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Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid

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Abstract

Nanofluids are broadly employed in heat transfer mediums to enhance their efficiency and heat transfer capacity. Thermophysical properties of nanofluids play a crucial role in their thermal behavior. Among various properties, the dynamic viscosity is one of the most crucial ones due to its impact on fluid motion and friction. Applying appropriate models can facilitate the design of nanofluidics thermal devices. In the present study, various machine learning methods including MPR, MARS, ANN-MLP, GMDH, and M5-tree are used for modeling the dynamic viscosity of CuO/water nanofluid based on the temperature, concentration, and size of nanostructures. The input data are extracted from various experimental studies to propose a comprehensive model, applicable in wide ranges of input variables. Moreover, the relative importance of each variable is evaluated to figure out the priority of the variables and their influences on the dynamic viscosity. Finally, the accuracy of the models is compared by employing the statistical criteria such as R-squared value. The models’ outputs disclosed that employing ANN-MLP approach leads to the most precise model. R-square value and average absolute percent relative error (AAPR) value of the model by using ANN-MLP model are 0.9997 and 1.312%, respectively. According to these values, ANN-MLP is a reliable approach for predicting the dynamic viscosity of the studied nanofluid. Additionally, based on the relative importance of the input variables, it is concluded that concentration has the highest relative importance; while the influence of size is the lowest one.

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Abbreviations

A :

Heat transfer area (m2)

Cp:

Specific heat (kj kg-1 °C−1)

d :

Nanoparticle diameter (m)

h :

Convective heat transfer coefficient (W m−2 °C−1)

h E :

Enhanced convective heat transfer coefficient

h NE :

Non-enhanced convective heat transfer coefficient

k :

Thermal conductivity (W m−1 °C−1)

L :

Tube length (m)

M :

Mass flow rate (kg s−1)

Q :

Heat transfer rate (W)

Re :

Reynolds number (dimensionless)

T :

Temperature (°C)

U :

Overall heat transfer coefficient (W m-2oc-1)

V :

Velocity (m2 s−1)

n :

Flow behavior index

\(\Delta T_{\text{lm}}\) :

Logarithmic mean temperature difference (°C)

\(\Delta P_{\text{nf}}\) :

Pressure drop

α :

Thermal diffusivity (m2 s−1)

\(\rho\) :

Density (kg m−3)

\(\vartheta\) :

Kinematic viscosity (m2 s−1)

\(\eta\) :

Performance evaluation analysis

\(\varphi_{\text{V}}\) :

Nanoparticle volume concentration (dimensionless)

f:

Fluid

i:

Inside

nf:

NANOFLUID

m:

Mean

out:

Outlet

p:

Particles

AAPRE:

Average absolute percent relative error

MLP:

Multi-layer perceptron

LM:

Levenberg–Marquardt

RMSE:

Root mean square error

MPR:

Multivariable polynomial regression

MARS:

Multivariate adaptive regression splines

GMDH:

Group method of data handling

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Mohammad Hossein Ahmadi & Behnam Mohseni-Gharyehsafa

  2. Department of Renewable Energy and Environmental Engineering, University of Tehran, Tehran, Iran

    Mahyar Ghazvini

  3. Sustainable Management of Natural Resources and Environment Research Group, Faculty of Environment and Labour Safety, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Marjan Goodarzi

  4. Department of Mechanical Engineering, Lovely Professional University, Punjab, 14411, India

    Ravindra D. Jilte & Ravinder Kumar

Authors
  1. Mohammad Hossein Ahmadi
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  2. Behnam Mohseni-Gharyehsafa
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  3. Mahyar Ghazvini
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  4. Marjan Goodarzi
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  5. Ravindra D. Jilte
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  6. Ravinder Kumar
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Corresponding authors

Correspondence to Mohammad Hossein Ahmadi, Marjan Goodarzi or Ravinder Kumar.

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Appendix

Appendix

The coefficients of Eq. 3 are obtained based on the equations presented as follows:

$$N_{2} = C_{4} + N_{94} \times N_{3} \times C_{5} + N_{94}^{2} \times C_{6} + N_{3} \times C_{7} + N_{3}^{2} \times C_{8}$$
$$N_{3} = C_{9} + N_{58} \times C_{10} + N_{58} \times N_{4} \times C_{11} + N_{58}^{2} \times C_{12} + N_{4} \times C_{13} + N_{4}^{2} \times C_{14}$$
$$N_{4} = C_{15} + N_{122} \times C_{16} + N_{122} \times N_{5} \times C_{17} + N_{122}^{2} \times C_{18} + N_{5} \times C_{19} + N_{5}^{2} \times C_{20}$$
$$N_{5} = C_{21} + N_{67} \times C_{22} + N_{67} \times N_{10} \times C_{23} + N_{67}^{2} \times C_{24} + N_{10} \times C_{25} + N_{10}^{2} \times C_{26}$$
$$N_{10} = C_{27} + N_{108} \times C_{28} + N_{108} \times N_{14} \times C_{29} + N_{14} \times C_{30} + N_{14}^{2} \times C_{31}$$
$$N_{14} = C_{32} + N_{27} \times N_{29} \times C_{33} + N_{27}^{2} \times C_{34} + N_{29} \times C_{35}$$
$$N_{29} = C_{36} + N_{142} \times C_{37} + N_{142}^{2} \times C_{38} + N_{40} \times C_{39}$$
$$N_{40} = C_{40} + N_{49} \times C_{41} + N_{49}^{2} \times C_{42} + N_{93} \times C_{43}$$
$$N_{93} = C_{44} + N_{134} \times C_{45} + N_{134}^{2} \times C_{46} + N_{162} \times C_{47}$$
$$N_{162} = C_{48} + N_{182} \times C_{49} + N_{182} \times N_{265} \times C_{50} + N_{182}^{2} \times C_{51} + N_{265} \times C_{52} + N_{265}^{2} \times C_{53}$$
$$N_{182} = C_{54} + d \times C_{55} + d \times N_{237} \times C_{56} + d^{2} \times C_{57} + N_{237} \times C_{58} + N_{237}^{2} \times C_{59}$$
$$N_{49} = C_{60} + N_{242} \times C_{61} + N_{242} \times N_{110} \times C_{62} + N_{242}^{2} \times C_{63} + N_{110} \times C_{64} + N_{110}^{2} \times C_{65}$$
$$N_{27} = C_{66} + N_{37} \times C_{67} + N_{45} \times C_{68} + N_{45}^{2} \times C_{69}$$
$$N_{45} = C_{70} + N_{231} \times C_{71} + N_{231} \times N_{78} \times C_{72} + N_{231}^{2} \times C_{73} + N_{78} \times C_{74} + N_{78}^{2} \times C_{75}$$
$$N_{78} = C_{76} + N_{135} \times N_{157} \times C_{77} + N_{135}^{2} \times C_{78} + N_{157} \times C_{79} + N_{157}^{2} \times C_{80}$$
$$N_{135} = C_{81} + N_{178} \times C_{82} + N_{178} \times N_{200} \times C_{83} + N_{178}^{2} \times C_{84} + N_{200}^{2} \times C_{85}$$
$$N_{178} = C_{86} + N_{245} \times C_{87} + N_{245} \times N_{250} \times C_{88} + N_{245}^{2} \times C_{89} + N_{250} \times C_{90} + N_{250}^{2} \times C_{91}$$
$$N_{37} = C_{92} + N_{42} \times C_{93} + N_{126} \times C_{94}$$
$$N_{126} = C_{95} + N_{195} \times C_{96} + N_{195} \times N_{154} \times C_{97} + N_{154} \times C_{98} + N_{154}^{2} \times C_{99}$$
$$N_{154} = C_{100} + N_{183} \times C_{101} + N_{183} \times N_{244} \times C_{102} + N_{183}^{2} \times C_{103} + N_{244} \times C_{104} + N_{244}^{2} \times C_{105}$$
$$N_{42} = C_{106} + N_{110} \times C_{107} + N_{110} \times N_{231} \times C_{108} + N_{110}^{2} \times C_{109} + N_{231} \times C_{110} + N_{231}^{2} \times C_{111}$$
$$N_{110} = C_{112} + N_{200} \times C_{113} + N_{200} \times N_{208} \times C_{114} + N_{200}^{2} \times C_{115} + N_{208} \times C_{116} + N_{208}^{2} \times C_{117}$$
$$N_{108} = C_{118} + N_{192} \times C_{119} + N_{192} \times N_{145} \times C_{120} + N_{192}^{2} \times C_{121} + N_{145} \times C_{122} + N_{145}^{2} \times C_{123}$$
$$N_{145} = C_{124} + N_{208} \times C_{125} + N_{208} \times N_{244} \times C_{126} + N_{208}^{2} \times C_{127} + N_{244} \times C_{128} + N_{244}^{2} \times C_{129}$$
$$N_{192} = C_{130} + N_{246} \times C_{131} + N_{246} \times N_{262} \times C_{132} + N_{246}^{2} \times C_{133} + N_{262} \times C_{134}$$
$$N_{67} = C_{135} + N_{267} \times C_{136} + N_{267} \times N_{80} \times C_{137} + N_{80} \times C_{138} + N_{80}^{2} \times C_{139}$$
$$N_{80} = C_{140} + N_{139} \times N_{150} \times C_{141} + N_{139}^{2} \times C_{142} + N_{150} \times C_{143}$$
$$N_{150} = C_{144} + N_{261} \times C_{145} + N_{261} \times N_{185} \times C_{146} + N_{261}^{2} \times C_{147} + N_{185} \times C_{148}$$
$$N_{185} = C_{149} + N_{248} \times C_{150} + N_{248} \times N_{262} \times C_{151} + N_{248}^{2} \times C_{152} + N_{262} \times C_{153}$$
$$N_{139} = C_{154} + N_{188} \times C_{155} + N_{188} \times N_{208} \times C_{156} + N_{188}^{2} \times C_{157} + N_{208} \times C_{158} + N_{208}^{2} \times C_{159}$$
$$N_{188} = C_{160} + N_{250} \times C_{161} + N_{250} \times N_{260} \times C_{162} + N_{250}^{2} \times C_{163} + N_{260} \times C_{164} + N_{260}^{2} \times C_{165}$$
$$N_{122} = C_{166} + N_{149} \times N_{152} \times C_{167} + N_{149}^{2} \times C_{168} + N_{152} \times C_{169} + N_{152}^{2} \times C_{170}$$
$$N_{152} = C_{171} + N_{203} \times C_{172} + N_{203} \times N_{244} \times C_{173} + N_{203}^{2} \times C_{174} + N_{244} \times C_{175} + N_{244}^{2} \times C_{176}$$
$$N_{244} = C_{177} + T \times N_{262} \times C_{178} + T^{2} \times C_{179} + N_{262} \times C_{180}$$
$$N_{203} = C_{181} + N_{237} \times C_{182} + N_{237} \times N_{267} \times C_{183} + N_{237}^{2} \times C_{184} + N_{267} \times C_{185} + N_{267}^{2} \times C_{186}$$
$$N_{267} = C_{187} + N_{268} \times C_{188}$$
$$N_{149} = C_{189} + N_{181} \times C_{190} + N_{181} \times N_{208} \times C_{191} + N_{181}^{2} \times C_{192} + N_{208} \times C_{193} + N_{208}^{2} \times C_{194}$$
$$N_{181} = C_{195} + N_{246} \times C_{196} + N_{246} \times N_{250} \times C_{197} + N_{246}^{2} \times C_{198} + N_{250} \times C_{199} + N_{250}^{2} \times C_{200}$$
$$N_{246} = C_{201} + N_{259} \times C_{202} + N_{259} \times N_{268} \times C_{203} + N_{259}^{2} \times C_{204} + N_{268} \times C_{205} + N_{268}^{2} \times C_{206}$$
$$N_{58} = C_{207} + N_{72} \times C_{208} + N_{72} \times N_{99} \times C_{209} + N_{72}^{2} \times C_{210} + N_{99} \times C_{211} + N_{99}^{2} \times C_{212}$$
$$N_{99} = C_{213} + N_{265} \times C_{214} + N_{265} \times N_{134} \times C_{215} + N_{265}^{2} \times C_{216} + N_{134} \times C_{217} + N_{134}^{2} \times C_{218}$$
$$N_{134} = C_{219} + N_{186} \times C_{220} + N_{186} \times N_{200} \times C_{221} + N_{186}^{2} \times C_{222} + N_{200}^{2} \times C_{223}$$
$$N_{186} = C_{224} + N_{248} \times N_{250} \times C_{225} + N_{248}^{2} \times C_{226} + N_{250} \times C_{227} + N_{250}^{2} \times C_{228}$$
$$N_{265} = C_{229} + N_{266} \times C_{230}$$
$$N_{266} = C_{231} + d \times C_{232} + d \times N_{268} \times C_{233} + d^{2} \times C_{234} + N_{268} \times C_{235}$$
$$N_{72} = C_{236} + N_{248} \times C_{237} + N_{248} \times N_{131} \times C_{238} + N_{248}^{2} \times C_{239} + N_{131} \times C_{240} + N_{131}^{2} \times C_{241}$$
$$N_{131} = C_{242} + N_{200} \times C_{243} + N_{200} \times N_{221} \times C_{244} + N_{200}^{2} \times C_{245} + N_{221} \times C_{246} + N_{221}^{2} \times C_{247}$$
$$N_{221} = C_{248} + T \times C_{249} + T \times N_{245} \times C_{250} + N_{245} \times C_{251} + N_{245}^{2} \times C_{252}$$
$$N_{94} = C_{253} + N_{208} \times C_{254} + N_{208} \times N_{161} \times C_{255} + N_{208}^{2} \times C_{256} + N_{161} \times C_{257} + N_{161}^{2} \times C_{258}$$
$$N_{161} = C_{259} + N_{195} \times C_{260} + N_{195} \times N_{211} \times C_{261} + N_{195}^{2} \times C_{262} + N_{211} \times C_{263} + N_{211}^{2} \times C_{264}$$
$$N_{211} = C_{265} + N_{245} \times C_{266} + N_{245} \times N_{262} \times C_{267} + N_{245}^{2} \times C_{268} + N_{262} \times C_{269} + N_{262}^{2} \times C_{270}$$
$$N_{245} = C_{271} + \phi \times C_{272} + \phi \times N_{259} \times C_{273} + \phi^{2} \times C_{274} + N_{259} \times C_{275} + N_{259}^{2} \times C_{276}$$
$$N_{195} = C_{277} + N_{249} \times C_{278} + N_{249} \times N_{250} \times C_{279} + N_{249}^{2} \times C_{280} + N_{250} \times C_{281}$$
$$N_{208} = C_{282} + \phi \times C_{283} + \phi \times N_{248} \times C_{284} + N_{248} \times C_{285} + N_{248}^{2} \times C_{286}$$
$$N_{248} = C_{287} + T \times C_{288} + T \times N_{259} \times C_{289} + N_{259}^{2} \times C_{290}$$
$$N_{44} = C_{291} + N_{231} \times C_{292} + N_{231} \times N_{70} \times C_{293} + N_{70} \times C_{294} + N_{70}^{2} \times C_{295}$$
$$N_{70} = C_{296} + N_{142} \times C_{297} + N_{142} \times N_{157} \times C_{298} + N_{142}^{2} \times C_{299} + N_{157} \times C_{300}$$
$$N_{157} = C_{301} + \phi \times C_{302} + \phi \times N_{183} \times C_{303} + \phi^{2} \times C_{304} + N_{183} \times C_{305} + N_{183}^{2} \times C_{306}$$
$$N_{183} = C_{307} + T \times C_{308} + T \times N_{237} \times C_{309} + T^{2} \times C_{310} + N_{237} \times C_{311} + N_{237}^{2} \times C_{312}$$
$$N_{237} = C_{313} + N_{259} \times N_{264} \times C_{314} + N_{259}^{2} \times C_{315} + N_{264} \times C_{316} + N_{264}^{2} \times C_{317}$$
$$N_{142} = C_{318} + N_{200} \times C_{319} + N_{200} \times N_{230} \times C_{320} + N_{200}^{2} \times C_{321} + N_{230} \times C_{322} + N_{230}^{2} \times C_{323}$$
$$N_{230} = C_{324} + \phi \times C_{325} + \phi \times N_{249} \times C_{326} + N_{249} \times C_{327} + N_{249}^{2} \times C_{328}$$
$$N_{200} = C_{329} + N_{250} \times C_{330} + N_{250} \times N_{262} \times C_{331} + N_{250}^{2} \times C_{332} + N_{262} \times C_{333} + N_{262}^{2} \times C_{334}$$
$$N_{262} = C_{335} + \phi \times C_{336} + \phi \times N_{264} \times C_{337} + \phi^{2} \times C_{338} + N_{264} \times C_{339} + N_{264}^{2} \times C_{340}$$
$$N_{250} = C_{341} + T \times N_{264} \times C_{342} + T^{2} \times C_{343} + N_{264} \times C_{344} + N_{264}^{2} \times C_{345}$$
$$N_{231} = C_{345} + N_{242} \times C_{346} + N_{242}^{2} \times C_{347} + N_{256} \times C_{348} + N_{256}^{2} \times C_{349}$$
$$N_{256} = C_{350} + N_{261} \times C_{351} + N_{261} \times N_{263} \times C_{352} + N_{261}^{2} \times C_{353} + N_{263} \times C_{354} + N_{263}^{2} \times C_{355}$$
$$N_{263} = C_{356} + N_{264} \times C_{357} + N_{264}^{2} \times C_{358}$$
$$N_{261} = C_{359} + \phi \times C_{360} + \phi \times N_{268} \times C_{361} + \phi^{2} \times C_{362} + N_{268}^{2} \times C_{363}$$
$$N_{242} = C_{364} + N_{249} \times C_{365} + N_{249} \times N_{260} \times C_{366} + N_{249}^{2} \times C_{367} + N_{260} \times C_{368}$$
$$N_{260} = C_{369} + N_{264} \times C_{370} + N_{264} \times N_{268} \times C_{371} + N_{268} \times C_{372}$$
$$N_{268} = C_{373} + d \times C_{374} + d^{2} \times C_{375} + T \times C_{376} + T^{2} \times C_{377}$$
$$N_{264} = C_{378} + d \times C_{379} + d \times \phi \times C_{380} + \phi \times C_{381} + \phi^{2} \times C_{381}$$
$$N_{249} = C_{382} + d \times C_{383} + d \times N_{259} \times C_{384} + N_{259} \times C_{385} + N_{259}^{2} \times C_{386}$$
$$N_{259} = C_{387} + T \times C_{388} + T \times \phi \times C_{389} + T^{2} \times C_{390} + \phi \times C_{391} + \phi^{2} \times C_{392}$$

Coefficients of the obtained equation by GMDH method

Coefficients

\(C_{1} = 0.000101888\)

\(C_{80} = 0.32448\)

\(C_{159} = 0.923782\)

\(C_{238} = 1.68764\)

\(C_{317} = - 0.0766093\)

\(C_{2} = - 0.104363\)

\(C_{81} = - 0.0101023\)

\(C_{160} = - 0.310685\)

\(C_{239} = - 0.824382\)

\(C_{317} = 0.412828\)

\(C_{3} = 1.1043\)

\(C_{82} = 0.987692\)

\(C_{161} = 0.260203\)

\(C_{240} = 1.45509\)

\(C_{318} = - 1.21146\)

\(C_{4} = 0.00463424\)

\(C_{83} = - 1.70049\)

\(C_{162} = 0.624555\)

\(C_{241} = - 0.861041\).

\(C_{319} = 0.63831\)

\(C_{5} = 1.04623\)

\(C_{84} = 0.744123\)

\(C_{163} = - 0.0902504\)

\(C_{242} = - 0.097183\)

\(C_{320} = 0.610329\)

\(C_{6} = - 0.531208\)

\(C_{85} = 0.957725\)

\(C_{164} = 1.12765\)

\(C_{243} = 0.323261\)

\(C_{321} = 0.571365\)

\(C_{7} = 0.99823\)

\(C_{86} = - 0.0479503\)

\(C_{165} = - 0.599282\)

\(C_{244} = - 1.28326\)

\(C_{322} = - 0.0619646\)

\(C_{8} = - 0.514871\)

\(C_{87} = 0.391676\)

\(C_{166} = - 0.0103216\)

\(C_{245} = 0.688311\)

\(C_{323} = 0.11707\)

\(C_{9} = - 0.00646188\)

\(C_{88} = - 0.90133\)

\(C_{167} = - 5.54871\)

\(C_{246} = 0.717225\)

\(C_{324} = - 0.0375356\)

\(C_{10} = 0.128504\)

\(C_{89} = 0.511768\)

\(C_{168} = 2.86973\)

\(C_{247} = 0.590964\)

\(C_{325} = 0.890901\)

\(C_{11} = - 3.91669\)

\(C_{90} = 0.612542\)

\(C_{169} = 0.977683\)

\(C_{248} = 0.852946\)

\(C_{326} = 0.042659\)

\(C_{12} = 1.92619\)

\(C_{91} = 0.387747\)

\(C_{170} = 2.68169\)

\(C_{249} = - 0.0191443\)

\(C_{327} = 0.0252424\)

\(C_{13} = 0.873272\)

\(C_{92} = - 0.00106979\)

\(C_{171} = - 0.0425017\)

\(C_{250} = 0.00977775\)

\(C_{328} = 0.678075\)

\(C_{14} = 1.99033\)

\(C_{93} = 0.779169\)

\(C_{172} = 0.413557\)

\(C_{251} = 0.468342\)

\(C_{329} = - 0.4052\)

\(C_{15} = - 0.00809587\)

\(C_{94} = 0.221451\)

\(C_{173} = - 0.447145\)

\(C_{252} = 0.0315315\)

\(C_{330} = 0.235947\)

\(C_{16} = - 0.0809861\)

\(C_{95} = 0.0418163\)

\(C_{174} = 0.280708\)

\(C_{253} = - 0.0260565\)

\(C_{331} = 0.289462\)

\(C_{17} = - 2.10663\)

\(C_{96} = - 1.29629\)

\(C_{175} = 0.614762\)

\(C_{254} = 0.242299\)

\(C_{332} = 0.15575\)

\(C_{18} = 1.06011\)

\(C_{97} = 0.236447\)

\(C_{176} = 0.161212\)

\(C_{255} = - 2.78707\)

\(C_{333} = 0.0172626\)

\(C_{19} = 1.08355\)

\(C_{98} = 2.26046\)

\(C_{177} = - 0.49192\)

\(C_{256} = 1.42008\)

\(C_{334} = 0.0896242\)

\(C_{20} = 1.04624\)

\(C_{99} = - 0.232186\)

\(C_{178} = - 0.0324272\)

\(C_{257} = 0.732819\)

\(C_{335} = - 0.208469\)

\(C_{21} = 0.00216347\)

\(C_{100} = - 0.018728\)

\(C_{179} = 0.000238997\)

\(C_{258} = 1.37033\)

\(C_{336} = 0.0367259\)

\(C_{22} = - 0.143179\)

\(C_{101} = 0.533494\)

\(C_{180} = 2.24323\)

\(C_{259} = - 0.0650417\)

\(C_{337} = 0.762861\)

\(C_{23} = - 6.2984\)

\(C_{102} = - 0.626631\)

\(C_{181} = - 0.552325\)

\(C_{260} = 1.11735\)

\(C_{338} = 0.264463\)

\(C_{24} = 3.13806\)

\(C_{103} = 0.363571\)

\(C_{182} = 1.16034\)

\(C_{261} = - 1.88654\)

\(C_{339} = - 0.221862\)

\(C_{25} = 1.13621\)

\(C_{104} = 0.472318\)

\(C_{183} = - 0.152476\)

\(C_{262} = 0.78825\)

\(C_{340} = - 0.0320775\)

\(C_{26} = 3.16102\)

\(C_{105} = 0.260478\)

\(C_{184} = 0.0324099\)

\(C_{263} = - 0.101772\)

\(C_{341} = 0.000232005\)

\(C_{27} = 0.00247886\)

\(C_{106} = 0.0519918\)

\(C_{185} = 0.549564\)

\(C_{264} = 1.09707\)

\(C_{342} = 1.94197\)

\(C_{28} = - 0.0939245\)

\(C_{107} = 1.49051\)

\(C_{186} = - 0.0801751\)

\(C_{265} = - 0.0669819\)

\(C_{343} = 0.0482569\)

\(C_{29} = - 0.0377296\)

\(C_{108} = 1.55086\)

\(C_{187} = - 2.45511e - 14\)

\(C_{266} = 0.625866\)

\(C_{344} = - 0.0334375\)

\(C_{30} = 1.09146\)

\(C_{109} = - 0.824814\)

\(C_{188} = 1\)

\(C_{267} = - 0.116374\)

\(C_{345} = 0.730331\)

\(C_{31} = 0.0380288\)

\(C_{110} = - 0.513527\)

\(C_{189} = - 0.0610567\)

\(C_{268} = 0.0851122\)

\(C_{346} = 0.0120662\)

\(C_{32} = - 0.0017645\)

\(C_{111} = - 0.723331\)

\(C_{190} = 0.479185\)

\(C_{269} = 0.430256\)

\(C_{347} = 0.300318\)

\(C_{33} = - 0.30608\)

\(C_{112} = - 0.0757237\)

\(C_{191} = - 2.51891\)

\(C_{270} = 0.0168316\)

\(C_{348} = - 0.0158454\)

\(C_{34} = 0.305889\)

\(C_{113} = 0.33649\)

\(C_{192} = 1.26255\)

\(C_{271} = 0.419449\)

\(C_{349} = 0.824475\)

\(C_{35} = 1.00155\)

\(C_{114} = - 1.01818\)

\(C_{193} = 0.531526\)

\(C_{272} = 0.071373\)

\(C_{350} = - 0.566858\)

\(C_{36} = 0.00811031\)

\(C_{115} = 0.562486\)

\(C_{194} = 1.25509\)

\(C_{273} = - 0.0764732\)

\(C_{351} = - 0.909547\)

\(C_{37} = - 0.316121\)

\(C_{116} = 0.690939\)

\(C_{195} = - 0.105501\)

\(C_{274} = 0.0118725\)

\(C_{352} = 0.719353\)

\(C_{38} = 0.000890796\)

\(C_{117} = 0.453357\)

\(C_{196} = 0.198447\)

\(C_{274} = 0.381078\)

\(C_{353} = 0.487611\)

\(C_{39} = 1.30864\)

\(C_{118} = 0.0405774\)

\(C_{197} = - 1.24815\)

\(C_{275} = 0.170643\)

\(C_{354} = 0.361379\)

\(C_{40} = - 0.00516988\)

\(C_{119} = - 0.682972\)

\(C_{198} = 0.801712\)

\(C_{276} = - 0.0357515\)

\(C_{355} = 0.272552\)

\(C_{41} = 0.726952\)

\(C_{120} = - 1.62233\)

\(C_{199} = 0.88487\)

\(C_{277} = 0.0644234\)

\(C_{356} = 0.699117\)

\(C_{42} = - 0.000557343\)

\(C_{121} = 1.0593\)

\(C_{200} = 0.430317\)

\(C_{278} = - 0.282133\)

\(C_{357} = 0.0501148\)

\(C_{43} = 0.277787\)

\(C_{122} = 1.62942\)

\(C_{201} = 0.203653\)

\(C_{279} = 0.272918\)

\(C_{358} = 1.38111\)

\(C_{44} = - 0.0168319\)

\(C_{123} = 0.569825\)

\(C_{202} = 0.390366\)

\(C_{280} = 0.978144\)

\(C_{359} = - 0.808385\)

\(C_{45} = 0.589344\)

\(C_{124} = - 0.0598019\)

\(C_{203} = - 0.0620935\)

\(C_{281} = - 0.268777\)

\(C_{360} = 0.242336\)

\(C_{46} = - 0.00180901\)

\(C_{125} = 0.487272\)

\(C_{204} = 0.123453\)

\(C_{282} = 0.15697\)

\(C_{361} = 0.0762794\)

\(C_{47} = 0.42606\)

\(C_{126} = - 0.587585\)

\(C_{205} = 0.498564\)

\(C_{283} = - 0.0671583\)

\(C_{362} = - 0.056754\)

\(C_{48} = - 0.461869\)

\(C_{127} = 0.339163\)

\(C_{206} = - 0.11775\)

\(C_{284} = 1.05643\)

\(C_{363} = - 0.117619\)

\(C_{49} = 1.10123\)

\(C_{128} = 0.548575\)

\(C_{207} = - 0.0181805\)

\(C_{285} = 0.053207\)

\(C_{364} = 0.627658\)

\(C_{50} = - 0.102883\)

\(C_{129} = 0.2424\)

\(C_{208} = 0.7355\)

\(C_{286} = 1.17291\)

\(C_{365} = - 0.171821\)

\(C_{51} = 0.0212951\)

\(C_{130} = - 0.244032\)

\(C_{209} = - 3.08926\)

\(C_{287} = - 0.0122227\)

\(C_{366} = 0.14714\)

\(C_{52} = 0.437009\)

\(C_{131} = 0.67702\)

\(C_{210} = 1.5533\)

\(C_{288} = 0.00508263\)

\(C_{367} = 0.506213\)

\(C_{53} = - 0.0565768\)

\(C_{132} = - 0.153503\)

\(C_{211} = 0.270941\)

\(C_{289} = 0.131202\)

\(C_{368} = 1.32753\)

\(C_{54} = - 1.85921\)

\(C_{133} = 0.104918\)

\(C_{212} = 1.53537\)

\(C_{290} = 0.0458628\)

\(C_{369} = - 0.584228\)

\(C_{55} = 0.0123188\)

\(C_{134} = 0.57586\)

\(C_{213} = - 0.247\)

\(C_{291} = - 0.427528\)

\(C_{370} = 0.630552\)

\(C_{56} = - 0.0853752\)

\(C_{135} = - 0.177773\)

\(C_{214} = 0.278115\)

\(C_{292} = 0.121753\)

\(C_{371} = - 0.436317\)

\(C_{57} = 0.00181104\)

\(C_{136} = 0.120413\)

\(C_{215} = - 0.0257353\)

\(C_{293} = 1.38838\)

\(C_{372} = 0.665559\)

\(C_{58} = 3.40407\)

\(C_{137} = - 0.071364\)

\(C_{216} = - 0.046605\)

\(C_{294} = - 0.116904\)

\(C_{373} = 0.034239\)

\(C_{59} = 0.0106707\)

\(C_{138} = 1.09733\)

\(C_{217} = 0.994315\)

\(C_{295} = - 0.00686398\)

\(C_{374} = 0.00141164\)

\(C_{60} = 0.0504876\)

\(C_{139} = 0.0115078\)

\(C_{218} = 0.00778078\)

\(C_{296} = - 0.229736\)

\(C_{375} = 0.0299823\)

\(C_{61} = - 0.466463\)

\(C_{140} = - 0.0153086\)

\(C_{219} = - 0.0172416\)

\(C_{297} = - 0.402938\)

\(C_{376} = - 0.00100677\)

\(C_{62} = 1.59557\)

\(C_{141} = - 0.379483\)

\(C_{220} = 0.968397\)

\(C_{298} = 0.402785\)

\(C_{377} = 0.684088\)

\(C_{63} = - 0.753976\)

\(C_{142} = 0.378227\)

\(C_{221} = - 3.23657\)

\(C_{299} = 1.23205\)

\(C_{378} = 0.0156286\)

\(C_{64} = 1.45038\)

\(C_{143} = 1.01053\)

\(C_{222} = 1.51645\)

\(C_{300} = - 0.167241\)

\(C_{379} = - 0.0408816\)

\(C_{65} = - 0.840024\)

\(C_{144} = - 0.0770843\)

\(C_{223} = 1.72465\)

\(C_{301} = 0.129632\)

\(C_{380} = 0.709821\)

\(C_{66} = - 0.0027522\)

\(C_{145} = - 0.334871\)

\(C_{224} = - 0.11309\)

\(C_{302} = - 0.0204449\)

\(C_{381} = 0.106289\)

\(C_{67} = 0.645283\)

\(C_{146} = - 0.0572972\)

\(C_{225} = - 0.839589\)

\(C_{303} = - 0.00991822\)

\(C_{382} = 0.294528\)

\(C_{68} = 0.357355\)

\(C_{147} = 0.0424457\)

\(C_{226} = 0.611569\)

\(C_{304} = 1.02603\)

\(C_{383} = 0.00952678\)

\(C_{69} = - 0.000333621\)

\(C_{148} = 1.42441\)

\(C_{227} = 1.11301\)

\(C_{305} = 0.0175164\)

\(C_{384} = - 0.0136107\)

\(C_{70} = 0.0509705\)

\(C_{149} = - 0.300251\)

\(C_{228} = 0.206438\)

\(C_{306} = 0.97181\)

\(C_{385} = 0.701702\)

\(C_{71} = - 0.432526\)

\(C_{150} = 0.661217\)

\(C_{229} = 5.20337e - 14\)

\(C_{307} = - 0.0310457\)

\(C_{386} = 0.11125\)

\(C_{72} = 0.59224\)

\(C_{151} = - 0.164548\)

\(C_{230} = 1\)

\(C_{308} = 0.00691791\)

\(C_{387} = 2.0898\)

\(C_{73} = - 0.237332\)

\(C_{152} = 0.108739\)

\(C_{231} = 0.6293\)

\(C_{309} = 0.000166844\)

\(C_{388} = - 0.06113\)

\(C_{74} = 1.39527\)

\(C_{153} = 0.641363\)

\(C_{232} = - 0.00699525\)

\(C_{310} = 0.61922\)

\(C_{389} = - 0.0125589\)

\(C_{75} = - 0.350248\)

\(C_{154} = - 0.0471113\)

\(C_{233} = 0.0286574\)

\(C_{311} = 0.0230335\)

\(C_{390} = 0.000781484\)

\(C_{76} = - 0.0142586\)

\(C_{155} = 0.530502\)

\(C_{234} = - 0.000789405\)

\(C_{312} = 0.425166\)

\(C_{391} = 0.16349\)

\(C_{77} = - 0.89183\)

\(C_{156} = - 1.85411\)

\(C_{235} = 0.273677\)

\(C_{313} = - 0.229788\)

\(C_{392} = 0.0882907\)

\(C_{78} = 0.56676\)

\(C_{157} = 0.930771\)

\(C_{236} = 0.0548395\)

\(C_{314} = 0.248291\)

 

\(C_{79} = 1.00512\)

\(C_{158} = 0.468605\)

\(C_{237} = - 0.472487\)

\(C_{315} = 0.467571\)

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Ahmadi, M.H., Mohseni-Gharyehsafa, B., Ghazvini, M. et al. Comparing various machine learning approaches in modeling the dynamic viscosity of CuO/water nanofluid. J Therm Anal Calorim 139, 2585–2599 (2020). https://doi.org/10.1007/s10973-019-08762-z

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  • DOI: https://doi.org/10.1007/s10973-019-08762-z

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