Optimization of convective fin systems: a holistic approach

 A numerical analysis of natural convection heat transfer and entropy generation from an array of vertical fins, standing on a horizontal duct, with turbulent fluid flow inside, has been carried out. The analysis takes into account the variation of base temperature along the duct, traditionally ignored by most studies on such problems. One-dimensional fin equation is solved using a second order finite difference scheme for each of the fins in the system and this, in conjunction with the use of turbulent flow correlations for duct, is used to obtain the temperature distribution along the duct. The influence of the geometric and thermal parameters, which are normally employed in the design of a thermal system, has been studied. Correlations are developed for (i) the total heat transfer rate per unit mass of the fin system (ii) total entropy generation rate and (iii) fin height, as a function of the geometric parameters of the fin system. Optimal dimensions of the fin system for (i) maximum heat transfer rate per unit mass and (ii) minimum total entropy generation rate are obtained using Genetic Algorithm. As expected, these optima do not match. An approach to a `holistic' design that takes into account both these criteria has also been presented. Received on 22 February 2001 / Published online: 29 November 2001     

Entropy minimization in micro-scale evaporating thin liquid film in capillary tubes

An analysis has been provided for the entropy generated for the micro/nano scale heat and mass transfer in a capillary tube in terms of the gradients of velocity, temperature and concentration as well as the physical properties of the fluid. The heat and mass transfer rates are assumed to be uniform on the surface of the capillary tube. The optimum tube diameter that corresponds to the minimization of entropy generated and minimization of fluid flow resistance is about 1 mm. We have applied the method of thermodynamic optimization to capillary driven systems. The objective was to identify the geometric configuration that maximized performance by minimizing the entropy generated when the flow rate is prescribed.     

Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

A rotating channel with staggered pin‐fins is formulated numerically and optimized for performance (heat transfer/required pumping power) using a Kriging meta‐model and hybrid multi‐objective evolutionary algorithm. Two design variables related to cooling channel height, pin diameter, and spacing between the pins are selected for optimization, and two‐objective functions related to the heat transfer and friction loss are employed. A design of experiment is performed, and 20 designs are generated by Latin hypercube sampling. The objective function values are evaluated using a Reynolds‐averaged Navier–Stokes solver, and a Kriging model is constructed to obtain a Pareto‐optimal front through a multi‐objective evolutionary algorithm. Rotation in a cooling channel with staggered pin‐fins induces Coriolis force that causes a heat transfer discrepancy between the trailing (pressure) and leading (suction) surfaces, with a higher Nusselt number on the trailing surface. The tradeoff between the two competing objective functions is determined, and the distribution of the Pareto‐optimal solutions in the design space is discussed through k‐means clustering. In the optimal designs, with a decrease in spacing between the pins, heat transfer is enhanced whereas friction loss is increased. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance evaluation and optimization of semi-dimpled slit fin

In this paper, the semi-dimpled slit fin is proposed and the characteristics of heat transfer and fluid flow are analyzed based on the orthogonal experiment design method. A serial studies on the effects of fin pitch, arrangement of semi-dimple, dimple radius on heat transfer and flow characteristics of semi-dimpled slit fin are investigated. The computational results show fin pitch (Fp) has significantly effected on the performance of heat transfer and fluid flow, the influence of arrangement of semi-dimple, the dimple radius (R) and the opening direction of semi-dimples dwindle. At the same time, compared to the general semi-dimpled slit fin, the heat transfer coefficient and JF factors of the optimized fin increase by 10.7–25.1 and 2.6–7.7 %, respectively. When Re ≤ 1,521, the overall performance of slit fin is better than that of optimized fin; while Re > 1,521, the overall performance of optimized fin is better than that of slit fin. Finally, the performance evaluation plot of enhanced heat transfer of heat exchanger is applied to analyze the optimized fin, it can be seen that optimization fin have better heat transfer performance under the same power consumption.     

Enhanced multi‐objective optimization of a dimpled channel through evolutionary algorithms and multiple surrogate methods

Using a multi‐objective evolutionary algorithm (MOEA) and enhanced surrogate approximations, the present study demonstrates the numerical analysis and optimization of staggered‐dimple channels. Two surrogates, the response surface approximation (RSA) model and the Kriging (KRG) model, are applied in light of the surrogate fidelity of the approximate analysis. An enhanced Pareto‐optimal front is obtained by performing local resampling of the Pareto‐optimal front, which provides relatively more accurate Pareto‐optimal solutions in the design space for each surrogate model. Three dimensionless design variables are selected, which are related to geometric parameters, namely, the channel height, dimple print diameter, dimple spacing, and dimple depth. Two objective functions are selected that are related to the heat transfer and pressure loss, respectively. The objective‐function values are numerically evaluated through Reynolds‐averaged Navier–Stokes analysis at the design points that are selected through the Latin hypercube sampling method. Using these numerical simulations two surrogates, viz, the RSA and Kriging models, are constructed for each objective function and a hybrid MOEA is applied to obtain the Pareto‐optimal front. For the particular implementation of surrogate models, it is observed that Pareto‐optimal predictions of the RSA model are better than those of the KRG model, whereas the KRG model predicts equally well at the off‐Pareto‐region (region away from the Pareto‐optimal solutions), which is not the case with the RSA model. The local resampling of the Pareto‐optimal front increases the fidelity of the approximate solutions near the Pareto‐optimal region. The ratios of the channel height to the dimple print diameter and of the dimple print diameter to the dimple pitch are found to be more sensitive along the Pareto‐optimal front than the ratio of the dimple depth to the print diameter. The decrease of the ratio of the channel height to the dimple diameter and the increase of the ratio of the dimple print diameter to the pitch lead to greater heat transfer at the expense of the pressure loss, whereas the ratio of the dimple depth to the print diameter is rather insensitive to Pareto‐optimal solutions. Pareto‐optimal solutions at higher values of the Nusselt number are associated with higher values of the pressure loss due to the increased recirculation, mixing of fluid and vorticity generation. Copyright © 2010 John Wiley & Sons, Ltd.     

Entropy analysis for third grade fluid flow with Vogel model viscosity in annular pipe

The steady-state flow of a third grade fluid between concentric circular cylinders is considered and entropy generation due to fluid friction and heat transfer in the annular pipe is examined. Depending upon the fluid viscosity, entropy generation in the flow system varies. The third grade fluid is employed to account for the non-Newtonian effect while Vogel model is accommodated for temperature-dependent viscosity. The analysis is based on perturbation technique. The closed form solutions for velocity, temperature and entropy fields are presented. Entropy generation due to fluid friction and heat transfer in the flow system is formulated. The influence of viscosity parameters A and B on the entropy generation number is investigated. It is found that entropy generation number reduces with increasing viscosity parameter A, which is more pronounced in the region close to the annular pipe inner wall and opposite is true for increasing viscosity parameter B.     

Comparison of derivative free Newton‐based and evolutionary methods for shape optimization of flow problems

The object of this study is to investigate two derivative free optimization techniques, i.e. Newton‐based method and an evolutionary method for shape optimization of flow geometry problems. The approaches are compared quantitatively with respect to efficiency and quality by using the minimization of the pressure drop of a pipe conjunction which can be considered as a representative test case for a practical three‐dimensional flow configuration. The comparison is performed by using CONDOR representing derivative free Newton‐based techniques and SIMPLIFIED NSGA‐II as the representative of evolutionary methods (EM). For the shape variation the computational grid employed by the flow solver is deformed. To do this, the displacement fields are scaled by design variables and added to the initial grid configuration. The displacement vectors are calculated once before the optimization procedure by means of a free form deformation (FFD) technique. The simulation tool employed is a parallel multi‐grid flow solver, which uses a fully conservative finite‐volume method for the solution of the incompressible Navier–Stokes equations on a non‐staggered, cell‐centred grid arrangement. For the coupling of pressure and velocity a pressure‐correction approach of SIMPLE type is used. The possibility of parallel computing and a multi‐grid technique allow for a high numerical efficiency. Copyright © 2006 John Wiley & Sons, Ltd.     

The thermodynamic design of heat and mass transfer processes and devices

This review article places in perspective the new work devoted both to the analysis of the thermodynamic irreversibility of heat and mass transfer components and systems and to the design of these devices on the basis of entropy generation minimization. The review focuses on the fundamental mechanisms responsible for the generation of entropy in heat and fluid flow and on the design tradeoff of balancing the heat transfer irreversibility against the fluid flow irreversibility. Applications are selected from the fields of heat exchanger design, thermal energy storage, and mass exchanger design. This article provides a comprehensive, up-to-date review of second-daw analyses published in the heat and mass transfer literature during the last decade.     

A study on heat transfer of the optimization in circular fins of parabolic profile with variable thermal parameters

Circular fins are used extensively in heat exchange devices to increase the heat transfer. For economic purposes, the traditional approach to the optimization of fins consists of minimizing the comsumption (investment) of fin material for the excution of a specified heat transfer task. The minimum weight cooling fin has optional profile to be a concave parabola. Therefore, the optimum geometric dimensions of circular fins of parabolic profile with variable thermal parameters are studied. The effect of the two pertinent physical parameters-thermal conductivity variation parameter α and the index of the heat transfer coefficient variationm upon the optimum geometric dimensions is also studied. The results pressented can be used as the design guideline for engineering practice.     

CFD‐based optimization of aerofoils using radial basis functions for domain element parameterization and mesh deformation

A novel domain element shape parameterization method is presented for computational fluid dynamics‐based shape optimization. The method is to achieve two aims: (1) provide a generic ‘wrap‐around’ optimization tool that is independent of both flow solver and grid generation package and (2) provide a method that allows high‐fidelity aerodynamic optimization of two‐ and three‐dimensional bodies with a low number of design variables. The parameterization technique uses radial basis functions to transfer domain element movements into deformations of the design surface and corresponding aerodynamic mesh, thus allowing total independence from the grid generation package (structured or unstructured). Independence from the flow solver (either inviscid, viscous, aeroelastic) is achieved by obtaining sensitivity information for an advanced gradient‐based optimizer (feasible sequential quadratic programming) by finite‐differences. Results are presented for two‐dimensional aerofoil inverse design and drag optimization problems. Inverse design results demonstrate that a large proportion of the design space is feasible with a relatively low number of design variables using the domain element parameterization. Heavily constrained (in lift, volume, and moment) two‐dimensional aerofoil drag optimization has shown that significant improvements over existing designs can be achieved using this method, through the use of various objective functions. Copyright © 2008 John Wiley & Sons, Ltd.     

Shape optimization of a body located in incompressible flow using adjoint method and partial control algorithm

The purpose of this study is to obtain an optimal shape of a body located in an incompressible viscous flow. The optimal shape of the body is defined so as to minimize the fluid forces acting on it by determining the surface coordinates based on the finite element method and the optimal control theory. The performance function, which is used to judge the optimality of a shape, is defined as the square sum of the drag and lift forces. The minimization problem is solved using an adjoint equation method. The gradient in the adjoint equation is affected by the finite element configuration. The use of a finite element mesh whose shape is appropriate for the procedure is important in shape optimization. If the finite element mesh used is not suitable for computations, the exact gradient is not calculated. Therefore, a structured mesh is used for the adjacent area of the body and all finite element meshes are refined using the Delaunay triangulation at each iteration computation. The weighted gradient method is applied as the minimization technique. Using an algorithm in which all nodal coordinates on the surface of the body are employed and starting from a circle as an initial shape, a front‐edged and rear‐round shape is obtained because of the vortices at the back of the body. To overcome this difficulty, we introduced the partial control algorithm, in which some of the nodal coordinates on the surface of the body are updated. From four cases of computational studies, we reveal that the optimal shape has both sharp front and sharp rear edges. All computations are conducted at Reynolds number Re=250. The minimum value of the performance function is obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

Entropy generation in flow field subjected to a porous block in a vertical channel

Entropy generation in the flow field subjected to a porous block situated in a vertical channel is examined. The effects of channel inlet port height (vertical height between channel inlet port and the block center), porosity, and block aspect ratio on the entropy generation rate due to fluid friction and heat transfer in the fluid are examined. The governing equations of flow, heat transfer, and entropy are solved numerically using a control volume approach. Air is used as the flowing fluid in the channel. A uniform heat flux is considered in the block and natural convection is accommodated in the analysis. It is found that entropy generation rate due to fluid friction increases with increasing inlet port height, while this increase becomes gradual for entropy generation rate due to heat transfer for the inlet port height exceeding 0.03 m. The porosity lowers entropy generation rate due to fluid friction and heat transfer. The effect of block aspect ratio on entropy generation rate is notable; in which case, entropy generation rate increases for the block aspect ratio of 1:2.     

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     

Multi‐scale time integration for transient conjugate heat transfer

The quasi‐steady assumption is commonly adopted in existing transient fluid–solid‐coupled convection–conduction (conjugate) heat transfer simulations, which may cause non‐negligible errors in certain cases of practical interest. In the present work, we adopt a new multi‐scale framework for the fluid domain formulated in a triple‐timing form. The slow‐varying temporal gradient corresponding to the time scales in the solid domain has been effectively included in the fluid equations as a source term, whilst short‐scale unsteadiness of the fluid domain is captured by a local time integration at a given ‘frozen’ large scale time instant. For concept proof, validation and demonstration purposes, the proposed methodology has been implemented in a loosely coupled procedure in conjunction with a hybrid interfacing treatment for coupling efficiency and accuracy. The present results indicate that a much enhanced applicability can be achieved with relatively small modifications of existing transient conjugate heat transfer methods at little extra cost. Copyright © 2016 John Wiley & Sons, Ltd.     

An analytical method for the optimum thermal design of convective longitudinal fin arrays

The paper analyzes the problem of the optimum thermal design of free and forced convection fin arrays composed of longitudinal fins with constant thickness. Two different optimization problems have been considered: the minimization of the weight for a given heat flow and the maximization of the heat flow for a given weight. Two different geometrical configurations of the fin array have been considered: closed array and open array. The procedure for the optimization is provided in a general case and a complete analytical solution of the problem, for the case with the tip approximated as being insulated, is developed. The paper contains several illustrative examples of the application of the proposed optimization procedure.     

Groove geometry effects on turbulent heat transfer and fluid flow

The present work represents a two-dimensional numerical prediction of forced turbulent flow heat transfer through a grooved tube. Four geometric groove shapes (circular, rectangular, trapezoidal and triangular) were selected to perform the study, as well as two aspect ratios of groove-depth to tube diameter (e/D = 0.1 and 0.2). The study focuses on the influence of the geometrical shapes of grooves and groove-depth on heat transfer and fluid flow characteristics for Reynolds number ranging from 10,000 to 20,000. The characteristics of Nusselt number, friction factor and entropy generation are studied numerically by the aid of the computational fluid dynamics (CFD) commercial code of FLUENT. It is observed that the best performance occurs with the lower depth-groove ratio, whereas it is found that the grooved tube provides a considerable increase in heat transfer at about 64.4 % over the smooth tube and a maximum gain of 1.52 on thermal performance factor is obtained for the triangular groove with (e/D = 0.1).     

Entropy generation analysis of natural convective radiative second grade nanofluid flow between parallel plates in a porous medium

The present article explores the entropy generation of radiating viscoelastic second grade nanofluid in a porous channel confined between two parallel plates. The boundaries of the plates are maintained at distinct temperatures and concentrations while the fluid is being sucked and injected periodically through upper and lower plates. The buoyancy forces, thermophoresis and Brownian motion are also considered due to the temperature and concentration differences across the channel. The system of governing partial differential equations has been transferred into a system of ordinary differential equations(ODEs) by appropriate similarity relations, and a shooting method with the fourth-order Runge-Kutta scheme is used for the solutions. The results are analyzed in detail for dimensionless velocity components. The temperature, concentration distributions, the entropy generation number, and the Bejan number corresponding to various fluid and geometric parameters are shown graphically. The skin friction, heat and mass transfer rates are presented in the form of tables. It is noticed that the temperature profile of the fluid is enhanced with the Brownian motion, whereas the concentration profile of the fluid is decreased with the thermophoresis parameter, and the entropy and Bejan numbers exhibit the opposite trend for the suction and injection ratio.     

CFD‐based multi‐objective optimization method for ship design

This paper concerns development and demonstration of a computational fluid dynamics (CFD)‐based multi‐objective optimization method for ship design. Three main components of the method, i.e. computer‐aided design (CAD), CFD, and optimizer modules are functionally independent and replaceable. The CAD used in the present study is NAPA system, which is one of the leading CAD systems in ship design. The CFD method is FLOWPACK version 2004d, a Reynolds‐averaged Navier–Stokes (RaNS) solver developed by the present authors. The CFD method is implemented into a self‐propulsion simulator, where the RaNS solver is coupled with a propeller‐performance program. In addition, a maneuvering simulation model is developed and applied to predict ship maneuverability performance. Two nonlinear optimization algorithms are used in the present study, i.e. the successive quadratic programming and the multi‐objective genetic algorithm, while the former is mainly used to verify the results from the latter. For demonstration of the present method, a multi‐objective optimization problem is formulated where ship propulsion and maneuverability performances are considered. That is, the aim is to simultaneously minimize opposite hydrodynamic performances in design tradeoff. In the following, an overview of the present method is given, and results are presented and discussed for tanker stern optimization problem including detailed verification work on the present numerical schemes. Copyright © 2006 John Wiley & Sons, Ltd.     

Entropy analysis of unsteady magneto-nanofluid flow past accelerating stretching sheet with convective boundary condition

The unsteady laminar magnetohydrodynamics(MHD) boundary layer flow and heat transfer of nanofluids over an accelerating convectively heated stretching sheet are numerically studied in the presence of a transverse magnetic field with heat source/sink. The unsteady governing equations are solved by a shooting method with the Runge-KuttaFehlberg scheme. Three different types of water based nanofluids, containing copper, aluminium oxide, and titanium dioxide, are taken into consideration. The effects of the pertinent parameters on the fluid velocity, the temperature, the entropy generation number, the Bejan number, the shear stress, and the heat transfer rate at the sheet surface are graphically and quantitatively discussed in detail. A comparison of the entropy generation due to the heat transfer and the fluid friction is made with the help of the Bejan number. It is observed that the presence of the metallic nanoparticles creates more entropy in the nanofluid flow than in the regular fluid flow.