Superposability in Hydrodynamic and MHD Flow ()

Shruti Rastogi^{}, Brijender Nath Kaul^{}, Sanjeev Rajan^{}

Department of Mathematics, Hindu College, Moradabad, India.

**DOI: **10.4236/ojfd.2015.52018
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Department of Mathematics, Hindu College, Moradabad, India.

In this paper, phenomena of superposability and self superposability in hydrodynamics and magneto hydrodynamics have been discussed. One of the most important applications of superposability in hydrodynamics is the construction of exact analytic solution of the basic equation of fluid dynamics. Kapur and Bhatia have given a simple idea that if two velocity vectors have self superposable and mutually superposable motion then sum or difference of these two is self superposable and *vice versa* and if each of the vector is superposable on the third then their sum and difference are also superposable on the third. For superposability in magneto-hydrodynamics many mathematicians like Ram Moorthy, Ram Ballabh, Mittal, Kapur & Bhatia and Gold & Krazyblocki have defined it in various ways, especially Kapur & Bhatia generalized the well-known work on superposability by Ram Ballabh to the case of viscous incompressible electrically conducting fluids in the presence of magnetic field. We found the relationship of two basic vectors for two important curvilinear coordinate systems for their use in our work. We’ve found the equations of div, *curl *and *grad* for a unit vector in parabolic cylinder coordinates and ellipsoidal coordinates for further use.

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Rastogi, S. , Kaul, B. and Rajan, S. (2015) Superposability in Hydrodynamic and MHD Flow. *Open Journal of Fluid Dynamics*, **5**, 151-170. doi: 10.4236/ojfd.2015.52018.

Conflicts of Interest

The authors declare no conflicts of interest.

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