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ABSTRACT
Adaptive Neuro-Fuzzy Inference System (ANFIS) opens a new gateway in understanding the complex behaviors and phenomena for different fields such as heat transfer in nanoparticles. The ANFIS method is a shortcut to find a nonlinear relation between input and output and results in valid outcomes, especially in engineering phenomena, which is used here for determining the convective heat transfer coefficient. Using the ANFIS, the critical parameters in heat transfer including convective heat transfer coefficient and pressure drop are determined. To realize this issue, the thermophysical properties of non-covalently and covalently functionalized multiwalled carbon nanotubes-based water nanofluid were investigated experimentally. The results of simulation and their comparison with the experimental results showed an excellent evidence on the validity of the model, which can be expanded for other conditions. The proposed method of ANFIS modeling may be applied to the optimization of carbon-based nanostructure-based water nanofluid in a circular tube with constant heat flux.
Nomenclature
| q″ | = | heat flux (W·m−2) |
| Q | = | heat transfer rate (W) |
| A | = | cross section of the tube (m2) |
| I | = | current (A) |
| V | = | voltage (V) |
| D | = | diameter (m) |
| L | = | tube length (m) |
| E | = | error |
| f | = | output of the fuzzy model |
| = | water mass flow rate (kg·s−1) | |
| Cp | = | specific heat of water (J·kg−1·K−1) |
| h | = | heat transfer coefficient (W·m−2·K−1) |
| T | = | temperature (°C) |
| U | = | velocity (m·s−1) |
| Oi | = | calculated output value |
| p, q, r | = | linear parameters in the consequent parts of the fuzzy rules |
| x, y | = | inputs of the fuzzy model |
| ΔP | = | pressure drop (Pa) |
| µ | = | viscosity (Pa.s) |
| μAi(x) | = | membership function of the corresponding linguistic label |
| μBj(x) | = | membership function of the corresponding linguistic label |
| σ | = | isotropic spread of Gaussian basis function |
| wi | = | weight function of layer 4 |
| = | normalized the weight function | |
| Subscripts | = | |
| Nf | = | nanofluid |
| B | = | bulk fluid |
| W | = | wall |
Nomenclature
| q″ | = | heat flux (W·m−2) |
| Q | = | heat transfer rate (W) |
| A | = | cross section of the tube (m2) |
| I | = | current (A) |
| V | = | voltage (V) |
| D | = | diameter (m) |
| L | = | tube length (m) |
| E | = | error |
| f | = | output of the fuzzy model |
| = | water mass flow rate (kg·s−1) | |
| Cp | = | specific heat of water (J·kg−1·K−1) |
| h | = | heat transfer coefficient (W·m−2·K−1) |
| T | = | temperature (°C) |
| U | = | velocity (m·s−1) |
| Oi | = | calculated output value |
| p, q, r | = | linear parameters in the consequent parts of the fuzzy rules |
| x, y | = | inputs of the fuzzy model |
| ΔP | = | pressure drop (Pa) |
| µ | = | viscosity (Pa.s) |
| μAi(x) | = | membership function of the corresponding linguistic label |
| μBj(x) | = | membership function of the corresponding linguistic label |
| σ | = | isotropic spread of Gaussian basis function |
| wi | = | weight function of layer 4 |
| = | normalized the weight function | |
| Subscripts | = | |
| Nf | = | nanofluid |
| B | = | bulk fluid |
| W | = | wall |