On the Uniqueness of MHD Aligned Flows with given Streamlines

Abstract

Physical conditions and geometric implications are determined if two stationary, MHD aligned flows have the same streamline patterns. This study is carried out for incompressible and irrotational compressible plane flows; incompressible axially symmetric flow and incompressible spatial doubly laminar flow.

Hodograph transformations and solutions in variably inclined MHD plane flows

“…Taking the first approach, we eliminate functions HI and//2 from the system of equations (2), by using equations (4), and obtain the following system of six partial differential equations: …”

“…to be the Legendre transform function for the system of equations (33), (34) such that F'(q) 4: 0, F"(q) 4= 0. Using (41) in (33), we find that a* (q, 0) satisfies qF" (q) ~0 (cot a*) + F' (q) = qF" (q) and, therefore, its integration yields…”

“…These results were often achieved by employing well established fluid-dynamical techniques. For example, in the case of an inviscid incompressible fluid in steady flow, Ladikov [2] has derived two Bernoulli type equations for orthogonal flows, Kingston and Talbot [3] have classified all orthogonal flows as radial, vortex, rectilinear or as certain types of spirals, Chandna and Nath [4] have established uniqueness properties for aligned flows and Waterhouse and Kingston [5] have determined all possible flow configurations for the constantly inclined case. Chandna et al [6][7][8][9][10][11][12][13] have published a series of results for the steady viscous incompressible flow problem, obtaining various flow properties, geometries and solutions in the aligned, orthogonal and constantly inclined cases.…”

Some solutions for finitely conducting viscous MHD plane flows

“…Thus one can eliminate u and v from the system (2) by using equation (4). One then obtains a system of equations to be solved for //,, H2, h, w, j and a as functions of x, y.…”