ulti-objective tube flattening (H) and porous layer thickness ratio

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

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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.

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