We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid. 1. Introduction The inadequacy of the classical Navier-Stokes theory for describing rheological complex fluids has led to the development of several theories of non-Newtonian fluids. Non-Newtonian fluid flows play important role in several industrial manufacturing processes. Few such examples include drilling mud, polymer solutions or melts, and certain oils and greases as well as many other emulsions. Due to the prominent applications in the modern technology and industries, many researchers made attempt to study different non-Newtonian fluid flow problems. One of the popular non-Newtonian fluid models which attracted the interest of several researchers in fluid mechanics is the couple stress fluid model proposed by Stokes [1]. Couple stress fluid model is a simple generalization of the classical Newtonian fluid model that allows the sustenance of couple stresses and body couples in the fluid medium. This theory completely describes the possible effects of couple stresses assuming that the fluid has no microstructure at the kinematical level, so that the kinematics of motion is fully determined by the velocity field [2]. The concept of couple stresses arises due to the way in which the mechanical interactions in the fluid medium are modeled and the stress tensor for this fluid is not symmetric. The couple stress fluid theory has many industrial and scientific applications and can be used to model the flow of synthetic fluids, polymer thickened oils, liquid crystals, animal blood, and synovial fluid present in synovial joints [2, 3]. It has interesting applications in the theory of lubrication. Numerous researchers have studied the hydrodynamic lubrication of squeeze film flows considering the lubricant to be couple stress fluid and found that the couple stress fluid increases the load carrying capacity of the journal bearing (see Naduvinamani et al. [4], Naduvinamani et al. [5, 6], and Lin and Hung [7] and the references therein). The study of
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