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Statistical regression and artificial neural network analyses of impinging jet experiments

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Abstract

The purpose of this paper is to focus on the experimentally obtained results of impinging jet applications by the help of two different analysis methods. Circular round pipes (D = 7.9, 10.8, 13.8 and 23.1 mm) have been used as the impinging jets. The heat transfer is calculated with Nusselt number (Nu). The variable parameters are the dimensionless jet-to-impingement plate distance (z/D), Reynolds number (Re) and dimensionless temperature measurement points on the heated surface (x/L, y/L). Some important analysis methods such as artificial neural network (ANN), statistical regression, and uncertainty analysis are applied to the obtained data. It is shown that the ANN application is not simply a classification analysis; it is actually an application of the convergence of functions. As a result, by considering random data, 4.57% convergence level is obtained regarding the pipe diameter. The software STATISTICA 5.0 is used to estimate new empirical correlations nonlinearly. The smallest regression coefficient for the correlations is 0.87, while the highest value is 0.99. The result of the uncertainty analyses showed that the total uncertainties are in the agreeable range; 8% for Nu, and 2.89% for Re.

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Abbreviations

A :

heat transfer area (m2)

b h j (k):

biases of the hidden layer

b h1 (n):

biases of the output layer

C l :

specific heat (J/kg °C)

D :

inner diameter of each pipe (m)

g :

gravitational acceleration (m/s2)

h fg :

latent heat of vaporization (J/kg)

h :

local heat transfer coefficient (W/m2 C°)

\( \bar{h} \) :

average heat transfer coefficient (W/m2 C°)

Ja :

Jacob number

k :

thermal conductivity (W/m C°)

(k):

training pattern index

L :

height of the vertical plate (m)

N :

number of inputs, outputs, biases

Nu :

Nusselt number

\( \overline{Nu} \) :

average Nusselt number

N U (k):

output of the neural network

Q :

rate of heat (W)

R 2 :

regression coefficient

Re :

Reynolds number (−)

T :

temperature (°C)

U i (k):

features

W :

uncertainty of each parameter (%)

W i o j (k):

weights from the input to the hidden layer

W o j (k):

weights from the hidden to the output layer

x, y :

coordinates on surface (m)

X j (k):

outputs of the hidden layer neurons

z :

jet to plate distance (m)

μ :

dynamic viscosity (kg/ms)

ν :

kinematic viscosity of air (m2/s)

ρl :

density (kg/m3)

\( \dot{V} \) :

volumetric flow rate of air (m3/s)

cond :

condensation

impinged :

after impingement

j :

jet

l :

liquid

local :

local

losses :

losses (heat)

surf :

surface

sat :

saturation state

w :

wall

v :

vapor

0 :

stagnation point

m, n :

correlation exponents

C, k, p, q :

correlation coefficients

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Nevin Celik

  2. Department of Mechanical Educations, University of Firat, 23119, Elazig, Turkey

    Irfan Kurtbas

  3. Department of Computer Engineering, University of Sakarya, 54187, Adapazari, Turkey

    Nejat Yumusak

  4. Department of Mechanical Engineering, University of Firat, 23279, Elazig, Turkey

    Haydar Eren

Authors
  1. Nevin Celik
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  2. Irfan Kurtbas
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  3. Nejat Yumusak
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  4. Haydar Eren
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Corresponding author

Correspondence to Nevin Celik.

Additional information

Dr. Nevin Celik is a Post Doctoral Fellowship in University of Minnesota since August 2007.

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Celik, N., Kurtbas, I., Yumusak, N. et al. Statistical regression and artificial neural network analyses of impinging jet experiments. Heat Mass Transfer 45, 599–611 (2009). https://doi.org/10.1007/s00231-008-0454-9

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  • DOI: https://doi.org/10.1007/s00231-008-0454-9

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