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Abstract
In this paper the Adaptive Neuro-Fuzzy Inference System (ANFIS) is used for the prediction of thermal efficiency and thermal resistance of a two-phase closed thermosyphon (TPCT). Aqueous suspensions of pristine multiwalled carbon nanotubes (CNTs) and functionalized CNTs with ethylene diamine were used as nanofluid in the TPCT. The experimental results regarding the TPCT performance including thermal efficiency and thermal resistance were modeled by the ANFIS technique. The ANFIS network was initiated by 70% of experimental data, and 30% of primary data were considered for testing and checking the suitability of the ANFIS model. The modeling results were compared with five arithmetical criteria. The arithmetical criteria suggested that the obtained modeling by ANFIS is valid and it could be expanded for other conditions. Also, to determine optimal ranges of experimental conditions, three-dimensional diagrams were traced by the modeling data. The proposed method of ANFIS modeling may be applied for optimization of other TPCTs with different configurations.
NOMENCLATURE
| A, B | = | nonlinear parameters in the consequent parts of the fuzzy rules |
| AARE | = | absolute average relative error |
| ANFIS | = | adaptive neuro-fuzzy inference system |
| ARE | = | average relative error |
| CNT | = | multiwalled carbon nanotube |
| Cp | = | specific heat of water, J kg−1 K−1 |
| E | = | error |
| f | = | output of the fuzzy model |
| I | = | current, A |
| = | water mass flow rate, kg s−1 | |
| MAE | = | mean absolute error |
| MSE | = | mean square error |
| M, N | = | number of points in data set |
| N | = | number of data samples |
| Oi | = | calculated output value |
| p, q, r | = | linear parameters in the consequent parts of the fuzzy rules |
| Q | = | power, W |
| R | = | resistance, °C W−1 |
| R2 | = | absolute fraction of variance |
| T | = | temperature, °C |
| = | average temperature, °C | |
| TPCT | = | two-phase closed thermosyphon |
| V | = | voltage, V |
| X | = | output data |
| x, y, c | = | inputs of the fuzzy model |
| Greek Symbols | = | |
| η | = | efficiency of TPCT |
| μAi (x) | = | membership function of corresponding linguistic label |
| μBj (x) | = | membership function of corresponding linguistic label |
| σ | = | isotropic spread of Gaussian basis function |
| wi | = | weight function of layer 4 |
| = | normalized the weight function | |
| Subscripts | = | |
| cond | = | condenser section |
| evap | = | evaporator section |
| exp | = | experimental |
| in | = | input |
| out | = | output |
| pre | = | predicted |
| th | = | thermal |
Additional information
Notes on contributors
Mehdi Shanbedi
Mehdi Shanbedi is a Ph.D. student in the School of Chemical Engineering at the Ferdowsi University of Mashhad, Iran, under the supervision of Dr. Saeed Zeinali Heris. He received his M.Sc. in chemical engineering in 2011 from Ferdowsi University of Mashhad. He is currently working on nanofluid flow and nano material synthesis. His research interests include two-phase heat transfer, heat pipes and thermosyphon, heat transfer enhancement, and boiling heat transfer.
Ahmad Amiri
Ahmad Amiri is an M.Sc. graduate in chemical engineering at the Ferdowsi University of Mashhad, Iran. He received his M.Sc. in chemical engineering in 2011 from Ferdowsi University of Mashhad. His research focused on the functionalization and purification of carbon nanostructures, heat transfer phenomenon, and synthesis of nano material and nano-composite.
Sajjad Rashidi
Sajjad Rashidi is an M.Sc. graduate at Ferdowsi University of Mashhad, Mashhad, Iran, under the supervision of Prof. Ali Ahmadpour. He is currently working on artificial neural network and fuzzy and adaptive fuzzy-neural network modeling.
Saeed Zeinali Heris
Saeed Zeinali Heris is an associate professor in the Ferdowsi University of Mashhad. He took his Ph.D. in chemical engineering from Isfahan University of Technology in 2006. He worked on heat transfer performance of nanofluids as his Ph.D. thesis. He graduated from Isfahan University of Technology with an M.S. degree in 1999. His research interests are non-Newtonian flow and heat transfer, energy system, heat transfer enhancement, thermosyphon, and nanofluid. He has published more than 80 articles in well-recognized journals and proceedings.
Majid Baniadam
Majid Baniadam is an assistant professor of chemical engineering at Ferdowsi University of Mashhad. He obtained his B.Sc. from Ferdowsi University of Mashhad in 1999 and his M.Sc. and Ph.D. degrees from Shiraz University in 2002 and 2009, respectively. Now he is working on carbon nanotubes purification and functionalization and their applications in nanofluids.