Intricate dynamics of rotational buoyancy, magnetic field, Hall current, and infrared radiation in a Casson fluid medium

Rotational buoyancy assumes a substantial role in a multitude of natural and engineering systems, with particular emphasis on astrophysical and geophysical scenarios. The primary objective of this study is to delve into the intricate dynamics of a rotational flow subjected to forces from rotational buoyancy, magnetic field, Hall effects, and infrared radiation in a Casson fluid medium adjacent to a thermal plate. The LT technique is harnessed to yield the closed‐form solutions for the dimensionless governing flow system. Through graphical analyzes, the physical implications of key contextual parameters are elucidated. Our findings demonstrate that Hall currents and rotational buoyancy forces jointly act to restrict primary fluid motion while amplifying secondary motion. An upswing in the Casson parameter leads to a marked reduction in the magnitude of the velocity components. Furthermore, intensified infrared radiation results in a more flattened thermal distribution. The primary directional shear stress attenuates, while an inverse bias is observed for the shear stress along the secondary direction, particularly with higher values of the Hall and rotation parameters. The insights gained from this study have practical implications for the design and operation of various systems involving rotational components, such as rotary machinery, automotive systems, and industrial automation, and contribute to weather forecasting and climate modelling.