Journal of the Chinese Institute of Engineers, Vol. 28, No. 4, pp. 569-578 (2005) 569 UNSTEADY UNIDIRECTIONAL MHD FLOWS OF A NON-NEWTONIAN FLUID SATURATED IN A POROUS MEDIUM I-Chung Liu ABSTRACT Some exact solutions for unsteady unidirectional MHD flows of a class of non- Newtonian fluid saturated in a porous medium are obtained, including flows driven by oscillating pressure gradient, oscillating surfaces in their own planes, suddenly started surfaces, and so on. Besides, the frictional forces on the surfaces are also studied. Generally the flow is retarded by the effects of both the magnetic field and the presence of a porous medium; however, the effect of viscoelasticity of the second grade fluid on the flow behavior is rather complicated. This study is essentially an extension of work by Rajagopal (1982) and Hayat et al . (2000). Key Words: non-Newtonian fluid, unsteady unidirectional flow, MHD flow, porous medium. *I. C. Liu is with the Department of Civil Engineering, National Chi Nan University, Nantou, Taiwan 545, R.O.C. (Tel: 886-49- 2918085; Fax: 886-49-2918679; Email: icliu@ncnu.edu.tw) I. INTRODUCTION Many materials such as polymer solutions, drill- ing mud, elastomers, certain oils and greases and many other emulsions are classified as non-Newtonian fluids. There are many models describing many properties, but not all, of non-Newtonian fluids. These models or constitutive equations, however, can not describe all the behaviors of these non-Newtonian fluids, for example, normal stress differences, shear- ing thinning or shearing thickening, stress relaxation, elastic effects and memory effects, etc. Among these models, the fluid of differential type, for example, fluids of second grade and third grade, have received much attention in the past due to their elegance and simplicity (Dunn and Rajagopal, 1995). In general, the flow problems involving the sec- ond grade fluid are of the third order partial differen- tial equations rather than the second order partial dif- ferential equations for a usual viscous fluid. Hence an additional boundary condition is usually required to solve a well-posed problem (Rajagopal and Gupta, 1984; Rajagopal, 1995). However, under certain conditions, such as the present work, this is unneces- sary since the terms in the governing equations of order higher than the second disappear due to the simple geometric configuration and flow conditions. Several studies of the flows of second grade fluids can be found in Ting (1963), Markovitz and Coleman (1964), Rajagopal and Gupta (1981), Rajagopal (1982) and Chandna and Oku-Ukpong (1994). For example, Rajagopal (1982) considered the exact so- lutions to unsteady flows under a variety of flow situations. Recently Akyildiz (1998) studied the flows of a third grade fluid film driven by an upper oscillating surface while the lower surface is free. The flows driven by a plane suddenly set in motion have been studied by Erdogan (1995) for a non-Newtonian fluid. Hayat el al. (2000) and Siddiqui et al. (1999) have examined second grade fluid flows due to periodically oscillating surfaces using the Fourier transform method, and, due to os- cillating pressure gradient and suddenly-started surface, using the method of separation of variables. More recently, Hayat et al (2004) studied a variety of transient flows of second grade fluid. They used the method of separation of variables to find the large- time solutions and the method of Laplace transform to obtain the small-time solutions. Some non-Newtonian fluids might be conduc- tors of electricity, for example, nuclear slurries, mer- cury amalgams and some lubrication oils (Sarpkaya, 1961). When these electrically conducting fluids are moving in a magnetic field, there will be no doubt that the flow characteristics may be influenced by magnetic effects, different from those without a