Influence of Magnetic Field on Two‐Phase Dusty Fluid Flow and Solute Dispersion in a Rectangular Channel With Rotation

Herein, we study two‐phase flow of a dusty viscous fluid in a long rectangular channel and focus on the combined effects of a vertical magnetic field and rotational motion. By coupling the governing equations for the fluid and particle phases with appropriate boundary conditions and using Laplace transforms, analytical solutions for the velocity distributions are derived. The special interest is the unsteady transport of solute particles driven both by convection and diffusion. A series solution is derived by applying the long‐time approximation approach developed by Sankarasubramanian and Gill to describe the time development of the mean solute concentration. Further, the variation of the diffusive, convective, and dispersive coefficients with time, as well as the axial concentration profile, is studied in detail. From the results, it is revealed that solute diffusion remains the dominant mode of transport and is not affected by either the magnetic field/rotational motion, whereas convection is stronger in the presence of rotation, further enhancing overall solute transport. The outcome is essential for biomedical, chemical, and aerospace engineering, where the motion of particles and the distribution of solutes must be managed.