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

Abstract

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.

Lattice Boltzmann simulation of natural convection of ethylene glycol-alumina nanofluid in a C-shaped enclosure with MFD viscosity through a parallel computing platform and quantitative parametric assessment

“…It is widely used to train the sample data prior to any machine learning model development. It is based on Gauss-Newton and steepest descent methods, which analyse the convergence criteria to obtain an optimal solution [19,46,47]. In short, LM algorithm takes all the input parameters into account, and develops surface responses which can be considered as a trust region.…”

“…Therefore, average Nu augmented. In order to build the correlation based on the data from table 4, LM data training algorithm was considered to interpolate the data within this range, as described by He et al [48] and Himika et al [19]. Since the range of Ra was bigger than f and average Nu, a logarithmic conversion was conducted for Ra for the ease of correlation development.…”

“…Therefore, the effect of magnetic field at different inclination angles will impact the heat transfer characteristics of nanofluid inside any enclosure. This interaction between the fluid flow and electrically conducting fluid on heat transfer application is also known as magnetohydrodynamics (MHD) [18][19][20]. In general, a strong magnetic field works against the heat transfer mechanism and therefore, the possible impact of magnetic fields inside a heat transfer system needs to be understood.…”

Exploring the Influence of Induced Magnetic Fields and Double-Diffusive Convection on Carreau Nanofluid Flow through Diverse Geometries: A Comparative Study Using Numerical and ANN Approaches

“…These models have been employed for the purpose of constructing predictive models for cardiovascular ailments, including hypertension, atherosclerosis, and aneurysms. Through the examination of extensive patient cohorts, researchers have the ability to instruct artificial neural network models to forecast the likelihood of disease development by utilizing diverse demographic, genetic, and environmental determinants [14][15][16][17][18][19][20]. Shilpa and Leela [21] explore the effects of local thermal nonequilibrium, induced magnetic field, and radiative heat on the magnetohydrodynamic mixed convective flow in the vertically circular permeable region.…”

Simulation of an Elastic Rod Whirling Instabilities by Using the Lattice Boltzmann Method Combined with an Immersed Boundary Method

“…The pressure and velocity fields can then be obtained by evaluating the hydrodynamic moments of PDF [18]. Because of its several advantages [19] compared to the conventional Navier-Stokes equations solvers, in recent decades, LBM has been widely used as an alternative CFD tool to conduct mathematical analysis on various multiphysics problems [20][21][22][23][24][25]. Research on developing a numerical technique based on coupling LBM and IBM for solving fluid-structure interaction (FSI) problems has attained considerable attention among the CFD community to utilize the features of both LBM and IBM.…”