Quaternions in Joukowski Transformation

Abstract

Conformal mappings have been exploited for a long time in a number of physical problems arising in aerodynamics, thermal equilibrium, electrostatics, fluid flow and so on. These complex-valued functions are implemented with just a single complex variable z. However, in this study, quaternions are introduced into a Joukowski transformation, a conformal map used in the study of fluid flow around airfoils. Analysis is effected so as to determine the properties of this transformation function and spheres of both Euclidean and hyperbolic geometry are executed in this expedition.