Natural convection flow between moving boundaries

Abstract

The laminar steady natural convection flow of viscous, incompressible fluid between two moving vertical plates is considered. It is assumed that the plates are moving in opposite direction with equal velocity. The two-point boundary value problem governing the flow is characterized by a non-dimensional parameter K. It is solved numerically using shooting method and the Newton-Raphson method to locate the missing initial conditions. The numerical results reveal that no solution exists beyond a critical value of K and that dual solutions exist for values of K less than this critical value. An approximate solution, using Collatz iterative method, is also given which is simple and sufficiently accurate. Finally the stability of the two solutions is discussed.

Keywords: Shooting methos, Collatz methods, stability analysis.