Neural network architecture for magnetized hybrid nanofluids with heat generation, absorption, and velocity slip

When compared to regular nanofluids (NFs), fluids such as hybrid NFs (HNFs) show remarkable potential due to their excellent thermal behavior and thermophysical features. A base fluid is mixed with two distinct nanoparticles to create HNFs. According to numerous academics, traditional coolants, particularly those that function at high temperatures, could take the place of HNFs. These NFs are therefore less harmful to the environment and also result in energy savings. The primary goal of HNFs is to improve heat transfer efficiency, and their benefits have raised relatively optimistic expectations for their use. This study uses neural networks to assess a 2D magnetic HNF while taking into account the impacts of slip velocity, convection, heat production, and absorption $${\mathrm{(2D - MHNF - HPA)}}$$. The work especially studies a composite NF consisting of $${\mathrm{A}}{{\mathrm{l}}_2}{{\mathrm{O}}_3} - {\mathrm{Cu}}/{{\mathrm{H}}_2}{\mathrm{O}}$$, where water acts as the base fluid, while copper and alumina function as solid nanoparticles. The ability of current composite NFs to improve heat transfer efficiency is recognized. The study employs the Levenberg–Marquardt (LM) scheme within artificial neural networks (ANNs) $${\mathrm{(LMS - ANNs)}}$$ to assess the impact of multiple factors on velocity and temperature distributions, such as the solid copper volume fraction, heat generation/absorption, magnetohydrodynamics $${\mathrm{(MHDs)}}$$, mixed convection, and velocity slip. Using similarity variables makes it easier to convert non-linear partial differential equations (PDEs) into non-linear ordinary differential equations (ODEs). By adjusting various parameters, a three-step procedure that uses the Lobatto IIIA technique, which produces a variety of datasets for the $${\mathrm{(LMS - ANNs)}}$$. Through a multi-stage method, the proposed $${\mathrm{LMS - ANNs}}$$ model is thoroughly tested, validated, and trained. To confirm its dependability, performance comparisons are done against recognized benchmarks. The efficacy of the proposed $${\mathrm{LMS - ANNs}}$$ model is further validated by regression analysis, mean squared error $${\mathrm{(MSE)}}$$ assessment, and histogram analyses, which demonstrate an exceptional accuracy between $${10^{ - 8}}$$ and $${10^{ - 10}}$$. When compared to other approaches and reference models, this performance sets it apart.