Electromagnetohydrodynamic flow through a periodically grooved channel

This paper harnesses the spectral approach to study electromagnetohydrodynamics (EMHD) flow through an undulating 2D microchannel for a Newtonian fluid. The present study aims to investigate EMHD flow through a periodically patterned channel for large values of corrugation amplitude (surface roughness) relative to the channel height, Hartmann number and a wide range of wavelengths. A mathematical model is developed for the hydraulic permeability and the velocity field using the Fourier approach. By imposing a small pattern amplitude constraint, asymptotic analysis was employed to investigate the model presented in the literature. In the present study, hydraulic permeability is shown to strongly depend on the Hartmann number, pattern amplitude and wavelength. The spectral method predicts a monotonic decrease in hydraulic permeability irrespective of pattern amplitude at a small dimensionless wavelength (λ = 1) and Hartmann number (Ha < 1). At large wavelengths (λ > 3), the hydraulic permeability demonstrates an augmentation corresponding to the pattern amplitude. At intermediate wavelength ( 2.5 < λ < 3 ), the permeability of the channel firstly decreases and then increases with pattern amplitude. For large Hartmann numbers ( H a ≫ 1 ) , the prediction from the spectral model exhibits a similar trend as a function of wavelength. Across a range of wavelengths, the spectral model captured the permeability minima for various large Hartmann number values. The spectral model is significantly faster than the finite-element-based numerical simulation, with computational efficiency ranging from 150 to 250 times higher. The existence of a limited pattern amplitude and Hartmann number for small-large wavelength patterns, at which the permeability of the channel is minimized, is one example of a prediction from the spectral model that is beyond the resolution of currently accessible asymptotic theories.