Simulation and accurate prediction of unsteady nonlinear convection flow by artificial neural network using numerical data

In the present article, time-dependent Casson fluid flow over an oscillating plate under the nonlinear Oberbeck–Boussinesq approximation is considered. The present problem aligns with Stokes's second problem, which is used to describe the flow motion due to oscillatory surface. The set of the governing equations consists of fluid velocity, temperature, and mass transfer. These equations are first nondimensionalzed by using the appropriate scaling. The heat transfer process has been investigated in the presence of additional effects, such as Joule heating, viscous dissipation, and heat generation source. The well-known Buongiorno model is employed for mass transfer due to the Brownian motion and thermal migration of nanoparticles. The irreversibility in the system, due to the Joule heating, viscous dissipation, and heat generation source is also investigated for various values of parameters. The finite difference method has been used to obtain the numerical solution for the present problem. The obtained numerical solutions are subsequently integrated into an artificial neural network (ANN) model. The ANN model is trained by using the famous Levenberg–Marquardt (LM) backpropagation algorithm. The performance of the model has been assessed by using a range of statistical methods, such as mean squared error, regression analysis, curve fitting, and error histograms. The model shows high accuracy, with absolute errors ranging from 10−4 to 10−5. The impact of key parameters on fluid, velocity, heat, and mass transfer phenomena is depicted graphically and numerically. In the absence of solutal convection, i.e., when Gc=0, it is observed that thermal convection has significant impact on the fluid flow and heat transfer. However, in the case of solutal convection, the reverse effect has been observed when thermal convection is absent, i.e., Gr=0. The presence of both thermal and solutal convection (Gr=Gc=0) plays crucial in shaping the fluid thermodynamics. The fluid velocity is enhanced in this case. Other physical quantities such as skin friction coefficient as well as Nusselt and Sherwood number are investigated for different flow parameters. Skin friction coefficient decays as the thermal and solutal Grashof number values are increased. The increment in random motion of nanoparticles causes a reduction in both the Nusselt and Sherwood numbers. Augmentation in entropy profile has been observed due to enhancement in magnetic and Brinkman number. Consistency between computational and ANN results for skin friction, Nusselt number, and Sherwood number is observed, which confirms the accuracy of our model. We believe that the present results are beneficial in biomedical engineering for optimizing blood flow in oscillatory environments, in microfluidic devices for precise fluid manipulation, and in industrial cooling systems for enhancing heat transfer efficiency. Additionally, they contribute to geophysical fluid dynamics by improving the understanding of buoyancy-driven flows in natural systems.