Intelligent computing for entropy generation in Jeffrey nanofluid through radiated flow

This study explores the Entropy generation in the Flow of Jeffery Nanomaterial Model (EFJNM) past a variable thicked surface by considering joule heating effect, convectively heated surface, nonlinear radiative heat flux, and convective boundary conditions via Artificial Back Propagated Levenberg Marquardt Neural Networks (ABP-LMNNs). The ODEs system is obtained by implementing suitable transformation on PDEs for EFJNM. Applying homotopy analysis method (HAM) to create dataset for ABP-LMNNs by the variation of physical parameters of EFJNM. The reference datasets are then segmented in validation/training/testing process to scrutinize the approximated solution for EFJNM and further to compare it with standard solution. The better performance is further investigated by MSE based curves, regression fitting, absolute error, error histogram analysis. Results reveals that performance in form of MSE is in ranges of 10⁻⁹, 10⁻¹¹, 10⁻⁹, 10⁻⁹, 10⁻¹⁰, 10⁻⁹, 10⁻¹⁰, 10⁻⁹, and 10⁻¹⁰ with 494, 285, 496, 219, 71, 167, 194, 121, 179, and 738, respectively, for all scenarios. The impact of variants of EFJNM on velocity, entropy production rate, temperature, and concentration are also analyzed. As the entropy generation increase with the increment in Deborah number and Brinkman number. The velocity increases with the escalation in Deborah number and wall thickness variable whereas decreases with the increase in relaxation to retardation ratio. The absolute errors of effective parameters for velocity are 10⁻⁷-10⁻⁴, 10⁻⁷-10⁻³, 10⁻⁷-10⁻⁴, and 10⁻⁶-10⁻³, the absolute errors for temperature are 10⁻⁷-10⁻³, 10⁻⁷-10⁻³, and 10⁻⁷-10⁻⁴ whereas the absolute errors for concentration are 10⁻⁸-10⁻⁴, 10⁻⁸-10⁻³, and 10⁻⁸-10⁻⁴, which show the accuracy of proposed ABP-LMNNs. Abbreviations: ABP-LMNNs, Artificial back propagated Levenberg Marquardt Neural Networks; EFJNM, Entropy generation in the Flow of Jeffery Nanomaterial Model; HAM, Homotopy analysis method.