using genetic algorithms. A set of compromised solutions, known as the tradeoff surface, is obtained. The tradeoff information between the two objectives is exploited in terms of multi-functionality of the sandwich panels, and the relation between the two objectives is quantified in the present study. The detailed configurations and dimensions of the sandwich panels at the optima are provided. Some basic characteristics of the sandwich panels with prismatic cores have been observed in terms of their multi-functionality.     

Analysis of conjugate laminar natural convection between finitely top heating vertical channel flow

Conjugate laminar natural convection between finitely conducting vertical parallel plates is studied numerically. Since the heat transfer coefficient along the plate is undetermined and is strongly dependent on both the channel fluid flow and the thermal properties of the plate. The energy equation for the plate and the thermal boundary layer equation for the fluid between the parallel plates are coupled and solved by employing the finite-difference technique. Results of the distribution of local heat transfer coefficient, local heat flux and temperature along the plate are presented. The effects of Grashof number, fluid-to-wall conductivity ratio, and channel height-to-width ratios on heat transfer phenomena between the plates have been discussed. The tested range of Grashof number was up to 10⁶, the fluid-to-wall conductivity ratio of 0, 0.01 and 0.02, and channel height-to-width ratio varied between 0.5 and 5. These results indicate that conduction has a significant influence on the total heat transfer rate, particularly at high Grashof numbers and high fluid-to-wall conductivity ratios. When the length of the plates increases, the total heat transfer rate firstly increases and then maintains at a constant value.Die laminare freie Konvektion zwischen endlichen, wärmeleitenden, vertikalen und parallelen Wänden wird hier numerisch erforscht. Da der Wärmeübertragungskoeffizient längs der Wand nicht eindeutig bestimmt werden kann, ist er vom Kanalfluidstrom und den thermischen Eigenschaften der Wand stark abhängig. Die Energiegleichungen für die Wand und die Gleichung der Grenzfläche für das Fluid zwischen den parallelen Wänden sind zusammengefügt und für die Verwendung von Finite-Differenzenverfahren aufgelöst worden. Das Ergebnis der Verteilung des lokalen Wärmeübergangskoeffizienten, des lokalen Wärmestroms und der Temperatur längs der Wand wird dargestellt. Die Einwirkungen der Grashof-Zahl, das Leitfähigkeitsverhältnis von Fluid zu Wand und das Verhältis zwischen Höhe und Breite des Kanals bei dem Wärmeübergangsphänomen zwischen den Wänden sind besprochen worden.Der untersuchte Bereich der Grashof-Zahl erstreckt sich bis zu 10⁶, das Verhältnis der Wärmeleitfähigkeit von Fluid zu Wand lag bei 0, 0,01 und 0,02 und das Höhen-Breite-Verhältnis des Kanals variierte zwischen 0,5 und 5. Dieses Ergebnis weist auf den bedeutenden Einfluß der Wärmeleitfähigkeit auf den gesamten Wärmeübertragungswert bei besonders hohen Grashof-Zahlen und hohem Wärmeleitfähigkeitsverhältnis von Fluid zu Wand hin. Wenn die Länge der Wände zunimmt, dann steigt als erstes der gesamte Wärmeübertragungswert und behält danach einen konstanten Wert bei.     

Filtration model of longitudinal flow in a finned cylindrical channel

The problem of laminar flow of a viscous incompressible fluid in a finned circular tube is considered. A solution is obtained in the form of series in eigenfunctions of the Laplace operator; the coefficients in the series are found numerically. For the same problem, a simpler filtration approximation is proposed in which the system of fins is modeled by a radially inhomogeneous porous layer, and fluid flow in it is described by the Brinkman equation. A formula for the effective permeability of the porous medium is obtained by varying the number and height of fins. The formula provides an accurate evaluation of the mean flow velocity and viscous drag coefficient in finned channels.     

Multi-swingby optimization of mission to Saturn using global optimization algorithms

Based on the trajectory design of a mission to Saturn, this paper discusses four different trajectories in various swingby cases. We assume a single impulse to be applied in each case when the spacecraft approaches a celestial body. Some optimal trajectories ofEJS, EMS, EVEJS and EVVEJS flying sequences are obtained using five global optimization algorithms： DE, PSO, DP, the hybrid algorithm PSODE and another hybrid algorithm, DPDE. DE is proved to be supe- rior to other non-hybrid algorithms in the trajectory optimi- zation problem. The hybrid algorithm of PSO and DE can improve the optimization performance of DE, which is vali- dated by the mission to Saturn with given swingby sequences. Finally, the optimization results of four different swingby sequences are compared with those of the ACT of ESA.     

Turbulent forced convection of nanofluid in a wavy channel using two phase model

Two phase mixture model is used to numerically simulate the turbulent forced convection of Al₂O₃-Water nanofluid in a channel with corrugated wall under constant heat flux. Both mixture and single phase models are implemented to study the nanofluid flow in such a geometry and the results have been compared. The effects of the volume fraction of nanoparticles, Reynolds number and amplitude of the wavy wall on the rate of heat transfer are investigated. The results showed that with increasing the volume fraction of nanoparticles, Reynolds number and amplitude of wall waves, the rate of heat transfer increases. Also the results showed that the mixture model yields to higher Nusselt numbers than the single phase model in a similar case.     

FC-72 pool boiling from finned surfaces placed in a narrow channel: preliminary results

This paper presents an experimental study dealing with the basic nucleate boiling concerning two finned surfaces placed in a narrow channel. The influence of both the channel width and the orientation of the base surface (horizontal or vertical) are discussed. The experiments were performed in a saturated pool of FC-72 while the channel widths investigated were 2.0 mm and 0.5 mm. The experimental data are compared with those obtained in the case of the unconfined situation of the extended surfaces. Channel width reduction does not affect the heat transferred to the liquid in the case of vertical orientation of the base surface, while it causes a drastic reduction in the heat transfer behavior in the case of a horizontal base surface. For the latter situation, vapor stagnation in the gap was observed after the maximum heat flux had been reached. Received on 13 August 1998     

Computation of conjugate heat transfer in the turbulent mixed convection regime in a vertical channel with multiple heat sources

This paper presents the results of a comprehensive numerical study to analyze conjugate, turbulent mixed convection heat transfer from a vertical channel with four heat sources, uniformly flush-mounted to one of the channel walls. The results are presented to study the effect of various parameters like thermal conductivity of wall material (k _s), thermal conductivity of flush-mounted discrete heat source (k _c), Reynolds number of fluid flow (Re _s), modified Richardson number (Ri ⁺) and aspect ratio (AR) of the channel. The standard k-ε turbulence model, modified by including buoyancy effects with physical boundary conditions, i.e. without wall functions, has been used for the analysis. Semi-staggered, non-uniform grids are used to discretise the two dimensional governing equations, using finite volume method. A correlation, encompassing a wide range of parameters, is developed for the non-dimensional maximum temperature (T ^*) using the asymptotic computational fluid dynamics (ACFD) technique.     

Optimal tuning of fractional controllers using genetic algorithms

This study addresses the optimization of fractional algorithms for the discrete-time control of linear and non-linear systems. The paper starts by analyzing the fundamentals of fractional control systems and genetic algorithms. In a second phase the paper evaluates the problem in an optimization perspective. The results demonstrate the feasibility of the evolutionary strategy and the adaptability to distinct types of systems.     

Magnetohydrodynamic mixed convection in a vertical channel

The problem of combined free and forced convective magnetohydrodynamic flow in a vertical channel is analysed by taking into account the effect of viscous and ohmic dissipations. The channel walls are maintained at equal or at different constant temperatures. The velocity field and the temperature field are obtained analytically by perturbation series method and numerically by finite difference technique. The results are presented for various values of the Brinkman number and the ratio of Grashof number to the Reynolds number for both equal and different wall temperatures. Nusselt number at the walls is determined. It is found that the viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. It is also found that the analytical and numerical solutions agree very well for small values of ε.     

离散结构的遗传形状优化设计

离散结构的形状优化问题，设计变量是不同性态的连续／离散混合变量，优化收敛困难。本文利用遗传算法实现其全局最优设计，以空间２５杆桁架结构为例，进行了多变量、多工况的结构形状遗传优化设计。为减少结构重分析次数，引入了Ｓｔｅａｄｙｓｔａｔｅ算法。结果表明结构形状的遗传优化设计方法是可行的。     

Laminar forced convection conjugate heat transfer over a flat plate

Coupled heat transfer between laminar forced convection along and conduction inside a flat plate wall is theoretically studied. The laminar convective boundary layer is analyzed by employing the integral technique. The energy equations for the fluid and the plate wall are combined under the condition of the continuity in the temperature and heat flux at the fluid-solid interface. The analysis results in a simple formal solution. Expressions have been obtained for calculating local Nusselt number, wall heat flux and temperature along the plate, all are functions of the local Brun number, Br _x , which is a measure of the ratio of the thermal resistance of the plate to that of the convective boundary layer. The results indicate that for Br _x ≥0.15, neglecting the plate resistance will results in an error of more than 5% in Nusselt number. Comparison of the present solution with other previous studies has been made. The solution may be of a considerable theoretical and practical interest. Received on 19 August 1998     

Transient oscillatory conjugate natural convection in a tall water cavity

A two-dimensional numerical simulation was conducted to investigate the effects of the heat capacity of the heated wall on the transient oscillatory convection in a tall cavity. Results were particularly obtained for water (Pr=6) in a tall cavity (A=6) with constant-heat-flux heating on one side and isothermal cooling on the opposing side. Significant wall heat capacity effects were found. Specifically, a heated wall of finite heat capacity can slow down the flow evolution process to steady state at low Rayleigh number and damp the flow oscillation during the initial developing period at high Rayleigh number. In periodic flow atRa* _H =4.4×10¹⁰ the wall heat capacity significantly reduces the amplitude of the temperature oscillation. A quasi-periodic flow atRa* _H =4.8×10¹⁰ was found to become periodic when the wall heat capacity was included. The wall heat capacity does not shown noticeable effect when the flow is chaotic forRa* _H =6.0×10¹⁰.In einer zweidimensionalen numerischen Simulationsrechnung wurde der Einfluß der Wärmekapazität einer beheizten Wand auf die nichtstationäre oszillatorische Konvektion in einem großen Behälter untersucht. Die Resultate beziehen sich speziell auf Wasser (Pr=6), einen tiefen Behälter (H/W=6) und konstanten Wärmezufluß auf der einen und isotherme Kühlung auf der anderen Wandseite. Es traten signifikante Effekte in Abhängigkeit von der Wandwärmekapazität auf. Insbesondere vermag eine beheizte Wand begrenzter Wärmekapazität bei niedrigen Rayleigh-Zahlen die Entwicklung des Strömungsprozesses bis zum Stationärzustand abzubremsen und bei hohen Rayleigh-Zahlen die Strömungsoszillationen während der Einschwingphase zu dämpfen. Bei periodischem Strömungszustand undRa* _H =4,4·10¹⁰ verringert die Wandkapazität die Amplitude der Temperaturschwingung beträchtlich. Es zeigte sich ferner, daß ein quasiperiodischer Strömungszustand beiRa* _H =4,8·10¹⁰ periodisch wird, wenn die Wandkapazität Einfluß nimmt. Letztere hatte keine nachweisbaren Wirkungen bei chaotischem Strömungszustand mitRa* _H =6,0·10¹⁰.     

Mixed convection heat transfer from a horizontal channel with protruding heat sources

A numerical investigation is carried out to study fluid flow and heat transfer characteristics of conjugate mixed convection from a two dimensional horizontal channel with four protruding heat sources mounted on one of the finite thick channel walls. The flow is assumed as laminar, hydrodynamically and thermally developing. Water and FC70 are the fluids under consideration. The geometric parameters such as spacing between the channel walls (S), size of protruding heat sources (L_h×t_h), thickness of substrate (t) and spacing between heat sources (b) are fixed. Results are presented to show the effect of parameters such as Re_S, Gr_S^*, Pr, k_p/k_f and k_s/k_f on fluid flow and heat transfer characteristics. Using the method of asymptotic expansions, correlations are also presented for the maximum temperature of heat source.     

Computation of conjugate natural convection heat transfer from a rectangular fin on a partially heated horizontal base

In this study, a numerical investigation has been carried out to reveal the mechanism of fluid flow and heat transfer from a vertical rectangular fin attached to a partially heated horizontal base. The problem is a conjugate conduction-convection heat transfer problem with open boundaries. The governing equations for the problem are the conservation of mass, momentum and energy equations for the fluid and the heat conduction equation for the fin. The control volume technique based on the SIMPLEC algorithm with a nonstaggerred grid arrangement is employed to solve the governing equations. The effect of the heated base, on the mechanism of the fluid flow and heat transfer, is numerically investigated. Temperature distribution and flow patterns around the fin are plotted to support the discussion. Results are obtained for air at laminar and steady flow. Received on 15 May 1997     

Developing laminar convection in a vertical double-passage channel

 The effect of the presence of a thin, perfectly conductive baffle on the development of laminar convection in a vertical channel has been investigated numerically. The channel has different constant wall temperatures which are higher than those at the entrance. Velocity and temperature profiles have been presented. The effect of the different parameters on heat transfer in the channel has been discussed. The occurrence of flow reversal has been observed in some cases but examination of this phenomenon has been considered to be beyond the scope of the present work. For long channels, the numerical solutions approach the fully developed flow analytical solution. Finally, the results showed that higher values of Nu_h can be obtained when the baffle is near the hot wall. Received on 23 May 2000     

Turbulent free convection in a vertical converging channel

This paper presents the results of experimental and numerical investigations of the problem of turbulent natural convection in a converging-plate vertical channel. The channel has two isothermally heated inclined walls and two adiabatic vertical side walls. The parameters involved in this study are the channel geometry represented by the channel width at exit, the inclination of the heated walls and the temperature difference between the heated walls and the ambient. The investigation covered modified Rayleigh numbers up to 10⁸ in the computational study and up to 9.3 × 10⁶ in the experimental work. The experimental measurements focused on the velocity field and were carried out using a PIV system and included measurements of the mean velocity profiles as well as the root-mean-square velocity and shear stress profiles. The experiments were conducted for an inclination angle of 30°, a gap width of 10 mm and two temperature differences (∆T=25.4°C and 49.8°C). The velocity profiles in the lower part of the channel indicated the presence of two distinct layers. The first layer is adjacent to the heated plate and driven by buoyancy forces while the second layer extends from the point of maximum velocity to the channel center plane and driven mainly by shear forces. The velocity profile at the upper portion of the channel has shown the merging of the two boundary layers growing over the two heated walls. The measured values of the Reynolds shear stress and root mean square of the horizontal and vertical velocity fluctuation components have reached their maximum near the wall while having smaller values in the core region. The computational results have shown that the average Nusselt number increases approximately linearly with the increase of the modified Rayleigh number when plotted on log–log scale. The variation of the local Nusselt number indicated infinite values at the channel inlet (leading edge effect) and high values at the channel exit (trailing edge effect). For a fixed value of the top channel opening, the increase of the inclination angle tended to reduce flow velocity at the inlet section while changing the flow structure near the heated plates in such a way to create boundary-layer type flow. The maximum value of the average Nusselt number occurs when θ = 0 and decreases with the increase of the inclination angle. On the other hand, the increase of the channel width at exit for the same inclination angle caused a monotonic increase in the flow velocity at the channel inlet.     

Turbulent natural convection scaling in a vertical channel

Using direct numerical simulation (DNS) data, this study appraises existing scaling laws in literature for turbulent natural convection of air in a differentially heated vertical channel. The present data is validated using past DNS studies, and covers a range of Rayleigh number, Ra between 5.4 × 10⁵ and 2.0 × 10⁷. We then appraise and compare the various scaling laws proposed by Versteegh and Nieuwstadt, 1999, Hölling and Herwig, 2005, Shiri and George, 2008, George and Capp, 1979 with the profiles of the mean temperature defect, mean streamwise velocity, normal velocity fluctuations, temperature fluctuations and Reynolds shear stress. Based on the arguments of an inner (near-wall) and outer (channel centre) region, the data is found to support a minus one-third power law for the mean temperature in an overlap region. Using the inner and outer temperature profiles, an implicit heat transfer equation is obtained and we show that a correction term is non-negligible for the present Ra range when compared with explicit equations found in literature. In addition, we determined that the mean streamwise velocity and normal velocity fluctuations collapse in the inner region when using the outer velocity scale. We also find that the temperature fluctuations scale in inner coordinates, in contrast to the outer scaling behaviour reported in the past. Lastly, we show evidence of an incipient proportional relationship between friction velocity, u_τ, and the outer velocity scale, u_o, with increasing Ra.