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Determination of heat capacity of ionic liquid based nanofluids using group method of data handling technique

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Abstract

In this study a group method of data handling model has been successfully developed to predict heat capacity of ionic liquid based nanofluids by considering reduced temperature, acentric factor and molecular weight of ionic liquids, and nanoparticle concentration as input parameters. In order to accomplish modeling, 528 experimental data points extracted from the literature have been divided into training and testing subsets. The training set has been used to predict model coefficients and the testing set has been applied for model validation. The ability and accuracy of developed model, has been evaluated by comparison of model predictions with experimental values using different statistical parameters such as coefficient of determination, mean square error and mean absolute percentage error. The mean absolute percentage error of developed model for training and testing sets are 1.38% and 1.66%, respectively, which indicate excellent agreement between model predictions and experimental data. Also, the results estimated by the developed GMDH model exhibit a higher accuracy when compared to the available theoretical correlations.

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Abbreviations

ai :

unknown coefficient of polynomial

a :

vector of quadratic polynomial coefficients

A:

coefficients matrix

Cp:

heat capacity, kJ/(kg.K)

\( \widehat{f} \) :

approximated function

GMDH:

group method of data handling

M:

number of observation

MAPE:

mean absolute percentage error

MSE:

mean square error

Mw:

molecular weight, gr/grmol

NEILs:

nanoparticle enhanced ionic liquids

n:

number of experimental data points

R2 :

coefficient of determination

T:

temperature, K

Tc:

critical temperature, K

Tr:

reduced temperature \( \left({T}_r=\raisebox{1ex}{$ T$}\!\left/ \!\raisebox{-1ex}{${T}_c$}\right.\right) \)

U:

third middle layer function

W:

first middle layer function

xi :

input parameter

X:

vector of input parameters

y:

output value

\( \overset{-}{\mathrm{y}} \) :

average value of output

ŷ:

predicted output

Y:

vector of target values

Z:

second middle layer function

ρ :

density, kg/m3

φ:

nanoparticle concentration, vol%

ω :

acentric factor

cal:

model predictions

exp:

experimental value

f:

fluid

NEIL:

nanoparticle enhanced ionic liquid

nf:

nanofluid

np:

nanoparticle

IL:

ionic liquid

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Authors and Affiliations

  1. Process and Equipment Technology Development Division, Research Institute of Petroleum Industry, P.O.Box: 14665-1998, Tehran, Iran

    Maryam Sadi

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  1. Maryam Sadi
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Correspondence to Maryam Sadi.

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Sadi, M. Determination of heat capacity of ionic liquid based nanofluids using group method of data handling technique. Heat Mass Transfer 54, 49–57 (2018). https://doi.org/10.1007/s00231-017-2091-7

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  • DOI: https://doi.org/10.1007/s00231-017-2091-7

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