Abstract
The dynamic viscosity of MWCNT−Al2O3 (40:60)/SAE50 nanofluid (NF) is investigated. NF viscosity modeling is also performed using the response surface methodology (RSM). Several different models are proposed, including modified and unmodified cubic, quartic and fifth models, and the best modeling is selected using the parameters R2, Adjusted R2, Predicted R2 and Square root of the residual mean square (Std. Dev.). The results show that the fifth-order model has values of 0.9997, 0.9997, 0.9996 and 2.39 for R2, Adjusted R2, Predicted R2 and Std. Dev. parameters, respectively, which indicates high accuracy of modeling. Using the perturbation diagram, it was found that among the parameters of temperature, solid volume fraction (φ) and shear rate (γ), the temperature parameter has the greatest effect on the dynamic viscosity of NF. The trend of changes in viscosity also shows that φ and γ have little effect on viscosity. Due to the importance of low viscosity in fluid flow and pumping, the optimal values of NF viscosity are presented, including dynamic viscosity equal to 108.092 cP in φ=0.063 and T=49.998 °C and γ=7,866.7786 s−1.
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Abbreviations
- MSs:
-
mean squares
- R2 :
-
regression coefficient
- R 2 adj :
-
adjusted regression coefficient
- R 2pre :
-
predicted regression coefficient
- SSmod :
-
sum of the squares of the model
- SStot :
-
sum of squares
- SSres :
-
the total squares of the remaining model
- T:
-
temperature
- X:
-
independent parameter
- w:
-
weight coefficient
- Y:
-
response
- yi :
-
acctual value
- ŷi :
-
predicted value
- ANN:
-
artificial neural network
- ANOVA:
-
analysis of variance
- DOE:
-
design of experiment
- EG:
-
ethylene glycol
- MWCNT:
-
multi walled carbon nanotube
- NF:
-
nanofluid
- RSM:
-
response surface methodology
- Std. Dev.:
-
square root of the residual mean square
- ε :
-
experimental error
- ξ :
-
controllable input variable
- γ :
-
shear rate
- φ :
-
solid volume fraction
- μ :
-
viscosity
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Esfe, M.H., Motallebi, S.M. & Toghraie, D. Modeling and optimization of dynamic viscosity of oil-based nanofluids containing alumina particles and carbon nanotubes by response surface methodology (RSM). Korean J. Chem. Eng. 39, 2800–2809 (2022). https://doi.org/10.1007/s11814-022-1156-6
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DOI: https://doi.org/10.1007/s11814-022-1156-6