1 A Mathematical Model on the Two –Phase Hepatic Blood Flow in Arterioles with Special Reference to Liver Cirrhosis Anil Kumar 1 , V. Upadhyay 2 , A. K. Agrawal 3 and P. N. Pandey4 1 Research Scholar, Dept. of Physical Sciences, M. G. C. G. Vishwavidyalay, Chitrakoot, Satna (M.P.), India 2,3 Associate Professor, Dept. of Physical Sciences, M. G. C.G. Vishwavidyalay, Chitrakoot, Satna (M.P.), India 4 Department of Mathematics, University of Allahabad. (U.P.), India I. Introduction 1.1 Structure and Function of Liver: Liver is a vital organ of human’s body. The human liver in adults weighs between 1.4-1.6 kilograms (3.1-3.6 pounds). It is a soft, pinkish- brown, triangular organ. It is both the largest internal organ and the largest gland in the human body. It is located in upper right quadrant of Abdomen. The liver can be divided into functional units called lobules. The liver has 2 main lobes: the larger right lobe and smaller left lob. Each lobe is divided into segments. The lobes are separated by a band of tissue called the falciform ligament, which help attach the liver to the diaphragm. Liver lobes are surrounded by a thick capsule, mostly overlaid with reflected periforinum [2].The liver has wide range of functions generally cite it being around 500. Liver plays an important role in human body like decomposition of red blood cells, protein production, blood clotting to cholesterol, produce bile which helps indigestion. Many bio chemical reactions occur in liver like synthesis and breakdown of small and complex molecules The liver has most complicated circulation of any organ. It receives blood from two main sources: approximately 80% is partially deoxygenated blood from the hepatic portal vein, which collects all the blood from that leaves different tissues and the remainder is fully Abstract: In this investigation, we are considering the two phase blood flow in arterioles presented here. P.N. Pandey and V. Upadhyay have considered the blood flow has two phased, one of which is that of red blood cells and other is plasma. They have also applied the non-Newtonian power law model in bio fluid mechanical set-up. We have collected a clinical data in the case of Liver Cirrhosis. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of Liver Cirrhosis infection. The graphical presentation for particular parametric value is much closer to the clinical observation. Keywords: Liver Cirrhosis, Hematocrit, Hepatic Blood Flow, non-Newtonian power law model, circulatory sub-system, Liver etc.