Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes

Numerical Solutions

Kuppalapalle Vajravelu,Swati Mukhopadhyay

• Publisher: Academic Press
• Year: 2015
• ISBN:
  9780128037850
• Topic: Mathematik
• Subtopic: Angewandte Mathematik

Most of the equations governing the problems related to science and engineering are nonlinear in nature. As a result, they are inherently difficult to solve. Analytical solutions are available only for some special cases. For other cases, one has no easy means but to solve the problem must depend on numerical solutions.

Fluid Flow, Heat and Mass Transfer at Bodies of Different Shapes: Numerical Solutions presents the current theoretical developments of boundary layer theory, a branch of transport phenomena. Also, the book addresses the theoretical developments in the area and presents a number of physical problems that have been solved by analytical or numerical method. It is focused particularly on fluid flow problems governed by nonlinear differential equations. The book is intended for researchers in applied mathematics, physics, mechanics and engineering.

• Addresses basic concepts to understand the theoretical framework for the method
• Provides examples of nonlinear problems that have been solved through the use of numerical method
• Focuses on fluid flow problems governed by nonlinear equations

Part I

Methods and Applications

1

Numerical methods

Abstract

The aim of this chapter is to present an effective numerical technique for the solution of boundary layer fluid flow and heat/mass transfer problems. The governing equations for fluid mechanics are an inherently nonlinear set of partial differential equations and form a boundary value problem (BVP). Only for a few cases are the exact solutions available. Because of the inability of obtaining exact or analytical solutions of the problems arising in the fields of science and engineering, numerical methods became a powerful tool to deal with these problems. To solve linear BVPs, there are various methods available. The shooting method is one of the most efficient methods for the solution of both linear and nonlinear BVPs. The method is easy to apply, and the convergence of this method depends on a good initial choice of slopes.

Keywords

Boundary value problems

nonlinear equations

numerical solutions

shooting method

linear interpolation

Newton’s method

Runge-Kutta method

The governing equations of fluid flow problems are generally of a nonlinear and boundary value type. Usually, the exact solutions of the boundary value problems (BVPs) are very difficult to obtain, and so we have to use numerical methods. For some special classes of flow problems, a set of partial differential equations are transformed into a set of ordinary differential equations with the help of similarity variables. The transformed (final) equations then can be solved analytically or numerically. The procedure for finding a numerical solution for a BVP is generally more difficult than that of...