This study presents approximate analytical solutions for the velocity and volume flow rate of an electrically 
conducting, incompressible, and viscous Jeffrey fluid flowing through an asymmetric corrugated channel between 
two slit microparallel plates under electromagnetohydrodynamic conditions. The study uses the perturbation 
method to describe the periodic sinusoidal waves with small amplitude that characterize the corrugations of the 
two walls, which can be either in phase or half-period out of phase. The study also examines how the corrugations 
affect the velocity of the EMHD flow by performing numerical computations. The results show the dependence 
of the velocity profiles and mean velocity parameter on various factors, including Reynolds number (𝑅𝑒), 
Hartmann number (𝐻𝑎), Porous Medium (𝐷𝑎) , dimensionless wave number (𝜆) of the wall perturbation, and the 
dimensionless relaxation time (𝜆1) and retardation time(𝜆2). The findings of this study have important 
implications for understanding the behavior of non-Newtonian fluids within asymmetric corrugated channels under 
electromagnetohydrodynamic conditions.