Spline Functions and Their Applications To Fluid Flow Problems

Abstract

quotSplines are used extensively at Boeing and throughout much of the industrial world. Cubic splines are used in the numerical solution of differential equations which arises in several complex systems such as physics, chemistry, fluid mechanics, viscoelasticity, signal processing, mathematical biology, bioengineering and various applications in many branches of science and engineering. Spline solution is developed for solving a system of boundary value problems. Cubic splines are applied in image interpolation and digital filtering. To know the behavior of fluids in motion, the physical phenomena are observed, the fundamental laws are verified, the thermodynamical properties are examined and the characteristic mathematical formulations are made. Thus, the problems of fluid flow are analyzed and understood. In fluid flow problems, when fluid flows, change in temperature appears. Therefore, the study of heat transfer problems in fluid flow has received the attention of scientists, in view of its application and importance in several fields of engineering and technology. Another branch of fluid mechanics is the Magneto hydrodynamics (MHD) which is the science of the motion of electrically conducting fluids under magnetic fields. Variety of problems related to Magneto hydrodynamic boundary layer flows, fluid between two parallel plates, Magneto hydrodynamic boundary layer model for power law fluid, radiation effects on MHD boundary layer stagnation point flow are solved and analyzed here using spline collocation method. In most of the problems the influence of velocity and temperature profile are checked by changing the magnetic parameter, Grashoff number, Prandtl number and squeeze number.The applications we have examined are few but sufficient enough to illustrate the effectiveness and potentialities of spline collocation method. It is hoped that others will be able to apply the method with successful results and our experience will help them to obtain solutions to increasingly more difficult and complicated problem