Thermal flow of dust particulates-laden fluid in a slanted channel subject to magnetic force, radiant heat flux, and slip and periodic thermal conditions

In aerospace and automotive industries, the control of thermal flows and particulate matter is crucial for the efficient operation of engine cooling systems and optimizing the aerodynamics of vehicles. Understanding the dynamics of natural phenomena such as the movement of volcanic ash, dust storms, and other astrophysical and geophysical flows influenced by thermal and magnetic forces is essential. Within this framework, the primary objective of our study is to develop a model and simulate the heat-driven movement of a solid dust particulate-embedded fluid influenced by thermal emission and magnetic forces in a slanted channel. Our approach utilizes the Casson fluid model to represent the dusty fluid’s characteristics. The model takes into account emerging factors like buoyancy force, radiant heat flux, velocity slip condition, and periodic thermal boundary conditions. To mathematically describe the time-dependent flow, partial differential equations are employed, and compact-form solutions are derived. A series of graphs and tables are constructed to demonstrate the aftermath of various contextual parameters on flow profiles and related quantities. These visual aids effectively portray the changes in the flow dynamics under different conditions. The research reveals that in the fluid phase (FP), the velocity and thermal fields generally display higher values, whereas in the dust phase (DP), these values are lower within the channel. As particles’ concentration parameter upsurges, the thermal curve declines, irrespective of whether it is FP or DP. Additionally, the shear stresses at the channel walls intensify with increased particle relaxation time. Notably, pronounced periodic temperature fluctuations at the right wall significantly influence the heat transfer rates at both channel walls. This research can aid in designing more effective air filtration systems, refining vehicle design for improved aerodynamics, and managing particulate pollutants in industrial settings.