Hodograph method in non-Newtonian MHD transverse fluid flows

Abstract

Equations for steady plane flows of non-Newtonian electrically conducting fluids of finite and infinite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the stream-function when the magnetic field is normal to the flow plane. Four examples are worked out to illustrate the developed theory. Solutions and geometries for these examples are determined.

Exact Solution of Second Grade Fluid in a Rotating Frame through Porous Media Using Hodograph Transformation Method

“…Introducing L(u, v) in the system (16)- (19), with j, w 1 , w 2 , given by (15), (20) respectively, it follows that (16) is identically satisfied and the system may be replaced by…”

“…In the studies of non-Newtonian fluids not only the non-linearities increase considerably, in comparison to the non-linearities occurring in the inertia part of the Navier-Stokes equations, but in certain cases the order of differential equation also increase. In case of a homogenous incompressible fluid of second grade, it is found that the governing equations are, in general, of third order, as compared to the second order Navier-Stokes equations [15] [16]. For obtaining exact solutions transformation techniques involving inverse or semi-inverse methods are used for reformulation of equations in solvable form.…”

“…Ames [18] has given an excellent survey to this method together with applications to various other fields. Hodograph transformation method is used in various fields of research such as gas dynamics [19] [20], linear viscous fluids [21], non-Newtonian fluids [22] [23] and MHD Newtonian and non-Newtonian fluid flows [15] [24]. Chandna, Barron and Smith [21] applied hodograph transformation in steady plane flow.…”

“…Chandna, Barron and Chew [26] used this method to study variably inclined incompressible MHD plane flow. Chandna and Nguyen [15] used this approach to study non-Newtonian MHD transverse fluid flows. Siddiqui, Kaloni and Chandna [22] used this method to study incompressible second grade fluid.…”

Flow of MHD micropolar fluid through porous medium: a hodograhic approach for exact solution

“…Ames [4]. In several research papers of varied area such as gas dynamics [23,19], viscous fluids [16], non-Newtonian fluids [51,44], and MHD Newtonian and non-Newtonian fluid flows [65,17] hodograph transformation method has been widely used. A large number of authors [16,14,5,15,59,61,66,2,43,42,56,36,33,53,34,54,58,69] applied this technique to study various MHD and non-MHD fluid flows.…”