Electrical conductivity and pH modelling of magnesium oxide–ethylene glycol nanofluids

Abstract

Nanofluids as new composite fluids have found their place as one of the attractive research areas. In recent years, research has increased on using nanofluids as alternative heat transfer fluids to improve the efficiency of thermal systems without increasing their size. Therefore, the examination and approval of different novel modelling techniques on nanofluid properties have made progress in this area. Stability of the nanofluids is still an important concern. Research studies on nanofluids have indicated that electrical conductivity and pH are two important properties that have key roles in the stability of the nanofluid. In the present work, three different sizes of magnesium oxide (MgO) nanoparticles of 20, 40 and 100 nm at different volume fractions up to 3% of the base fluid of ethylene glycol (EG) were studied for pH and electrical conductivity modelling. The temperature of the nanofluids was between 20 and $70^{\circ }\hbox {C}$ for modelling. A genetic algorithm polynomial neural network hybrid system and an adaptive neuro-fuzzy inference system approach have been utilized to predict the pH and the electrical conductivity of MgO–EG nanofluids based on an experimental data set.

Appendix I

$$\begin{aligned} L_{11}= & {} a_{1,0} +a_{1,1} \cdot \phi +a_{1,2} \cdot d_{\mathrm{p}} +a_{1,3} \cdot \phi \cdot d_{\mathrm{p}} \\&+\,a_{1,4} \cdot \phi ^{2}+a_{1,5} \cdot d_{\mathrm{p}} ^{2} \\ L_{21}= & {} a_{2,0} +a_{2,1} \cdot T+a_{2,2} \cdot \phi +a_{2,3} \cdot d_{\mathrm{p}} \cdot T\\&+\,a_{2,4} \cdot T^{2}+a_{2,5} \cdot \phi ^{2} \\ L_{31}= & {} a_{3,0} +a_{3,1} \cdot T+a_{3,2} \cdot d_{\mathrm{p}} +a_{3,3} \cdot T\cdot d_{\mathrm{p}} \\&+\,a_{3,4} \cdot T^{2}+a_{3,5} \cdot d_{\mathrm{p}} ^{2} \\ L_{12}= & {} a_{4,0} +a_{4,1} \cdot T+a_{4,2} \cdot L_{11} +a_{4,3} \cdot T\cdot L_{11} \\&+\,a_{4,4} \cdot T^{2}+a_{4,5} \cdot L_{11} ^{2} \\ L_{22}= & {} a_{5,0} +a_{5,1} \cdot L_{21} +a_{5,2} \cdot L_{11} +a_{5,3} \cdot L_{21} \cdot L_{11} \\&+\,a_{5,4} \cdot L_{21} ^{2}+a_{5,5} \cdot L_{11} ^{2} \\ L_{32}= & {} a_{6,0} +a_{6,1} \cdot L_{31} +a_{6,2} \cdot L_{21} +a_{6,3} \cdot L_{31} \cdot L_{21}\\&+\,a_{6,4} \cdot L_{31} ^{2}+a_{6,5} \cdot L_{21} ^{2} \\ L_{13}= & {} a_{7,0} +a_{7,1} \cdot L_{12} +a_{7,2} \cdot L_{22} +a_{7,3} \cdot L_{12} \cdot L_{22} \\&+\,a_{7,4} \cdot L_{12} ^{2}+a_{7,5} \cdot L_{22} ^{2} \\ L_{23}= & {} a_{8,0} +a_{8,1} \cdot d_\mathrm{p} +a_{8,2} \cdot L_{32} +a_{8,3} \cdot d_\mathrm{p} \cdot L_{32}\\&+\,a_{8,4} \cdot d_\mathrm{p} ^{2}+a_{8,5} \cdot L_{32} ^{2} \\ \hbox {EC}= & {} a_{9,0} +a_{9,1} \cdot L_{13} +a_{9,2} \cdot L_{23} +a_{9,3} \cdot L_{13} \cdot L_{23}\\&+\,a_{9,4} \cdot L_{13} ^{2}+a_{9,5} \cdot L_{23} ^{2} \end{aligned}$$

$L_{ij }$ is the i-th output in the j-th layer for the GA-PNN model.

$$\begin{aligned}&\left[ {a_{i,j} } \right] \\&\quad =\begin{array}{cccccc} 0.027747876&{} 3.822604153&{} 0.462429558&{} -0.374659514&{} -0.004205517&{} 0.045114086 \\ 0.751137821&{} 0.145938521&{} 5.011703576&{} -0.000502634&{} -0.103220539&{} 0.003901322 \\ 0.015971668&{} 0.235979845&{} 0.266171545&{} -0.001501415&{} -0.002750727&{} 0.001161073 \\ -3.283067536&{} 0.095068789&{} 0.819407225&{} -0.000315974&{} -0.000331478&{} 0.003277455 \\ 1.389849061&{} 0.64959239&{} 0.116319437&{} -0.125388437&{} -0.097872314&{} 0.235336051 \\ 1.193873934&{} -0.25706559&{} 0.982727589&{} 0.012610029&{} -0.000454244&{} 0.00173388 \\ 1.105115316&{} 1.489550714&{} -0.683855075&{} -0.098269034&{} -0.027494652&{} 0.133113803 \\ 0.010619241&{} 0.176968505&{} 0.67971365&{} -0.002261029&{} -0.005051182&{} 0.008740201 \\ 0.028571409&{} 1.176834459&{} -0.191474172&{} 0.057362616&{} 0.072612493&{} -0.129341963 \\ \end{array} \end{aligned}$$

Appendix II

$$\begin{aligned} L_{11}= & {} a_{1,0} +a_{1,1} \cdot \phi +a_{1,2} \cdot d_{\mathrm{p}} +a_{1,3} \cdot \phi \cdot d_{\mathrm{p}} \\&+\,a_{1,4}\cdot \, \phi ^{2}+a_{1,5} \cdot d_{\mathrm{p}} ^{2} \\ L_{21}= & {} a_{2,0} +a_{2,1} \cdot T+a_{2,2} \cdot \phi +a_{2,3} \cdot d_{\mathrm{p}} \cdot T\\&+\,a_{2,4} \cdot T^{2}+a_{2,5} \cdot \phi ^{2} \\ L_{12}= & {} a_{3,0} +a_{3,1} \cdot T+a_{3,2} \cdot d_{\mathrm{p}} +a_{3,3} \cdot T\cdot d_{\mathrm{p}} \\&+\,a_{3,4} \cdot T^{2}+a_{3,5} \cdot d_{\mathrm{p}} ^{2} \\ L_{22}= & {} a_{4,0} +a_{4,1} \cdot T+a_{4,2} \cdot L_{11} +a_{4,3} \cdot T\cdot L_{11} \\&+\,a_{4,4} \cdot T^{2}+a_{4,5} \cdot L_{11} ^{2} \\ L_{32}= & {} a_{5,0} +a_{5,1} \cdot L_{21} +a_{5,2} \cdot L_{11} +a_{5,3} \cdot L_{21} \cdot L_{11} \\&+\,a_{5,4} \cdot L_{21} ^{2}+a_{5,5} \cdot L_{11} ^{2} \\ L_{13}= & {} a_{6,0} +a_{6,1} \cdot L_{31} +a_{6,2} \cdot L_{21} +a_{6,3} \cdot L_{31} \cdot L_{21}\\&+\,a_{6,4} \cdot L_{31} ^{2}+a_{6,5} \cdot L_{21} ^{2} \\ L_{23}= & {} a_{7,0} +a_{7,1} \cdot L_{12} +a_{7,2} \cdot L_{22} +a_{7,3} \cdot L_{12} \cdot L_{22} \\&\,+a_{7,4} \cdot L_{12} ^{2}+a_{7,5} \cdot L_{22} ^{2}\\ pH= & {} a_{8,0}+a_{8,1} \cdot d_\mathrm{p}+a_{8,2}\cdot L_{32}+a_{8,3}\cdot d_\mathrm{p}\cdot L_{32}\\&+\,a_{8,4}\cdot d^{2}_\mathrm{p}+a_{8,5}\cdot L^{2}_{32} \end{aligned}$$

$L_{ij }$is the i-th output in the j-th layer for the GA-PNN model.

$$\begin{aligned}&\left[ {a_{i,j} } \right] \\&\quad =\begin{array}{cccccc} 0.033444754&{}0.57742064&{}0.557373458&{}-0.096976696&{}-0.004692827&{}0.000620553 \\ 9.898066327&{}-0.023691553&{}1.141784359&{}0.0000969&{}-0.210843577&{}-0.005661005 \\ -44.23417905&{}0.112053455&{}10.03507958&{}0.0000876&{}-0.447629593&{}-0.01478803 \\ 134.3682947&{}11.80598176&{}-28.47847853&{}0.200363275&{}1.615464421&{}-1.281415173 \\ -42.30134392&{}12.29220823&{}-2.444815909&{}-0.732689135&{}0.070198963&{}0.200862777 \\ -1.052141722&{}2.065814262&{}-0.846199307&{}-0.042050653&{}0.055096649&{}-0.024438988 \\ -74.54960615&{}0.253862617&{}15.70866275&{}-0.000155682&{}-0.718791861&{}-0.026399959 \\ 0.404458237&{}-2.519092266&{}3.422661793&{}2.167188004&{}1.817553076&{}-3.979307098 \\ \end{array} \end{aligned}$$