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The objective of this book is to develop a mathematical model to solve flow problems in a doubly connected region bounded by two eccentric cylinders and obtain an analytical solution with reference to catheterized artery. Among the various abnormalities that can affect the arterial system the most prevalent is atherosclerosis, arising from the focal thickening of arterial wall and resulting in the oclusion of the artery one of the clinical procedures to clear this oclusion is balloon angioplasty, in which tiny balloon is threaded through an artery and then expanded to clear the blockage. The fluid motion in an artery cannot be calculated without specification of either the pressure gradient or the rate of mass flow in the artery. When the supply of nutrients is not sufficient to meet the needs of the tissues the artery dilates and the pressure gradient increases until the rate of blood flow rises to a level which ensures an adequate supply of nutrients. The scope of this book is to develop an analytical method to solve the partial differential equations arising from modeling the above said phenomenon.