Levenberg–Marquardt neural network and statistical study of Jeffrey fluid flow with electromagnetic, thermal, and homogeneous–heterogeneous reactions across a cylinder

The movement of non-Newtonian Jeffrey fluid on an extending cylindrical surface under the influence of a combination of the magnetic field, internal heat generation, and homogeneous-heterogeneous reaction. To evaluating the impact of various slip conditions, electromagnetic forces, reaction rate on momentum, energy and concentration by adopting a hybrid ANN numerical method. The implications are extended to the advanced thermal operations, polymer processing, chemical reactor and coating systems in which exact prediction of heat and mass transfer is required. The Levenberg-Marquardt neural network is trained on the associated high-fidelity dataset; it consists of a single layer of neurons (a hidden layer) with 10 neurons. The stable behavior of learning at 635 epochs of λ 1 , 355 epochs of Q , 594 epochs of S r and 287 epochs of L s is observed under all conditions. This work is novel, as the flow variables, Nusselt number, skin friction, and Sherwood number are analyzed simultaneously in a mixed numerical-ANN model, over a broad parameter space. The model has a very high verification with the maximum deviation of 0.1126%. The error in prediction of the ANN of the Nusselt number is quite insignificant and the absolute error and the percentage error are smaller than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>.</mml:mo> <mml:mn>32</mml:mn> <mml:mo>*</mml:mo> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and 0.001% respectively. The significant physical observations that relate to the velocity include; velocity is slowed down by up to 18%–22% due to increased magnetic field due to Lorentz resistance, and 10%–14% due to increased Jeffrey parameter. The magnetic effects raise the temperature by 12%–17% as a result of Joule heating and decrease by 8%–10% as a result of positive heat generation. The curvature increases the concentration by 9%–13% and decreases with an increase in Schmidt numbers by 15%–20%. Increases in the skin friction and Nusselt number by up to 5%–9%; and molecular diffusivity by up to 7%–12%, increase Sherwood number. All of these findings combine to indicate that the hybrid numerical-ANN model is a strong instrument in the capability to reproduce multidimensional flows at the boundary-layer and anticipate engineering parameters with an exceptionally high-quality accuracy.