Exploration of exergoeconomic evaluation through solar collector in magnetohydrodynamic Williamson hybrid nanofluid flow based on machine learning technique

Efficient heat management is essential for improving the performance of renewable energy systems, particularly in solar-based thermal technologies. To address this challenge, the present study investigates the exergoeconomic performance and thermophysical behavior of a magnetohydrodynamic Williamson hybrid nanofluid (WHNF) flowing over a continuously moving thin needle under the influence of a magnetic field, porosity, and non-uniform heat flux. The hybrid nanofluid, composed of AA7075–AA7072 nanoparticles dispersed in methanol, is analyzed to enhance heat transfer and energy conversion efficiency. The governing partial differential equations are transformed into ordinary differential equations using similarity variables and solved parametrically to examine variations in velocity, temperature, and entropy generation profiles. A machine learning framework based on Artificial Neural Networks (ANNs) is integrated to predict and optimize the thermophysical properties and exergy efficiency of the WHNF system. The graphical results are obtained by varying number of parameters like; $M$, $W_e$, $C$, $\mathrm{Pr}$, and $B$, for discussions of numerical results on $f^{\prime }\left(\eta \right)$ and $\theta \left(\eta \right)$ profile. A total of 76 datasets were generated, with 54 used for training, 11 for testing, and 11 for validation. The ANN results show strong predictive accuracy, with mean square error (MSE) values and absolute error (AE) within acceptable limits. The analysis reveals that increasing the magnetic parameter and porosity tends to reduce velocity while enhancing temperature gradients and entropy generation. Moreover, The $f^{\prime }\left(\eta \right)$ profile declines with growing differences of $M$ and $W_e$ while $f^{\prime }\left(\eta \right)$ increases growing differences of $C$. $\theta \left(\eta \right)$ profile declines with raising values of $Pr$ and AE noted between $-2to3\times {10}^{-4}$. Moreover, $\theta \left(\eta \right)$ profile increases due to increment in $B$ and $C$. The MSE penalties (testing, training, validation) WHNFs flow on thin moving needle lies between ${10}^{-10}to{10}^{00}.$ The gradients values lie around ${10}^{-8}$ for WHNFs on thin needle. EHA of WHNFs flow on thin moving needle recorded around ${10}^{-07}to{10}^{-06}$. The AE WHNFs flow on thin moving needle by using LMBNNs is noted between $-6\times {10}^{0}to8\times {10}^{-05}$ for all six scenarios. This study thus bridges computational fluid dynamics, nanofluid science, and artificial intelligence for advancing energy-efficient and sustainable heat transfer technologies.