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.
