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Hydromagnetic Unsteady Hele-Shaw Flow of A Rivlin – Ericksen Fluid Through Porous Media

S. Sreekanth, R.Saravana, S.Venkataramana and R. Hemadri Reddy.

In this paper, we study the unsteady Hele-Shaw flow of a visco-elastic Rivlin-Ericksen conducting fluid between two parallel walls z = ±h past a fixed circular cylinder x2 + y2 = a2 , -h £ z £ h under the time dependent pressure gradient through porous medium in the presence of a uniform transverse magnetic field. We have discussed the cases when the pressure gradient is (i) proportional to eint (ii) 0 for t < 0 and equal to a constant for t ³ 0 and (iii) proportional to e- nt . The expressions for the velocity component u and v of the fluid in x and y-directions are derived by using Laplace transform technique. The effects of magnetic parameter, visco-elastic parameter, porosity parameter, time, Reynolds number and suction parameter are discussed on the velocity components in different cases.