Abstract— Hydromagnetic pulsatile flow of an Oldroyd fluid in a channel of porous medium is investigated. The flow in the channel is bounded by rigid plates and is driven by an unsteady pressure gradient. The lower and upper plates are maintained at uniform temperatures T 0 and T 1 (>T 0 ) respectively. A uniform magnetic field is imposed along the direction normal to the flow. The expressions for the velocity field and the temperature distribution are obtained. The rate of heat transfer at the plates has also been calculated. We find that the increase in the frequency parameter R * gives rise to decrease in the velocity of the Oldroyd fluid in the channel. It is observed that the velocity decreases with increasing H 1 (which is the square root of sum of the squares of the Hartmann number and the permeability parameter). It is also observed that the temperature increases with the increase in the Prandtl number. Keywords— Heat transfer, MHD Pulsatile flow, Oldroyd fluid, Porous medium, I. INTRODUCTION HE study of MHD pulsatile flow of an Oldroyd fluid in a channel or porous pipe has recently become the object of scientific research because of its importance in biological applications in relation to haemodynamics and in industrial applications in relation to heat exchange efficiency. Pulsatile flow is composed of a steady component and a superimposed periodical time varying component called oscillation. Oscillating flow itself is a special pulsatile flow, which is governed by an oscillation only with a zero steady flow component. Pulsatile flow is frequently encountered with captivating applications in natural systems (circulatory system, respiratory system, vascular diseases) as well as engineering systems (reciprocating pumps, IC engines, pulse combustors). Other applications of pulsatile flows arise in the uretral transport, artherosclerosis, interaction with peristaltic flows, flows in curved arteries, cerebral hydrodynamics etc. Rockwell et al. [1] presented an excellent study discussing pulsatile flow in viscoelastic blood vessels. Chaturani and Upadhya [2] used a couple stress fluid model to study the pulsatile flow in tubes. The leakage to peripheral vessels from pulsatile flow in a principal vessel was discussed by S. Sreenadh is with the Sri Venkateswara University, Tirupati-517502 INDIA (e-mail: profsreenadh@gmail.com). E. Sudhakara, is with the Sri Venkateswara University, Tirupati-517502 INDIA (e-mail: sudhakare1983@gmail.com). J. Prakash is with the Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, BOTSWANA (corresponding author’s phone:0267 355 2949; e-mail: prakashj@mopipi.ub.bw). Chadwick [3]. An excellent computational study of pulsatile flow dwelling on nonlinear flow aspects was presented by Hung [4]. Chaturani and Palanisamy [5] studied the effects of periodic body acceleration on the pulsatile flow of blood using a casson model. Pedersen et al. [6] also studied experimentally a variety of pulsatile flows. Other non- Newtonian pulsatile flow studies include those by Sadeghipour and Hajari [7]. An alternative constitutive model for blood rheology was described by Yeleswarupu [8] who generalized the Oldroyd-B flow model with experimental correlation to flow data. Recent rheological biofluid dynamics studies include the models presented by Usha and Prema [9] who employed a particle-fluid suspension model of blood to study the pulsatile flow under periodic body acceleration in a circular conduit. More recently Eldabe et al. [10] studied the pulsatile hydromagnetic flow of an Eyring-Powell fluid in a parallel- plate channel with couple stress effects. They obtained finite difference solutions for the momentum equation and showed that couple stresses decreases flow velocity. For constant time the velocity was also shown to decrease with increasing pulsation pressure gradient; magnetic parameter was also found to depress velocity for a constant Reynolds number. Vajravelu et al. [11] have analyzed the pulsatile flow between permeable beds. Their study indicated that the maximum velocity is attained between the permeable beds and gradually the velocity decreases towards the upper permeable bed. A detailed study of non-Newtonian blood flow in small diameter vessels has been presented by Scott [12]. Ogulu et al. [13] have modeled pulsatile blood flow within a homogeneous porous bed in the presence of a uniform magnetic field with time-dependent suction. Srinivas et al. [14] studied on pulsatile hydromagnetic flow of an Oldroyd fluid with heat transfer. Avinash et al. [15] have analyzed pulsatile flow of a viscous stratified fluid of variable viscosity between permeable beds. In this paper, MHD pulsatile flow of an Oldroyd fluid in a channel of porous medium is considered. The fluid is driven by an unsteady pressure gradient. A uniform magnetic field is applied perpendicular to the channel. Expressions for the velocity and temperature are obtained analytically and numerical solutions are discussed with graphical representation. MHd Pulsatile Flow of an Oldroyd Fluid in a Channel of Porous Medium S. Sreenadh, E. Sudhakara, and J. Prakash T Int'l Journal of Advances in Mechanical & Automobile Engg. (IJAMAE) Vol. 1, Issue 1(2014) ISSN 2349-1485 EISSN 2349-1493 http://dx.doi.org/10.15242/IJAMAE.E1113541 56