Abstract
The effect of managing input data in artificial neural network (ANN) for retrieval of parameter in third-grade fluid problem is reported. Input data for the training of ANN model consist of training, validation and testing. Proper division of the input data among these three components of ANN plays a incredibly vital role in making the ANN model robust and accurate. A third-grade fluid flowing through two parallel plates is considered for applying the ANN due to its vast application in industries. Scaled conjugate gradient algorithm is used for training the neurons in ANN. The equations governing the physics of the problem are solved by semianalytical method, least square method (LSM). The temperature profile generated by the LSM for 14 different values of third-grade fluid parameter constitutes the input data. The input data are used to train the ANN model, and then an unknown temperature profile is fed into ANN to get the third-grade fluid parameter as output. In the development of ANN model, the input data are divided among different components of ANN with different combinations. The effect of input data division among different components of ANN, in retrieval of parameter, is studied.
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Abbreviations
- A :
-
Third-grade fluid parameter
- A c :
-
Area of cross-section of channel
- A1, A2, A3, An:
-
Kinematic tensor
- a0, a2, a4, a6, a8:
-
Constants
- Br:
-
Brinkman number
- b0, b2, b4, b6, b8, b10, b12:
-
Constants
- C p :
-
Specific heat (constant pressure)
- c 1, c 2 :
-
Constants
- c i :
-
Ith constant
- D :
-
Differential operator
- D/Dt :
-
Material derivative
- f :
-
Body force per unit volume
- g :
-
Function
- h :
-
Half depth of channel
- k th :
-
Thermal conductivity of liquid
- L :
-
Length (along flow direction)
- l 1 , l 2 :
-
Constants
- N :
-
Dimensionless pressure gradient
- Nu:
-
Nusselt number
- p * :
-
Pressure (Pa)
- Q :
-
Flow rate (m3/s)
- q :
-
Heat flux ratio
- q1, q2:
-
Heat fluxes at bottom and top plates
- R :
-
Residual
- S :
-
Summation of square of residual
- \( T_{{}}^{*} \) :
-
Temperature (K)
- \( T_{\text{m}}^{*} \) :
-
Bulk mean temperature
- \( T_{{{\text{w}}_{l} }}^{*} \) :
-
Temperature of the lower wall
- u :
-
Velocity along axial direction (Nondimensional)
- u N :
-
Velocity for Newtonian fluid (Nondimensional)
- u * :
-
Velocity along axial direction (m/s)
- u 0 :
-
Average velocity (m/s)
- V * :
-
Velocity vector (m/s)
- v, \( \tilde{v} \):
-
Functions
- x, y, z:
-
Nondimensional coordinates
- x*, y*, z*:
-
Dimensional coordinates
- w i :
-
Ith weight function
- α1, α2:
-
Material constants
- β :
-
Constant
- β1, β2, β3:
-
Material constants
- ρ :
-
Density (kg/m3)
- μ :
-
Dynamic viscosity of the fluid
- ϴ:
-
Temperature (nondimensional)
- ϴN:
-
Temperature for Newtonian fluid (nondimensional)
- Φi:
-
Base function
- τ :
-
Stress
- ANN:
-
Artificial neural network
- LSM:
-
Least square method
- SCG:
-
Scaled conjugate gradient
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Mishra, V.K., Pal, C., Chaudhuri, S., Hotta, S.K. (2021). Input Data Management for Parameter Retrieval by Artificial Neural Network in Third-Grade Fluid Flow Problem. In: Kumar, N., Tibor, S., Sindhwani, R., Lee, J., Srivastava, P. (eds) Advances in Interdisciplinary Engineering. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-9956-9_78
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DOI: https://doi.org/10.1007/978-981-15-9956-9_78
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