Journal of Advances in Mathematics and Computer Science

An axisymmetric initial-boundary-value model is developed for transient buoyancy-driven magnetohydrodynamic flow outside an infinitely long heated vertical cylinder in the presence of Hall current. The cylinder is impulsively set into axial motion, and an idealised, divergence-free radial magnetic field is prescribed in the exterior fluid. Cylindrical momentum balances and a generalised Ohm’s law couple the axial and azimuthal velocities. The magnetic flux density decays inversely with radius, and the local Hall parameter varies accordingly. A consistent nondimensional formulation gives a linear, coupled momentum system forced by an independently evolving radial heat-diffusion field. A fully implicit finite-difference scheme is used to calculate short-time solutions under controlled changes in magnetic intensity, wall Hall parameter, buoyancy forcing, and Prandtl number. At a dimensionless time of 0.5, doubling the magnetic parameter from 1 to 2 lowers the baseline axial velocity at a radius of 2 from 0.934 to 0.816, whereas increasing the buoyancy parameter from 10 to 20 raises it to 1.654. The azimuthal velocity depends indirectly on buoyancy through the Hall coupling. Temperature depends on Prandtl number and elapsed time but, within the stated approximation, not on the magnetic, Hall, or buoyancy parameters. Mesh refinement and exact limiting-case identities support the numerical implementation. The analysis provides a reproducible benchmark for an idealized radial-field cylindrical geometry rather than a prediction for unrestricted three-dimensional convection.