Stochastic numerical computing for entropy optimized of Darcy-Forchheimer nanofluid flow: Levenberg Marquardt Algorithm

Abstract

The work in hand examines the entropy generation of magnetohydrodynamic Darcy-Forchheimer nanofluid flow model (MHD-DFNM) over a stretched surface via Artificial back propagated neural networks with Levenberg Marquardt Algorithm (ABNN-LMA). Two types of nanoparticles i.e Silicon dioxide (SiO2) and Molybdenum disulfide (MoS2) and continuous phase liquid i.e propylene glycol is considered. The PDEs of MHD-DFNM are transformed into coupled ODEs via appropriate (similarity) transformations. The reference dataset is obtained by the variation of 1st and 2nd order slip parameters (γ1 and γ2), porosity parameter (β), viscosity parameter (λ), radiation parameter(R), volume friction coefficient(ϕ), heat generation/absorption parameter(Q), Biot number (B1) and Eckert number (Ec) from Homotopy Analysis Method (HAM). The reference data is executed in training/testing/validation sets to find and analyze the approximated solution of designed ABNN-LMA as well as it’s comparison with reference data solution. The better performance is consistently certified with Mean Squared Error (MSE) curves, regression index and error histogram study. Results reveal that, increase in values of porosity parameter declines the velocity profile for both SiO2 and MoS2 nanoparticles suspended in propylene glycol nanofluids. The thermal profile improves for both SiO2 − propylene glycol and MoS2 − propylene glycol nanofluids when heat generation parameter increases.