ESTIMATING THE VELOCITY DISTRIBUTION IN VISCOUS INCOMPRESSIBLE FLOW (COUETTE FLOW) BETWEEN TWO PARALLEL PLATES USING TRI -DIAGONAL MATRIX ALGORITHM

Numerical solutions to Viscous Incompressible flow between two parallel plates have been developed over the last half century. Multi-level techniques are successfully developed and applied for the same problem where significant speed-ups are achieved. Due to complexity of Navier-Stokes equation, obtaining analytical solutions for viscous flow problems if difficult sometimes. Obtaining exact solution of Navier-Stokes equation is possible for some classical cases of steady, laminar, viscous and incompressible flows. Numerical research in this area will help researchers to develop techniques which yield accurate and faster solutions. The present work is on estimating the velocity distribution in Couette flow between two parallel plates by using Newtonian fluids as lubricant. The resulting partial differential equations of Navier-Stokes equation after the boundary conditions are substituted are solved by Finite Difference Method. An algorithm named as “Tri Diagonal Matrix Algorithm” is generated for the same. By using MATLAB, numerical analysis is performed to obtain the velocity distribution between two parallel plates.