Study on thermophoretic deposition of particles and ratio of effective heat capacity: A collocation approach

The flow of Boger fluid across a slow-rotating disk with thermophoretic particle deposition has significant applications in areas requiring precise particle control and uniform coating. The slow rotation facilitates the regulation of heat gradients and improves transport rates in applications that require thermal and mass control. The study of Boger fluid dynamics driven by magnetic fields and thermophoretic particle deposition is relevant to cooling systems in rotating machinery, turbines, and disk-based devices that need precise thermal management. Inspired by these applications, the current research investigates the impact of a heat source/sink and a magnetic field on the unsteady flow of a Boger fluid across a slowly rotating disk with thermophoretic particle deposition. The governing partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) using similarity variables. The reduced non-dimensional ODEs are solved by employing the Chelyshkov polynomials-based collocation method (CH-PBCM), and the values obtained with CH-PBCM are associated with Runge Kutta-Fehlberg's fourth-fifth order (RKF-45) approach. The impact of several non-dimensionless parameters on the various profiles is illustrated graphically. The major findings of the study indicate that the velocity decays as the relaxation time ratio and magnetic parameter values increase. The temperature profile improves as the heat source/sink parameter values rise. The rise in values of the thermophoresis parameter intensifies the concentration profile.