The mathematical model of hydrodynamic dispersion through a porous medium is developed in the presence of transversely applied magnetic fields and axial harmonic pressure gradient. The solute introduce into the flow is experienced a first-order chemical reaction with flowing liquid. The dispersion coefficient is numerically determined using Aris’s moment equation of solute concentration. The numerical technique employed here is a finite difference implicit scheme. Dispersion coefficient behavior with Darcy number, Hartmann number and bulk flow reaction parameter is investigated. This study highlighted that the dependency of Hartmann number and Darcy number on dispersion shows different natures in different ranges of these parameters. © 2020, The Korean Society of Rheology and Springer.