ulti-objective

optimization of flat tubes partially filled with porous layer using ANFIS, GMDH

and NSGA II approaches

Ehsan

Rezaei, Department of Mechanical Engineering, Amirkabir University of

Technology (Tehran Polytechnic), 424 Hafez Ave., P.O. Box 15875-4413, Tehran,

Iran

Abbass

Abbassi, Department of Mechanical Engineering, Amirkabir University of

Technology (Tehran Polytechnic), 424 Hafez Ave., P.O. Box 15875-4413, Tehran,

Iran

In this article, modeling and multi-objective

optimization of fluid flow in flat tubes equipped with a porous layer is

performed using Computational Fluid Dynamics (CFD) techniques, Adaptive Neuro

Fuzzy Inference System (ANFIS), Grouped Method of Data Handling (GMDH) type ANN

and Non-dominated Sorting Genetic Algorithms (NSGA II). The design variables

are two geometrical parameters of tubes, tube flattening (H) and porous

layer thickness ratio (HP), Porosity (

), Entrance flow rate (Q) and Wall

heat flux (

. The objectives are to maximize the convection

heat transfer coefficient (h) and minimizing the pressure drop. At

first, problem is solved numerically in various flat tubes using CFD techniques

and two objective parameters in tubes are calculated. Numerical data of the

previous step will be applied to model h

and

using

ANFIS and Grouped Method of Data Handling (GMDH). In the next step, Pareto

based multi-objective optimization will be carry out by the use of GMDH model and

NSGA II algorithm. The results revealed that the ANFIS model yields better

prediction in comparison with methods and the obtained Pareto solution contains

important design information on flow parameters in flat tubes partially with

porous insert. The results show that the best configuration for the maximum

heat transfer and the minimum pressure loss is H=4mm and Hp=

0.75.

Keyword: Heat Transfer, Flat tubes, Porous medium,

Modeling, Optimization

Nomenclature

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. Introduction

The utilization of porous

medium inside the tube has attracted considerable attention due to its possible

potential in enhancing heat transfer performance, such heat exchangers, cooling

of electronic components, biological systems, geothermal engineering, solid

matrix heat exchangers, enhanced oil recovery, thermal insulation, and chemical

reactors and so on. Numerical and experimental studies on internal flows in a

tube have been examined to supply a deeper comprehension of the transport

mechanism of momentum and heat via fully or partially filled porous medium

tubes. The completely porous medium-filled tube may be penalized by increasing the

pressure drop, which in turns increases the cost of the pumping work.

Therefore, the partially porous medium filled tube may be an alternative way to

reduce the increment of pressure drop. A significant number of researches on

forced convection in partially filled porous tube and ducts have been performed

and reported in the literatures.

In a Numerical research,

Alazmi and Vafai 1 studied two different forms of constant heat flux boundary

condition with seven different sub-models. Effects of Reynolds number, Darcy

number, inertia parameter, porosity, particle diameter and solid-to-fluid

conductivity ratio were analyzed.. Shokouhmand et al. 2,3 investigated

thermal performance of a channel and compared with two configurations, and it

was found that the position of the porous insert has a significant influence on

the thermal performance of the channel. Rong et al. 4 numerically investigated

new axisymmetric lattice Boltzmann model to calculate the fluid flow and heat

transfer characteristics in a pipe filled with porous media. Effects of several

parameters, such as porous layer thickness, Darcy number, and porosity, on

thermal conductivity efficiency are investigated. They found that controlling

the thickness of the porous media can significantly improve heat transfer

performance and the influence of porosity is insignificant.

In LTE model, the

continuity of temperature and heat flux can be employed as the boundary

conditions at the interface. Because the temperatures of fluid and solid phases

in porous media are different for LTNE model, an additional thermal boundary

condition should be considered at the interface. Yang and Vafai 5 provided

three different interface models for the phenomenon of heat flux bifurcation

inside a composite system under LTNE conditions for the first time. They have

discussed the limitations of each model and the Nusselt number is obtained for

pertinent parameters. In another study by Yang and Vafai 6, exact solution

for five basic forms of thermal conditions at the interface between a fluid and

a porous medium under LTNE condition investigated.