Numerical framework of magnetized thermal Casson nanoliquid flow with time-dependent stretching channel enclosing chemical reaction effect and variable fluid properties: A Particle Swarm Optimization with stability

Nanofluids are a relatively new class of materials that have gained attention in recent years due to their unique physical and thermal properties. They are used as contrast agents in biomedicine, including for magnetic resonance imaging (MRI) and computed tomography (CT). Keeping the above applications in mind, this theoretical study intended to explore the consequence of transient magnetized Casson nanoliquid driven by a permeable bi-direction time-dependent stretching platform positioned inclined subject to nonlinear heat source/sink. The Brownian movement, thermophoretic force, chemical reaction, and variable internal heating impacts are incorporated into the proposed flow problem. The leading constitutive PDEs are diminished into coupled nonlinear self-similar dimensionless ODEs through pertinent non-dimensional quantities. The resulting problems are addressed utilizing “Particle Swarm Optimization (PSO)” and a hybrid shooting methodology inspired by the Runge–Kutta four (RK4) method. The novelty of this work is the investigation of the numerical solution of magnetized Casson nanoliquid enclosing thermal radiation and chemical reaction via PSO along with hybrid shooting technique over time-dependent stretching sheet, which has not been elaborated on to date. The physical appearance of relevant physical factors on different flow phenomena are evaluated via graphs. For the stability purpose of the numerical method Average Square Residue Error (ASRE) and Total Average Square Residue Error (TASRE) are computed. For the validation purpose the present work is associated with the available work and great correlation is found.