International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-9 Issue-1S5, December, 2019 185 Retrieval Number: A10451291S52019/2019©BEIESP DOI: 10.35940/ijeat.A1045.1291S52019 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Entrance Effects of Blood Model Casson Fluid in the Concentric Rings with Inner Ring Rotation Srinivasa Rao Nadiminti, A. Kandasamy Abstract:This research article analyzes the entrance effects in concentric rings with rotation of inner ring for the blood model Casson non-Newtonian fluid. The investigation is done with the assumption that, the inner ring rotates with a constant velocity along angular direction also the outer ring is at rest. The finite difference technique was applied to find the velocity profiles, variation of pressure in the radial coordinate direction. Calculation has been done for different annular gap values and Casson number. The compared results for different special cases was made and observed to be concordant. keywords: Entrance effect, Blood model Casson Fluid, Finite Difference technique, concentric rings. I. INTRODUCTION The effects in the entrance zone of concentric rings of laminar non-Newtonian fluid with inner ring rotation having technical applications like, heat exchangers design, turbo machinery and industries of polymer processing. Very often, laminar flow operations provide optimal conditions to maintain a less power pumping proportionally to the rate of heat transfer. Also in the field of nuclear reactors, this is happening when the cooling rates reduced. All the fluids which having practical applications are not obey Newtonian equation, so they are called as rheological fluids. Various suspensions such as coal, blood, food, paintings, polymer solutions. Here the blood model Casson fluid is taken, which belongs to the fluid class of flow with independent of time. The Newtonian fluid flow in the entrance zone problem in a concentric rings was studied by [4]. [8] analyzed the entrance effects of Bingham fluids in the concentric rings and analyzed the boundary layer thickness. [2] studied the relationship for the Casson fluid with outer ring rotation and inner ring is at rest between two rotating cylinders in the annular space. [11]used finite difference technique to analyze the non-Newtonian fluid in the geometry of concentric rings with the previous mentioned conditions. The relation of stress and strain for the Casson fluid is given by Fung [6] Revised Manuscript Received on December 15, 2019. Srinivasa Rao Nadiminti, Division of Mathematics, Department of Science and Humanities Vignan's Foundation for Science, Technology and Research (VFSTR) Vadlamudi, Guntur, Andhrapradesh - 522213, India. e- mail: srinudm@gmail.com A.Kandasamy, Department of Mathematical and Computational Sciences National Institute of Technology Karnataka, Mangalore, Karnataka-575025, India. e-mail: kandy@nitk.ac.in  1 2 =  0 1 2 +  1 2 _______________(1) Here shear stress is denoted by  ,  is strain rate. Yield value and Casson's viscosity denoted by  0 and   2 . This constitutive equation was successfully applicable to chocolate and blood. Further, Casson fluid flow with a side branch in a narrow tube has been investigated by [9]. Homogeneous porous medium for the flow of Casson fluid in a pipe has been considered by [5]. [1] investigated Magneto hydrodynamic flow with heat transfer for the non- Newtonian fluid in an eccentric rings. Analytical solution in the entrance region blood flow in a concentric annuli has been obtained by [3] assuming the blood to obey Casson model. Recently [7,10] analyzed the entrance effects of non-Newtonian flow in the concentric rings. The problem of Casson fluid in the concentric rings to the flow of the inlet region has been studied in the present work. The analysis was performed by taking the non- rotating outer ring is at rest and rotating the inner ring. Using the Prandtls boundary layer hypotheses, conservation equations of momentum, mass are solved and analyzed by finite difference technique. The algebraic system of equations in nonlinear form are obtained and was solved by the iterative method of Newton-Raphson. The compared results for different special cases was made and observed to be concordant. II. PROBLEM FORMULATION Fig.1 shows the geometrical Representation of the problem. The Casson fluid entered in to the concentric rings horizontally with R1 and R2 are the inner and outer radius respectively, with the uniform uniform velocity u0 along the axial direction with p0 as the initial pressure. The non rotating outer ring is at rest and the inner ring rotating with the angular velocity. The flow is axisymmetric, incompressible and laminar. The system of cylindrical polar coordinates apt to the geometry of the problem for the Casson fluid in the entrance are given by Fig.1: Geometrical Representation to the Physical Problem