Perturbation Analysis of Two‐Region Fluid Flow Under Magnetic Field and Chemical Reaction Effects

ABSTRACT This study investigates the behavior of Casson fluid flow subjected to a magnetic field and influenced by a first‐order chemical reaction within a two‐region channel. One region contains Casson fluid, while the other is occupied by a viscoelastic fluid. Both fluids are considered incompressible and electrically conducting, with constant transport properties. The system of governing equations, which is nonlinear and strongly coupled, is addressed analytically using a regular perturbation method, suitable for cases with a small Brinkman number. The analytical results demonstrate that increasing the Hartmann number from M = 4 to M = 8 reduces the peak dimensionless velocity by approximately 20%–30%, owing to the retarding Lorentz force. Conversely, increasing the width ratio and thermal conductivity ratio enhances the velocity and temperature distributions by approximately 15%–25% within the investigated parameter ranges. The first‐order chemical reaction parameter significantly suppresses both the concentration and flow fields, with concentration decreasing by approximately 20% as the reaction parameter increases from α = 0.1 to α = 2. These findings provide useful guidelines for the design of MHD heat transfer systems and chemically reacting transport processes.