ht. 1. Engng Sci. Vol. 24, No. 7. pp. 1183-1193. 1986 Rintcd in Gmt Britain OOZO-7225/86 S3.W + .oO pnsomon JoutnnIs Ltd UNSTEADY HYDROMAGNETIC FLOW IN A ROTATING CHANNEL IN THE PRESENCE OF INCLINED MAGNETIC FIELD G. S.SETH and S. K. GHOSH Department of Applied Sciences, Indian School of Mines, Dhanbad-826 004, India A~t~et-Unst~dy hydrom~netic flow of a viscous incompatible electrically conducting fluid in a rotating channel under the influence of a periodic pressure gradient and of uniform magnetic field, which is inchned with the axis of rotation, is investigated. Exact solution of the governing equations for the fully developed flow is obtained in closed form. The solution in dimensionless form contains three flow parameters, viz., zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF M (the Hartmann number), K2 (the rotation parameter), o (the frequency parameter) and one geometric parameter 6 (angle of inclination of the magnetic field with the positive direction of the axis of rotation). Asymptotic behaviour of the solution is analysed for large as well as small values of M2, KZ and w. For large values of&f*, K2 and w the flow is divided into two regions, viz., (i) boundary layer region and (ii)central coreregion. It is observed that there arise flow reversals in the direction of the pressure gradiem for large values of K2 and w whenw 2 2K2 and for small values of KZ and w when w < 2K2. 1. INTRODUCTION IN RECENT years the hydroma~etic flow in a rotating channel in the presence of an applied uniform magnetic field acting parallel to the axis of rotation has been considered by a number of research workers, taking into account the various aspects of the problem. Mention may be made of the works of Vidyanidhi [ 11, Nanda and Mohanty [Z], Mazumder [3], Datta and Jana [4], Seth and Jana [5], Seth and Maiti [6] and Seth et al. [7]. However, unsteady hydromagnetic flow in a rotating channel under the influence of an oscillating pressure gradient and of uniform magnetic field, which is inclined with the axis of rotation, has not received attention in literature. The importance of the study of such fluid flow problems lies in its application in various branches of geophysics, astrophysics and fluid engineering. In the present paper, we consider the unsteady flow of an electrically conducting viscous incompressible fluid within a parallel plate channel rotating with uniform angular velocity Q about an axis ~~n~c~~ to its plane under the action of a periodic pressure gradient and of a uniform magnetic field, which is inclined at an angle 8, with the positive direction of the axis of rotation. Exact solution of the governing equations for the fully developed flow is obtained in closed form. The mathematical formulation of the problem involves three flow parameters, viz. M(the Hartmann numher), K2 (the reciprocal of Ekman number), w (the frequency parameter) and one geometric parameter B (angle of inclination of the magnetic field with the positive direction of the axis of rotation). Asymptotic behaviour of the solution is analysed for large and small values of the flow parameters. It is observed that for large values of flow parameters, the flow is divided into two regions, viz. (i) boundary layer region and (ii) central core region. It is also found that for small values of M*, K2 and w, the primary flow is independent of rotation for every value of Bwhile the secondary flow is affected by the magnetic lield, rotation and oscillation of the fluid for every value of 8 except when 8 = n*. When B = nr, the secondary flow is unfits by the magnetic field. To study the ef5ect of the angle of inclination B of the magnetic field on flow field, the primary and secondary velocities are depicted graphically for various values of 6’ taking M2, K* and o fixed and w T = ?r/2 while shear stresses rX fR and r,,/R at n = 1 due to primary and secondary flows, respectively, are drawn versus fl for various values of K2 and w taking M* fixed and wT = n/2. It is interesting to note that there arise flow reversals in the direction of the pressure gradient for large values of K* and w when w 3 2K2 and for small values of K* and w when w < 2K2. It is also observed that there exists separation in the primary flow direction at the plate n = 1 when K2 = 2, zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLK w = 7 and B = 68” for w > 2K2. 1183