Hartmann flow over a permeable bed

Abstract

Hartmann flow past a permeable bed is investigated in the presence of a transverse magnetic field with an interface at the surface of the permeable bed. The flow above the bed, called Zone 1, is governed by the Hartmann equation and that below the bed, called Zone 2, is governed by the modified Darcy law. Solutions for these two zones are separately obtained and are matched at the interface using suitable boundary conditions. The mass efflux, change in volume rate of flow, the induced magnetic field and current density are evaluated to determine whether a magnetic method might be potentially useful in the study of pore-size distribution. We find that, for mercury flowing over a long permeable channel of width 0.7 cm, the effect of magnetic field (of strength 0.25 Web/m², i.e. the Hartmann number M = 8.8) in the presence of a porous wall (of porosity k = 5 × 10^-6 Darcy) is to retard the mass flow and to increase the friction factor relative to the corresponding quantities for non-magnetic flow. The amount of retardation is 22 per cent more than that obtained by Wallace et al. [12] in the experiments on the flow of mercury in porous media in a transverse magnetic field. Since the magnitude of retardation is related to the pore size distribution, our model is potentially useful to study the pore size distribution than that of Wallace et al. [12]. In addition, transition to turbulence occurs at a higher Reynolds number owing to the presence of a magnetic field.