Three-dimensional squeezing rotating channel flow of a hybrid nanofluid containing carbon nanotubes

This study examines the characteristics of the three-dimensional squeezing flow of a hybrid nanofluid in a rotating channel. The nanoparticles are considered as single-wall carbon nanotubes and multi-wall carbon nanotubes, with water as the base fluid. Using suitable similarity transformations, the governing equations are transformed into a set of ordinary differential equations. These resultant equations are solved numerically using the Haar wavelet collocation method for different values of the governing parameters. The effectiveness and convergence of the current method are evaluated by comparing the results with those obtained from the bvp4c solver. To complement these traditional numerical techniques, a physics-informed neural network (PINN) framework is employed to verify solution accuracy and enforce the underlying physical constraints across the domain. The study systematically examines the influence of key deep learning parameters, including learning rates, neuron configurations, activation functions, and the number of collocation and training data points, on the convergence behavior and accuracy of the PINN model. In addition, the evolution of the loss function and three-dimensional histograms of the residuals corresponding to the governing momentum and energy equations across the entire computational domain are analyzed to assess the model's stability and reliability. The residual-based analysis demonstrates the capability of the PINN framework to accurately approximate the governing partial differential equations while maintaining strong convergence characteristics. The influence of key governing parameters on the normal, axial, and tangential components of velocity, as well as the temperature distribution, is presented through graphs and examined in detail. Furthermore, the effects of carbon nanotube (CNT) volume fraction, suction rate, squeezing intensity, rotational speed, and nanoparticle type on skin friction profiles are presented graphically and analyzed. An increase in the CNT volume fraction enhances viscosity, leading to an increased normal velocity near the lower plate and reduced flow near the upper plate. The axial and transverse velocities exhibit opposing behavior across the channel height. Increasing values of the rotational parameter result in a decrease in both normal and axial velocities while significantly altering transverse velocities due to the Coriolis force.