ulti-objectiveoptimization of flat tubes partially filled with porous layer using ANFIS, GMDHand NSGA II approaches EhsanRezaei, Department of Mechanical Engineering, Amirkabir University ofTechnology (Tehran Polytechnic), 424 Hafez Ave., P.O. Box 15875-4413, Tehran,IranAbbassAbbassi, Department of Mechanical Engineering, Amirkabir University ofTechnology (Tehran Polytechnic), 424 Hafez Ave., P.

O. Box 15875-4413, Tehran,Iran In this article, modeling and multi-objectiveoptimization of fluid flow in flat tubes equipped with a porous layer isperformed using Computational Fluid Dynamics (CFD) techniques, Adaptive NeuroFuzzy Inference System (ANFIS), Grouped Method of Data Handling (GMDH) type ANNand Non-dominated Sorting Genetic Algorithms (NSGA II). The design variablesare two geometrical parameters of tubes, tube flattening (H) and porouslayer thickness ratio (HP), Porosity ( ), Entrance flow rate (Q) and Wallheat flux ( . The objectives are to maximize the convectionheat transfer coefficient (h) and minimizing the pressure drop. Atfirst, problem is solved numerically in various flat tubes using CFD techniquesand two objective parameters in tubes are calculated. Numerical data of theprevious step will be applied to model hand usingANFIS and Grouped Method of Data Handling (GMDH). In the next step, Paretobased multi-objective optimization will be carry out by the use of GMDH model andNSGA II algorithm.

The results revealed that the ANFIS model yields betterprediction in comparison with methods and the obtained Pareto solution containsimportant design information on flow parameters in flat tubes partially withporous insert. The results show that the best configuration for the maximumheat transfer and the minimum pressure loss is H=4mm and Hp=0.75.Keyword: Heat Transfer, Flat tubes, Porous medium,Modeling, OptimizationNomenclature Ai fuzzy sets ACi actual value ANFIS Adaptive Nero Fuzzy Inference System asf Specific fluid-to-solid surface area Bi fuzzy sets Cp specific heat, J/(kg K) Cf Friction factor d particle diameter, m Dh hydraulic diameter, m F Inertia parameter fi ANFIS system’s output H Tube height Hp Porous layer thickness h heat transfer coefficient, W/(m2 K) hsf fluid-to-solid heat transfer coefficient W/(m2 K) k thermal conductivity, W/(m K) kfe effective thermal conductivity of the fluid, W/m K kse effective thermal conductivity of the solid, W/m K K permeability (m2) L length of flat tube, m MRE% mean relative error MSE mean squared error Nu Nusselt number Oij ANFIS layers output P pressure, Pa PRi ANFIS predicted output pi linear output Pr Prandtl number Q Entrance flow rate q” heat flux, W/m2 qi linear output Re Reynolds number RE% relative error R2 correlation coefficient ri linear output T temperature, K V velocity, m/s W width of flat tube, mm Wi ANFIS normalized firing strength Z axial distance from inlet, m Greek symbols thermal diffusivity (=k/ Cp) (m2/s) porosity density, kg/m3 dynamic viscosity (kg/ m.s) wall shear stress (Pa) Subscripts 0 Plain tube e effective f fluid i inlet interface interface between the porous medium and the clear region p porous s solid w wall x X direction y Y direction z Z direction 1. IntroductionThe utilization of porousmedium inside the tube has attracted considerable attention due to its possiblepotential in enhancing heat transfer performance, such heat exchangers, coolingof electronic components, biological systems, geothermal engineering, solidmatrix heat exchangers, enhanced oil recovery, thermal insulation, and chemicalreactors and so on. Numerical and experimental studies on internal flows in atube have been examined to supply a deeper comprehension of the transportmechanism of momentum and heat via fully or partially filled porous mediumtubes.

The completely porous medium-filled tube may be penalized by increasing thepressure drop, which in turns increases the cost of the pumping work.Therefore, the partially porous medium filled tube may be an alternative way toreduce the increment of pressure drop. A significant number of researches onforced convection in partially filled porous tube and ducts have been performedand reported in the literatures. In a Numerical research,Alazmi and Vafai 1 studied two different forms of constant heat flux boundarycondition with seven different sub-models. Effects of Reynolds number, Darcynumber, inertia parameter, porosity, particle diameter and solid-to-fluidconductivity ratio were analyzed.

. Shokouhmand et al. 2,3 investigatedthermal performance of a channel and compared with two configurations, and itwas found that the position of the porous insert has a significant influence onthe thermal performance of the channel. Rong et al. 4 numerically investigatednew axisymmetric lattice Boltzmann model to calculate the fluid flow and heattransfer characteristics in a pipe filled with porous media.

Effects of severalparameters, such as porous layer thickness, Darcy number, and porosity, onthermal conductivity efficiency are investigated. They found that controllingthe thickness of the porous media can significantly improve heat transferperformance and the influence of porosity is insignificant.In LTE model, thecontinuity of temperature and heat flux can be employed as the boundaryconditions at the interface. Because the temperatures of fluid and solid phasesin porous media are different for LTNE model, an additional thermal boundarycondition should be considered at the interface. Yang and Vafai 5 providedthree different interface models for the phenomenon of heat flux bifurcationinside a composite system under LTNE conditions for the first time.

They havediscussed the limitations of each model and the Nusselt number is obtained forpertinent parameters. In another study by Yang and Vafai 6, exact solutionfor five basic forms of thermal conditions at the interface between a fluid anda porous medium under LTNE condition investigated.