Unsteady Hartmann two-phase flow: the Riemann-sum approximation approach - Jha, Basant K.; Babila, Christian T.; Isa, Sani (Zielona Góra: Uniwersytet Zielonogórski)
We consider the time dependent Hartmann flow of a conducting fluid in a channel formed by two horizontal parallel plates of infinite extent, there being a layer of a non-conducting fluid between the conducting fluid and the upper channel wall. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. The unsteady flow formation inside the channel is caused by a sudden change in the pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed into ordinary differential equations using the Laplace transform technique.
Keywords: Hartmann two-phase flow; unsteady flow; Riemann-sum approximation