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Exact solutions to an incompressible second-grade fluid flow equations

Naeem R. K., Zia S. S.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 1

71-85

Employing complex variables and complex functions the exact solutions to equations governing the motion of an incompressible second-grade fluid are determined.

A class of exact solutions to equations governing the steady plane flows of an incompressible fluid of variable viscosity via von Mises variables

Naeem R. K., Ali S. A.

International Journal of Applied Mechanics and Engineering

2001

Vol. 6, no 2

395-436

A class to exact solutions of equations governing the steady plane flows of an incompressible fluid of variable viscosity are determined using von ? Mises variables. Applications of some of the solutions to the boundary value problems are also indicated.

On the plane steady flows of a viscous incompressible fluid of finite electrical conductivity in the presence of a magnetic field

Naeem R. K., Shad Ahsan S. M.

Applied Mechanics and Engineering

2000

Vol. 5, no 4

897-911

Basic equations describing the motion of a viscous incompressible fluid of finite electrical conductivity in the presence of a magnetic field (1) for constant vorticity flows are recast in a new form. It is indicated that the other flow variables can be expressed either in terms of the magnetic flux function 'fi' or the stream function 'psi' where these functions satisfy a partial differential equation whose every solution, including Naeem (1996), is a solution to the basic flow equations and (2) for variable vorticity flows an unknown function f(r) is introduced in the basic flow equations. The solutions are determined and one solution admits, as a particular case, Naeem's solution by appropriately choosing the arbitrary constants therein. Some applications of the solutions to physically possible situations are also presented.