LBM-MHD Data-Driven Approach to Predict Rayleigh–Bénard Convective Heat Transfer by Levenberg–Marquardt Algorithm

This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top w...

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Bibliographic Details
Published in:Axioms 2023-02, Vol.12 (2), p.199
Main Authors: Himika, Taasnim Ahmed, Hasan, Md Farhad, Molla, Md. Mamun, Khan, Md Amirul Islam
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Approximation
Artificial intelligence
Artificial neural networks
Convection
Convective heat transfer
Data analysis
data-driven analysis
Electric currents
Fluid flow
Heat transfer
Inclination angle
lattice Boltzmann
Levenberg–Marquardt algorithm
Machine learning
Magnetic fields
Magnetohydrodynamics
Mathematical models
Neural networks
Nusselt number
Parameters
Rayleigh–Bénard convection
Segments
Simulation
Viscosity
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Summary:This study aims to consider lattice Boltzmann method (LBM)–magnetohydrodynamics (MHD) data to develop equations to predict the average rate of heat transfer quantitatively. The present approach considers a 2D rectangular cavity with adiabatic side walls, and the bottom wall is heated while the top wall is kept cold. Rayleigh–Bénard (RB) convection was considered a heat-transfer phenomenon within the cavity. The Hartmann (Ha) number, by varying the inclination angle (θ), was considered in developing the equations by considering the input parameters, namely, the Rayleigh (Ra) numbers, Darcy (Da) numbers, and porosity (ϵ) of the cavity in different segments. Each segment considers a data-driven approach to calibrate the Levenberg–Marquardt (LM) algorithm, which is highly linked with the artificial neural network (ANN) machine learning method. Separate validations have been conducted in corresponding sections to showcase the accuracy of the equations. Overall, coefficients of determination (R2) were found to be within 0.85 to 0.99. The significant findings of this study present mathematical equations to predict the average Nusselt number (Nu¯). The equations can be used to quantitatively predict the heat transfer without directly simulating LBM. In other words, the equations can be considered validations methods for any LBM-MHD model, which considers RB convection within the range of the parameters in each equation.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms12020199