Cattaneo-Christov heat flow model at mixed impulse stagnation point past a Riga plate: Levenberg-Marquardt backpropagation method

Saddiqa Hussain; Saeed Islam; Kottakkaran Sooppy Nisar; Muhammad Asif Zahoor Raja; Muhammad Shoaib; Mohamed Abbas; C Ahamed Saleel

doi:10.1016/j.heliyon.2023.e22765

Cattaneo-Christov heat flow model at mixed impulse stagnation point past a Riga plate: Levenberg-Marquardt backpropagation method

Heliyon. 2023 Nov 25;9(12):e22765. doi: 10.1016/j.heliyon.2023.e22765. eCollection 2023 Dec.

Authors

Saddiqa Hussain¹, Saeed Islam¹, Kottakkaran Sooppy Nisar^{2

3}, Muhammad Asif Zahoor Raja⁴, Muhammad Shoaib⁵, Mohamed Abbas⁶, C Ahamed Saleel⁷

Affiliations

¹ Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, College of Science and Humanities, Prince Sattam Bin Abdulaziz University, Al Kharj, Saudi Arabia.
³ School of Technology, Woxsen University, Hyderabad, 502345, Telangana State, India.
⁴ Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section .3, Douliou, Yunlin, 64002, Taiwan.
⁵ Yuan Ze University, AI Center, Taoyuan, 320, Taiwan.
⁶ Electrical Engineering Department, College of Engineering, King Khalid University, Abha, 61421, Saudi Arabia.
⁷ Department of Mechanical Engineering, College of Engineering, King Khalid University, Asir-Abha, 61421, Saudi Arabia.

Abstract

Applications of artificial intelligence (AI) via soft computing procedures have attracted the attention of researchers due to their effective modeling, simulation procedures, and detailed analysis. In this article, the designing of intelligence computing through a neural network that is backpropagated with the Levenberg-Marquardt method (NN-BLMM) to study the Cattaneo-Christov heat flow model at the mixed impulse stagnation point (CCHFM-MISP) past a Riga plate is investigated. The original model CCHFM-MISP in terms of PDEs is converted into non-linear ODEs through suitable similarity variables. A data set is generated for all scenarios of CCHFM-MISP through Lobatto IIIA numerical solver by varying Hartman number, velocity ratio parameter, inverse Darcy number, mixed impulse variable, non-dimensional constraint, Eckert number, heat generation variable, Prandtl number, thermal relaxation variable. To find the physical impacts of parameters of interest associated with the presented fluidic system CCHFM-MISP, the approximate solution of NN-BLMM is carried out by performing training (80 %), testing (10 %), and validation (10 %), and then the results are equated with the reference data to ensure the perfection of the proposed model. Through MSE, state transition, error histogram, and regression analysis, the outcomes of NN-BLMM are presented and analyzed. The graphical illustration and numerical outcomes confirm the authentication and effectiveness of the solver. Moreover, mean square errors for validation, training and testing data points along with performance measures lie around 10^-10 and the solution plots generated through deterministic (Lobatto IIIA) approach and stochastic numerical solver are matching up to 10^-6, which surely validate the solver NN-BLMM. The outcomes of $M$ and $B$ on velocity present the similar impacts. The velocity of material particles decreases under $D_{a}$ while, it increases through velocity ratio and magnetic parameters.

Keywords: Cattaneo-christov model; Heat generation; Intelligence computing; Levenberg-marquardt method; Riga plate; Stagnation point.