Fluid flow analysis in nanofluids within the absorbing pipe of a flat plate solar collector has implications in enhancing the strength of solar thermal energy systems, increasing the productivity of water and space heating units, and increasing the use of renewable energy in the industrial and condominium heating processes. The current study examines the effects of the inclination angle and porosity factor on the natural flow convection of a water–CuO nanofluid using an inclined cylindrical tube within a Flat-Plate Solar Collector (FPSC) system with measures the consequences of tilting angle and porosity of the porous medium to quantify the physical attributes of heat transfer and velocity. The Lobatto IIIA computing method is adopted to compute the dynamics of velocity and temporal distributions for the governing FPSC system by modulating parameters of interest including the Prandtl number, skin friction, Nusselt number, curvature parameter, Grashof number, and Reynolds number. A Lobatto IIIA data-driven neurostructure is designed using Deep Autoregressive Exogenous Neural Networks (DARX-NNs) trained with the Backpropagated Levenberg–Marquardt (BLM) algorithm, i.e., DARX-NNs-BLM for predictive solutions of FPSC systems. The FPSC dynamical systems restoration using the DARX-NNs-BLM technique is visually interpreted using juxtaposing time-series analysis and absolute error progression curves. The simulated results reveal mean squared errors ranging from 10–08 to 10–10 with further endorsement using heterogeneous error analysis on the histogram, and regression analytics for the numerous tendencies of the FPSC model. The DARX-NNs-BLM framework accurately replicates the temporal evolution and probabilistic features of FPSC systems, rendering a firm grounding for prospective studies into neurocomputational science pursuits.
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