Multi-objective shape optimization of a heat exchanger using parallel genetic algorithms

We perform in this paper a multi-objective design optimization concerning the blade shape of a heat exchanger, considering the coupled solution of the flow/heat transfer processes. For this, a genetic algorithm is used. The aim of the procedure is to find the geometry most favorable to simultaneously maximize heat exchange while obtaining a minimum pressure loss. An in-house computer package, called OPAL, performs the optimization process in a fully automatic manner. It calls the pre-processor to generate the computational geometry as well as the mesh, it then performs the numerical simulation of the coupled fluid flow/heat transfer problem using Fluent, calculates the output parameters, and iterates the procedure. The genetic algorithm relies on a relatively large number of simulations, which may result in a considerable computational effort, depending on the configuration. The procedure can thus be performed in parallel on a Linux PC cluster to reduce user waiting time. A nearly optimal speed-up is obtained for the present configuration.     

Estimation of unknown heat source function in inverse heat conduction problems using quantum-behaved particle swarm optimization

The estimation of temporal dependent heat source in transient heat conduction problem is investigated. A stochastic method known as quantum-behaved particle swarm optimization (QPSO) is used to estimate the heat source without a priori information on its functional form, which is classified as the function estimation by inverse calculation. Because of the ill-posedness of this kind of inverse problems, Tikhonov regularization method is applied in this paper to stabilize the solution. Numerical experiments indicate the validity and stability of the QPSO method. Comparison with the conjugate gradient method (CGM) is also presented in this paper.     

Robustness in the volume-to-point heat conduction optimization problem

This paper deals with the systematic and quantitative robustness analysis of solutions to the volume-to-point (VP) heat conduction optimization problem, including solutions by constructal theory (CT), bionic optimization (BO), simulated annealing (SA) as well as random solutions. The impacts of both load-induced and random failures are examined. All the solutions behave similarly during a failure. A tiny high-heat-flux-induced failure causes huge performance loss, which is the worst possible case. While the best case is a failure at positions of low heat flux, a large amount of which only causes a small performance loss. Random failure generally results in a loss roughly linear with failure amount, but sudden loss increase happens. Both intuitive and practical definitions of robustness are considered. Intuitively, a performance-robustness trade-off is seen for all the solutions, with poorer solutions being robuster. Practically things are different, with SA solutions both the best in performance and the robustest during a failure in the worst case. However, CT and BO solutions turn out to be robuster than SA solution in the best case, and CT solution may be more preferable in practice due to its regular geometry. With robustness taken into consideration, different solutions could be evaluated more comprehensively, the critical aspects concerning the practical realization of the solutions are also revealed, and furthermore the significance of robustness analysis in general VP problems is accentuated.     

Particle Swarm Optimization-based algorithms for solving inverse heat conduction problems of estimating surface heat flux

An inverse analysis of estimating a time-dependent surface heat flux for a three-dimensional heat conduction problem is presented. A global optimization method known as Particle Swarm Optimization (PSO) is employed to estimate the unknown heat flux at the inner surface of a crystal tube from the knowledge of temperature measurements obtained at the external surface. Three modifications of the PSO-based algorithm, PSO with constriction factor, PSO with time-varying acceleration of the cognitive and social coefficients, and PSO with mutation are carried out to implement the optimization process of the inverse analysis. The results show that the PSO with mutation algorithm is significantly better than other PSO-based algorithms because it can overcome the drawback of trapping in the local optimum points and obtain better inverse solutions. The effects of measurement errors, number of dimensionalities, and number of generations on the inverse solutions are also investigated.     

Wind turbines type and number choice using combinatorial optimization

The paper addresses the problem associated with the optimal wind park design. A combinatorial optimization model for wind turbines type and number choice and placement considering the given wind conditions and wind park area is developed. The wind park investment costs and the total power relation as function of wind turbines number and type are used as optimization criteria. The optimization problem is formulated as a single criterion mixed-integer nonlinear discrete combinatorial task. The different wind park conditions are introduced into optimization tasks formulation as variables relations and restrictions. Two basic wind directions cases are taken into consideration – uniform and predominant wind directions for two wind park area shapes – square and rectangular. The developed wind park design approach was tested numerically by solving of different optimization tasks formulations based on wind turbines real parameters data. The numerical testing shows the applicability of the developed optimization approach. Using it will help to find mathematically reasoned wind turbines choice as contradiction to the heuristic approaches.     

Iterative algorithms for solving inverse problems of heat conduction in multiply connected domains

The presented paper displays a method of solving the inverse problems of heat transfer in multi-connected regions, consisting in iterative solving of convergent series of the direct problems. For known temperature and flux values at the outer boundary of the region the temperature and flux values at the inner boundaries are sought (the cauchy problem for the Laplace equation). In case of such a formulation of the problem, the solution does not always exist, one of the conditions is met in the mean-square sense, providing the optimization criterion. The idea of the process consists in solving the direct problem in which the boundary condition is subject to iterative changes so as to attain minimum of the optimization criterion (the square functional). Two algorithms have been formulated. In the first of them the heat flux at the inner boundaries of the region, while in the other the temperature were subject to changes. Convergence of both the algorithms have been compared.The numerical calculation has been made for selected examples, for which an analytical solution is known. The effect of random disturbance of the boundary conditions on the solution obtained with iterative algorithms has been checked. Moreover, a function was defined, serving as convergence measure of the solution of the inverse problem solved with the algorithms proposed in the paper. The properties of the function give evidence that it tends to the value exceeding unity.     

Comparison of three sequential function specification algorithms for the inverse heat conduction problem

Three algorithms for implementing the sequential function specification method of estimating boundary heat flux in the inverse heat conduction problem are compared. They differ from one another in the type of piecewise function used to describe the heat flux and the assumed variation of heat flux over future time. The results of the comparison show that the algorithm that makes use of linear piecewise function for the heat flux and assumes linearly varying heat flux over future time performs slightly better than the other two algorithms.     

Inverse heat conduction problems by using particular solutions

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two‐dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least‐square and singular value decomposition (SVD) techniques are adopted to solve the ill‐conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20335     

Sensitivity analysis and shape optimization for transient heat conduction with radiation

Transient heat conduction problem is stated by the differential heat conduction equation, thermal boundary conditions on the external and internal boundary portions and the initial condition within the domain. Next an arbitrary behavioral functional is defined and its first-order sensitivities are determined using the material derivative concept as well as both the direct and adjoint approaches. The most used shape domain modifications are discussed in order to investigate the effect of design parameters on the integral radiation condition. The shape optimization problem is next formulated applying the obtained sensitivities. The illustration is the simple example of the shape optimization.     

Optimization of a liquefaction plant using genetic algorithms

This paper presents an optimization methodology for liquefaction/refrigeration systems in the cryogenic field. The Figure of Merit has been chosen as the evaluation index, and genetic algorithms as evaluation criteria. This methodology has been applied to an existing helium liquefaction system that works according to a Collins cycle. The results show the possibility of adjusting some of the thermal-pressure variables for the system in order to improve the Figure of Merit.     

Solution of inverse heat conduction problems using maximum entropy method

A solution scheme based on the maximum entropy method (MEM) for the solution of one-dimensional inverse heat conduction problem is proposed. The present work introduces MEM in order to build a robust formulation of the inverse problem. MEM finds the solution which maximizes the entropy functional under the given temperature measurements. In order to seek the most likely inverse solution, the present method converts the inverse problem to a non-linear constrained optimization problem. The constraint of the problem is the statistical consistency between the measured temperature and the estimated temperature. Successive quadratic programming (SQP) facilitates the maximum entropy estimation. The characteristic feature of the method is discussed with the sample numerical results. The presented results show considerable enhancement in the resolution of the inverse problem and bias reduction in comparison with the conventional methods.     

Relativistic heat conduction

The hyperbolic heat conduction equation (HHCE), which acknowledges the finite speed of heat propagation, is based on microscopic evidence from the kinetic theory and statistical mechanics. However, it was argued that the HHCE could violate the second law of thermodynamics. This paper shows that a HHCE-like equation (RHCE) can be derived directly from the theory of relativity, as a direct consequence of space-time duality, without any consideration of the microstructure of the heat-conducting medium. This approach results in an alternative expression for the heat flux vector that is more compatible with the second law. Therefore, the RHCE brings the classical field theory of heat conduction into agreement with other branches of modern physics.     

Design optimization of shell-and-tube heat exchanger using particle swarm optimization technique

Shell-and-tube heat exchangers (STHEs) are the most common type of heat exchangers that find widespread use in numerous industrial applications. Cost minimization of these heat exchangers is a key objective for both designer and users. Heat exchanger design involves complex processes, including selection of geometrical parameters and operating parameters. The traditional design approach for shell-and-tube heat exchangers involves rating a large number of different exchanger geometries to identify those that satisfy a given heat duty and a set of geometric and operational constraints. However, this approach is time-consuming and does not assure an optimal solution. Hence the present study explores the use of a non-traditional optimization technique; called particle swarm optimization (PSO), for design optimization of shell-and-tube heat exchangers from economic view point. Minimization of total annual cost is considered as an objective function. Three design variables such as shell internal diameter, outer tube diameter and baffle spacing are considered for optimization. Two tube layouts viz. triangle and square are also considered for optimization. Four different case studies are presented to demonstrate the effectiveness and accuracy of the proposed algorithm. The results of optimization using PSO technique are compared with those obtained by using genetic algorithm (GA).     

Investigating heat conduction in a sphere with heat absorption using generalized Caputo fractional derivative

In this paper, we study the ρ-Laplace transform and the finite sin-Fourier transform as powerful tools in solving fractional differential equations with generalized Caputo derivative. We use these transforms to solve the time-fractional heat equation with a generalized Caputo fractional derivative associated with heat absorption in spherical coordinates. We obtain the solutions in two cases of Dirichlet boundary conditions. The effect of the parameter $\rho$, which characterizes the generalized Caputo derivative is illustrated through some numerical examples.     

Solution of inverse heat conduction problem using the lattice Boltzmann method

In this paper the D2Q9 lattice Boltzmann method (LBM) was utilized for the solution of a two-dimensional inverse heat conduction (IHCP) problem. The accuracy of the LBM results was validated against those obtained from prevalent numerical methods using a common benchmark problem. The conjugate gradient method was used in order to estimate the heat flux test case. A complete error analysis was performed. As the LBM is attuned to parallel computations, its use is recommended in conjugation with IHCP solution methods.     

Solution of inverse heat conduction problem using the Tikhonov regularization method

It is hard to solve ill-posed problems, as calculated temperatures are very sensitive to errors made while calculating “measured” temperatures or performing real-time measurements. The errors can create temperature oscillation, which can be the cause of an unstable solution. In order to overcome such difficulties, a variety of techniques have been proposed in literature, including regularization, future time steps and smoothing digital filters. In this paper, the Tikhonov regularization is applied to stabilize the solution of the inverse heat conduction problem. The impact on the inverse solution stability and accuracy is demonstrated.     

Horizontal axis wind turbine systems: optimization using genetic algorithms

A method for the optimization of a grid‐connected wind turbine system is presented. The behaviour of the system components is coupled in a non‐linear way, and optimization must take into account technical and economical aspects of the complete system design. The annual electrical energy cost is estimated using a cost model for the wind turbine rotor, nacelle and tower and an energy output model based on the performance envelopes of the power coefficient of the rotor, C_P, on the Weibull parameters k and c and on the power law coefficient α of the wind profile. In this study the site is defined with these three parameters and the extreme wind speed V_max. The model parameters vary within a range of possible values. Other elements of the project (foundation, grid connection, financing cost, etc.) are taken into account through coefficients. The optimal values of the parameters are determined using genetic algorithms, which appear to be efficient for such a problem. These optimal values were found to be very different for a Mediterranean site and a northern European site using our numerical model. Optimal wind turbines at the Mediterranean sites considered in this article have an excellent profitability compared with reference northern European wind turbines. Most of the existing wind turbines appear to be well designed for northern European sites but not for Mediterranean sites. Copyright © 2001 John Wiley & Sons, Ltd.     

Optimization of network planning by the novel hybrid algorithms of intelligent optimization techniques

This paper proposes a new hybrid algorithm Meta-heuristic for the problem of network planning systems. The main goal of this paper is, to develop an efficient optimization tool which will minimise the cost functions of the stated optimization problems in network planning systems. The following are the objectives of the research: to investigate the capabilities of genetic algorithm, simulated annealing and tabu search for the defined optimization tasks; to develop a hybrid optimization algorithm which will produce improved iterations compared to those found by GA, SA, and TS algorithms. The performance of the hybrid algorithm is illustrated and six hybrid algorithms are developed, to improve the iterations obtained. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. It is advantageous to use exact DC load flow constraint equations based on the modified form of Kirchhoff's Second Law because the iterative process for line addition is not required. Hence, the computation time is decreased. Finally, the hybrid VI shows to be a very good option for network planning systems given that it obtains much accentuated reductions of iteration, which is very important for network planning.     

Topology optimization for thermal conductors considering design-dependent effects,including heat conduction and convection

In structural designs considering thermal loading, in addition to heat conduction within the structure, the heat convection upon the structure’s surface can significantly influence optimal design configurations. In this paper, we focus on the influence of design-dependent effects upon heat convection and internal heat generation for optimal designs developed using a topology optimization scheme. The method for extracting the structural boundaries for heat convection loads is constructed using a Hat function, and heat convection shape dependencies are taken into account in the heat transfer coefficient using a surrogate model. Several numerical examples are presented to confirm the usefulness of the proposed method.