The flow field of a slightly ionized gas between parallel cold-conducting plane walls is investigated theoretically. The gas flows in the direction parallel to conducting walls and the electric current flows in the direction perpendicular to walls. The whole region. is divided into three : the linear, non-linear and sheath regions where the linear diffusion equations, the continuum equations containing inertia terms and collisionless equations are used respectively. These solutions are matched to each other.
Voltage-current characteristic curve is obtained from the sum of potential differences in the three regions. The flow of gas is to increase the electric current between conducting walls. Ions enter the sheath region at the velocity approaching the ambipolar diffusion velocity and acceleration or deceleration of electrons to anode or cathode is enhanced when the current is higher than the value of O (M_e/M_i). (M_e and M_i are the mass of electrons and positive ions). When gas speed increases, the thickness of non-linear and sheath regions decreases. When electric current increases, the non-linear region grows and the sheath decreases in the anode side, and the change of thickness of cathode non-linear and sheath regions is relatively small compared with the anode side.

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The steady convection flow around an isothermal sphere, which is placed in an infinitely vast incompressible viscous fluid otherwise at rest is numerically investigated at high Grashof numbers using the patching ADI method previously proposed by the authors. In the method, to facilitate the solution procedure the whole flow field is partitioned expediently into two sections : a boundary layer region over the sphere surface and a plume region along the upper stagnation axis. In these two regions the governing Navier-Stokes and energy equations (in the stream function, vorticity and temperature version) with false transient term are discretised by Davis' scheme and solved alternately until a solution which can be continuated smoothly across the virtual boundary is attained. The fluid flow with P_r=0.72 is calculated and the velocity and temperature distributions are determined for G_rd=8×10⁵, 8×10⁶ and 8×10⁷. Therefrom the Nusselt numbers are evaluated, and correspondingly N_ud= 14.25, 23.90 and 41.09 are found, where P_r is the Prandtl number and G_rd the Grashof number based on the diameter of sphere and the temperature difference from the ambient fluid.

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