Heat transfer between two porous parallel plates of steady nano fludis with Brownian and Thermophoretic effects: A new stochastic numerical approach

Abstract The design of integrated numerical computing through back-propagated neural networks with Levenberg-Marquard system (BNN-LMS) is presented to explore the fluid mechanics problems governing the system of heat transfer between two porous parallel plates of steady nanofluids (HTPSNF) under the stimulus of thermophoretic and Brownian motion. By introducing the similarity transformations, the original system model HTPSNF in terms of PDEs is converted to nonlinear ODEs. Strength of Homotopy Analysis Method (HAM) is utilized the governing equations of original model HTPSNF to obtain the data set. Reference collection for the suggest BNN-LMS scheme is originated in terms of various scenarios associated HTPSNF such as Porosity parameter, Schmidt number, Brownian parameter, viscosity parameter, Prandlt number and thermophoric parameter. To uphold the trueness of the suggest BNN-LMS, the validation, training and testing process of BNN-LMS are accomplished to govern the estimate solution of HTPSNF for various cases and evaluation with reference results. The comparative studies and performance analyses based on outcomes of MSE, error histograms, correlation and regression intimate the effectiveness and virtue of designed LMBNN technique. Mean Square Errors in the ranges of 10−07 to 10−14 confirm the perfection of the presented methodology for the closed correspondence between suggested and reference results.