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ABSTRACT
In the present study, a feed-forward artificial neural network (ANN) was developed to estimate the Nusselt number (Nu), friction factor (f), and thermal performance (η) in a tube equipped with perforated twisted tape. The MSE and R2 values of the best network (4-10-3-3) are 0.04 and 0.9965, respectively. In addition, empirical equations were developed using the genetic algorithm. The MSE values of power-law equations for Nu, f and η are 2.7369, 4.13E-06, and 5.09E-05, respectively. Estimation of the developed ANN was found to be superior in comparison with the corresponding power-law equations.
Nomenclature
| A | = | heat transfer surface area |
| ANN | = | artificial neural network |
| BP | = | back-propagation |
| CP | = | specific heat of fluid |
| D | = | inside diameter of the test tube |
| d | = | diameter of perforated tape |
| f | = | friction factor = ΔP/((L/D)(ρU2/2)) |
| h | = | heat transfer coefficient |
| I | = | current |
| k | = | thermal conductivity of fluid |
| L | = | length of test section |
| M | = | mass flow rate |
| Nu | = | Nusselt number |
| P | = | flow pressure in stationary tube |
| ΔP | = | pressure drop |
| Pr | = | Prandtl number |
| Q | = | heat transfer rate |
| Re | = | Reynolds number = ρUD/µ |
| s | = | spaced-pitch length of perforated tape, mm |
| t | = | width of test tube |
| T | = | temperature |
| = | mean temperature | |
| U | = | mean axial flow velocity |
| V | = | voltage |
| W | = | twisted tape width, weight in ANN |
| X | = | input value of ANN |
| Y | = | output value of ANN |
| y | = | twisted tape pitch |
| ρ | = | fluid density |
| δ | = | twisted tape thickness |
| δi | = | vector of errors for each hidden layer neuron |
| δk | = | vector of errors for each output neuron |
| µ | = | fluid dynamic viscosity |
| η | = | thermal performance factor, momentum factor |
| θj | = | threshold between input and hidden layers |
| θk | = | threshold connecting hidden and output layers |
| fh() | = | logistic sigmoid activation function from input layer to hidden layer |
| fk() | = | logistic sigmoid activation function from hidden layer to output layer |
| ∝ | = | learning rate |
| Subscripts | = | |
| b | = | bulk |
| c | = | convection |
| i | = | inlet |
| o | = | outlet |
| p | = | plain |
| s | = | surface |
| t | = | twisted tape |
| w | = | Water |
Nomenclature
| A | = | heat transfer surface area |
| ANN | = | artificial neural network |
| BP | = | back-propagation |
| CP | = | specific heat of fluid |
| D | = | inside diameter of the test tube |
| d | = | diameter of perforated tape |
| f | = | friction factor = ΔP/((L/D)(ρU2/2)) |
| h | = | heat transfer coefficient |
| I | = | current |
| k | = | thermal conductivity of fluid |
| L | = | length of test section |
| M | = | mass flow rate |
| Nu | = | Nusselt number |
| P | = | flow pressure in stationary tube |
| ΔP | = | pressure drop |
| Pr | = | Prandtl number |
| Q | = | heat transfer rate |
| Re | = | Reynolds number = ρUD/µ |
| s | = | spaced-pitch length of perforated tape, mm |
| t | = | width of test tube |
| T | = | temperature |
| = | mean temperature | |
| U | = | mean axial flow velocity |
| V | = | voltage |
| W | = | twisted tape width, weight in ANN |
| X | = | input value of ANN |
| Y | = | output value of ANN |
| y | = | twisted tape pitch |
| ρ | = | fluid density |
| δ | = | twisted tape thickness |
| δi | = | vector of errors for each hidden layer neuron |
| δk | = | vector of errors for each output neuron |
| µ | = | fluid dynamic viscosity |
| η | = | thermal performance factor, momentum factor |
| θj | = | threshold between input and hidden layers |
| θk | = | threshold connecting hidden and output layers |
| fh() | = | logistic sigmoid activation function from input layer to hidden layer |
| fk() | = | logistic sigmoid activation function from hidden layer to output layer |
| ∝ | = | learning rate |
| Subscripts | = | |
| b | = | bulk |
| c | = | convection |
| i | = | inlet |
| o | = | outlet |
| p | = | plain |
| s | = | surface |
| t | = | twisted tape |
| w | = | Water |