Hall current, ion-slip and chemical reaction effects on unsteady MHD Casson fluid flow past an isothermal vertical plate in a rotating system with ramped mass diffusion and entropy generation analysis

Abstract

An exact analytical solution is developed for unsteady magnetohydrodynamic (MHD) flow of a Casson fluid past an impulsively started isothermal vertical plate in a rotating system, incorporating Hall current, ion-slip current, first-order chemical reaction, ramped wall concentration, and viscous dissipation. The coupled momentum, energy and species equations are reduced via a complex-velocity formulation and solved exactly by the Laplace transform; the inverse transform is evaluated numerically using the Gaver–Stehfest algorithm (degree 22), whose convergence is demonstrated to 6–7 significant figures and whose accuracy is confirmed against an independent finite-difference solution of the governing PDEs, with maximum absolute deviation of 1.7 × 10 ⁻⁶ in the primary velocity over the domain tested. A previously undocumented physical mechanism is identified: secondary (cross) flow persists even in the absence of rotation ( R  = 0) whenever Hall current is present ( m  ≠ 0), and vanishes only when both R  = 0 and m  = 0 jointly, showing that Hall current alone, not only Coriolis rotation, generates transverse flow in this configuration. The local entropy generation number Ns and Bejan number Be are derived explicitly and evaluated: near the wall, heat-transfer irreversibility dominates (Be ≈ 0.67–0.92 for Br = 0.2–1.0), while fluid-friction irreversibility takes over within one boundary-layer unit as Br increases. A quantitative Casson-versus-Newtonian comparison ( β  = 0.5 vs. β  → ∞) shows the yield-stress effect thickens the boundary layer by 58.5 % and, contrary to simple-diffusion intuition, increases the magnitude of the wall velocity gradient by 13.4 % at t  = 0.5, since buoyancy and Lorentz/Coriolis forcing prevent the thicker layer from simply flattening the near-wall slope. These results provide the first quantitatively validated entropy-generation and Bejan-number analysis for this parameter combination and clarify a Hall-current-driven transport mechanism not previously isolated in the literature.