Exact solutions for the unsteady ow of a Burgers uid between two side walls perpendicular to the plate M. Khan 1 ;a , Rabia Malik a , Corina Fetecau b and C. Fetecau c a Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan b Department of Theoretical Mechanics, Technical University of Iasi, 700050 Iasi ; Romania c Department of Mathematics, Technical University of Iasi, 700050 Iasi ; Romania Abstract: This paper represents the exact solutions for the unsteady ow of an in- compressible Burgers uid induced by the impulsive motion of a plate between two side walls perpendicular to the plate. Employing the Fourier sine transforms, the expressions for the velocity eld, the tangential stresses and the volume ux are ob- tained. The obtained solutions satisfy all imposed initial and boundary conditions and in the absence of the side walls reduce to the solutions corresponding to the ow over an innite at plate. The e/ect of the material parameters on the velocity eld and the tangential stress at the bottom wall is spotlighted by means of the graphical illustrations. Keywords: Burgers uid; Unsteady ow; Exact solutions. 1 Introduction Over the last few decades, due to wide ranging applications, considerable research e/orts have been paid to the study of non-Newtonian uids. Non-Newtonian uids are frequently encountered in engineering and industry such as plastics and polymers are handled exten- sively by chemical industry. Non-Newtonian uid is a broad class of uids in which the relation connecting the shear stress and the shear rate is not linear and hence no single con- stitutive relation exhibits the potentiality to predict all kinds of rheological characteristics of non-Newtonian uids. Therefore, in order to meet the growing need, several constitutive models were developed and analyzed to examine the non-Newtonian rheological character- istics such as second grade, Maxwell and Oldroyd-B uids. There is a growing body of literature [1  10] concerning such uids. Note that models of rate type such as Maxwell or Oldroyd-B uids can predict stresses relaxation and are used to describe ows in polymers processing. However, they cannot capture the complex rheological characteristics of many real uids like food product such as cheese and asphalt in geomechanics etc. Another rate type model due to Burgers [11] who developed a one-dimensional model that has proved useful in predicting the response of a variety of materials such as polymeric liquids, asphalts and asphalts mixture. The Burgers model has been generalized to a frame-indi/erent three- dimensional form by Krishnan and Rajagopal [12]. To the best of knowledge, the study of this frame-indi/erent three-dimensional model has not received much attention in spite of its diverse applications. We mention here some of the studies [13  22] made by using this model. 1 Corresponding author: Electronic mail: mkhan@qau.edu.pk; mkhan_21@yahoo.com (M. Khan) 1