PREDICTION OF STABILITY AND THERMAL CONDUCTIVITY OF SnO<sub>2</sub>NANOFLUID VIA STATISTICAL METHOD AND AN ARTIFICIAL NEURAL NETWORK

Kazemi-Beydokhti, A.; Azizi Namaghi, H.; Haj Asgarkhani, M. A.; Zeinali Heris, S.

doi:10.1590/0104-6632.20150324s00003518

Acessibilidade / Reportar erro

Brasil

Brazilian Journal of Chemical Engineering

Español English

Brasil

Español English

sumário « anterior atual seguinte »

Sumário

Process Systems Enginnering • Braz. J. Chem. Eng. 32 (4) • Oct-Dec 2015 • https://doi.org/10.1590/0104-6632.20150324s00003518 copy

PREDICTION OF STABILITY AND THERMAL CONDUCTIVITY OF SnO₂NANOFLUID VIA STATISTICAL METHOD AND AN ARTIFICIAL NEURAL NETWORK

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

Central composite rotatable design (CCRD) and artificial neural networks (ANN) have been applied to optimize the performance of nanofluid systems. In this regard, the performance was evaluated by measuring the stability and thermal conductivity ratio based on the critical independent variables such as temperature, particle volume fraction and the pH of the solution. A total of 20 experiments were accomplished for the construction of second-order polynomial equations for both target outputs. All the influential factors, their mutual effects and their quadratic terms were statistically validated by analysis of variance (ANOVA). According to the results, the predicted values were in reasonable agreement with the experimental data as more than 96% and 95% of the variation could be predicted by the respective models for zeta potential and thermal conductivity ratio. Also, ANN proved to be a very promising method in comparison with CCD for the purpose of process simulation due to the complexity involved in generalization of the nanofluid system.

Keywords
Nanofluid; Central composite design; Artificial neural network; Statistical; Stability; Thermal conductivity

Independent variables	Symbol	Coded and actual variable level
Independent variables	Symbol	Star-low	Low	Center	High	Star-high
		-1.68	-1	0	1	1.68
Temperature (°C)	X₁	28	35	45	55	62
Particle volume fraction (%vol)	X₂	1.3	2	3	4	4.7
Solution pH	X₃	4.6	6	8	10	11.4

		Coded input variable				Response variable
Std.	Run	A	B	C		Zeta potential (mV)		Thermal conductivity ratio
Std.	Run	A	B	C		Experimental	Predicted	Experimental	Predicted
1	3	-1	-1	-1	Factorial design	-19	-21.27	1.07	1.070
2	7	1	-1	-1		-27	-29.15	1.15	1.150
3	16	-1	1	-1		-25	-24.65	1.11	1.110
4	18	1	1	-1		-31	-32.53	1.19	1.190
5	9	-1	-1	1		-23	-25.43	1.09	1.094
6	14	1	-1	1		-34	-33.31	1.16	1.174
7	5	-1	1	1		-29	-28.81	1.13	1.134
8	15	1	1	1		-36	-36.69	1.23	1.214
9	11	-1.68	0	0	Axial points	-27	-27.59	1.08	1.070
10	19	1.68	0	0		-40	-40.83	1.21	1.205
11	20	0	-1.68	0		-30	-27.98	1.17	1.146
12	10	0	1.68	0		-33	-33.66	1.22	1.214
13	17	0	0	-1.68		-21	-19.34	1.10	1.095
14	12	0	0	1.68		-26	-26.33	1.14	1.135
15	6	0	0	0	Center points	-35	-34.21	1.18	1.180
16	8	0	0	0		-34	-34.21	1.16	1.180
17	2	0	0	0		-35	-34.21	1.20	1.180
18	1	0	0	0		-32	-34.21	1.17	1.180
19	4	0	0	0		-35	-34.21	1.19	1.180
20	13	0	0	0		-34	-34.21	1.18	1.180

Source of variation		Sum of square	df	Mean square	F value	P-value
Model		560.56	9	62.28	28.78	<0.0001	Significant
	X₁	212.44	1	212.44	98.17	<0.0001
	X₂	38.89	1	38.89	17.97	0.0017
	X₃	59.10	1	59.10	27.31	0.0004
	X₁X₂	4.50	1	4.50	2.08	0.1799
	X₁X₃	2.00	1	2.00	0.92	0.3590
	X₂X₃	0.50	1	0.50	0.23	0.6411
	X₁²	3.50	1	3.50	1.62	0.2325
	X₂²	20.74	1	20.74	9.58	0.0113
	X₃²	233.82	1	233.82	108.06	<0.0001
Residual		21.64	10	2.16
	Lack of fit	14.81	5	2.96	2.17	0.2081	Not significant
	Pure error	6.83	5	1.37
Total		582.20	19
	Std. Dev.	1.47		R ²		0.9628
	Mean	-30.30		Adjusted R²		0.9294
	C.V.%	4.85		Predicted R²		0.7890
	PRESS	122.86		Adequate precision		19.354

Source of variation		Sum of square	df	Mean square	F value	P-value
Model		0.040	9	4.479E-003	25.63	<0.0001	Significant
	X₁	0.022	1	0.022	126.11	<0.0001
	X₂	5.501E-003	1	5.501E-003	31.48	0.0002
	X₃	1.811E-003	1	1.811E-003	10.36	0.0092
	X₁X₂	1.125E-004	1	1.125E-004	0.64	0.4410
	X₁X₃	1.250E-005	1	1.250E-005	0.072	0.7946
	X₂X₃	1.125E-004	1	1.125E-004	0.64	0.4410
	X₁²	3.065E-003	1	3.065E-003	17.54	0.0019
	X₂²	1.380E-004	1	1.380E-004	0.79	0.3950
	X₃²	7.906E-003	1	7.906E-003	45.24	<0.0001
Residual		1.748E-003	10	1.748E-004
	Lack of fit	7.477E-004	5	1.495E-004	0.75	0.6213	Not significant
	Pure error	1.000E-003	5	2.000E-004
Total		0.042	19
	Std. Dev.	0.013	R ²	0.9584
	Mean	1.16	Adjusted R²	0.9210
	C.V.%	1.14	Predicted R²	0.8269
	PRESS	7.278E-003	Adequate precision	16.518

Optimum result	Coded factors			Zeta potential (mV)	Thermal conductivity ratio	Desirability
Optimum result	x₁	x₂	x₃	Zeta potential (mV)	Thermal conductivity ratio	Desirability
1	1	0.36	0.31	-38.22	----	0.915
2	0.94	0.98	0.42	----	1.23	1
3	1	0.81	0.3	-37.98	1.23	0.951

Parameter	Method	%AARE	%Std. Dev.
Zeta potential	ANN	0.872	1.121
Thermal conductivity ratio	ANN	0.376	0.268

Brazilian Society of Chemical Engineering Rua Líbero Badaró, 152 , 11. and., 01008-903 São Paulo SP Brazil, Tel.: +55 11 3107-8747, Fax.: +55 11 3104-4649, Fax: +55 11 3104-4649 - São Paulo - SP - Brazil
E-mail: rgiudici@usp.br

Acompanhe os números deste periódico no seu leitor de RSS

[1] *To whom correspondence should be addressed

Brasil

Brasil

PREDICTION OF STABILITY AND THERMAL CONDUCTIVITY OF SnO2NANOFLUID VIA STATISTICAL METHOD AND AN ARTIFICIAL NEURAL NETWORK

Abstract

PREDICTION OF STABILITY AND THERMAL CONDUCTIVITY OF SnO₂NANOFLUID VIA STATISTICAL METHOD AND AN ARTIFICIAL NEURAL NETWORK