Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 70, 2016 - Issue 1
152
Views
13
CrossRef citations to date
0
Altmetric
Original Articles

Application of intelligent methods for the prediction and optimization of thermal characteristics in a tube equipped with perforated twisted tape

, &
Pages 30-47 | Received 03 Sep 2015, Accepted 02 Dec 2015, Published online: 02 May 2016
 

ABSTRACT

In the present study, a feed-forward artificial neural network (ANN) was developed to estimate the Nusselt number (Nu), friction factor (f), and thermal performance (η) in a tube equipped with perforated twisted tape. The MSE and R2 values of the best network (4-10-3-3) are 0.04 and 0.9965, respectively. In addition, empirical equations were developed using the genetic algorithm. The MSE values of power-law equations for Nu, f and η are 2.7369, 4.13E-06, and 5.09E-05, respectively. Estimation of the developed ANN was found to be superior in comparison with the corresponding power-law equations.

Nomenclature

A=

heat transfer surface area

ANN=

artificial neural network

BP=

back-propagation

CP=

specific heat of fluid

D=

inside diameter of the test tube

d=

diameter of perforated tape

f=

friction factor = ΔP/((L/D)(ρU2/2))

h=

heat transfer coefficient

I=

current

k=

thermal conductivity of fluid

L=

length of test section

M=

mass flow rate

Nu=

Nusselt number

P=

flow pressure in stationary tube

ΔP=

pressure drop

Pr=

Prandtl number

Q=

heat transfer rate

Re=

Reynolds number = ρUD/µ

s=

spaced-pitch length of perforated tape, mm

t=

width of test tube

T=

temperature

=

mean temperature

U=

mean axial flow velocity

V=

voltage

W=

twisted tape width, weight in ANN

X=

input value of ANN

Y=

output value of ANN

y=

twisted tape pitch

ρ=

fluid density

δ=

twisted tape thickness

δi=

vector of errors for each hidden layer neuron

δk=

vector of errors for each output neuron

µ=

fluid dynamic viscosity

η=

thermal performance factor, momentum factor

θj=

threshold between input and hidden layers

θk=

threshold connecting hidden and output layers

fh()=

logistic sigmoid activation function from input layer to hidden layer

fk()=

logistic sigmoid activation function from hidden layer to output layer

=

learning rate

Subscripts=
b=

bulk

c=

convection

i=

inlet

o=

outlet

p=

plain

s=

surface

t=

twisted tape

w=

Water

Nomenclature

A=

heat transfer surface area

ANN=

artificial neural network

BP=

back-propagation

CP=

specific heat of fluid

D=

inside diameter of the test tube

d=

diameter of perforated tape

f=

friction factor = ΔP/((L/D)(ρU2/2))

h=

heat transfer coefficient

I=

current

k=

thermal conductivity of fluid

L=

length of test section

M=

mass flow rate

Nu=

Nusselt number

P=

flow pressure in stationary tube

ΔP=

pressure drop

Pr=

Prandtl number

Q=

heat transfer rate

Re=

Reynolds number = ρUD/µ

s=

spaced-pitch length of perforated tape, mm

t=

width of test tube

T=

temperature

=

mean temperature

U=

mean axial flow velocity

V=

voltage

W=

twisted tape width, weight in ANN

X=

input value of ANN

Y=

output value of ANN

y=

twisted tape pitch

ρ=

fluid density

δ=

twisted tape thickness

δi=

vector of errors for each hidden layer neuron

δk=

vector of errors for each output neuron

µ=

fluid dynamic viscosity

η=

thermal performance factor, momentum factor

θj=

threshold between input and hidden layers

θk=

threshold connecting hidden and output layers

fh()=

logistic sigmoid activation function from input layer to hidden layer

fk()=

logistic sigmoid activation function from hidden layer to output layer

=

learning rate

Subscripts=
b=

bulk

c=

convection

i=

inlet

o=

outlet

p=

plain

s=

surface

t=

twisted tape

w=

Water

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.