Unsteady Hartmann two-phase flow : semi-analytical approach

Abstract

Papers presented to the 11th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, South Africa, 20-23 July 2015.

Unsteady Hartmann two phase flows inside a parallel plate channel is considered due to sudden change in the applied pressure gradient. One of the fluids is assumed to be electrically conducting while the other fluid and the channel surfaces are assumed to be electrically non-conducting. The flow formation of conducting and non-conducting fluids is coupled by equating the velocity and shear stress at the interface. Both phases are incompressible and the flow is assumed to be fully-developed one- dimensional time dependent due to sudden change in applied pressure gradient. The relevant partial differential equations capturing the present physical situation are transformed in to ordinary differential equations using the Laplace transform technique. The ordinary differential equations are then solved exactly in the Laplace domain under relevant initial, boundary and interface conditions. The Riemann-sum approximation method is used to invert the Laplace domain into time domain. The solution obtained is validated by assenting comparisons with the closed form solutions obtained for steady states which has been derived separately and also by the implicit finite difference method. Variation of time-dependent velocity, mass flow rate and skinfriction (on channel surfaces) for various physical parameters involved in the problem are reported and discussed with the help of line graphs. There is an excellent agreement between time dependent solution and steady state solution at large value of time. Also velocity and mass flow rate decreases with increase of Hartmann number while it increases with increase in time.