Critical behaviour of the solution of hydromagnetic flows in convergent-divergent channels

Abstract

In this thesis under the title "Critical behavior 0 f the Solution of Hydromagnetie Flows in Com'ergent.Divcrgent Channels", two problems have been studied namely Hydromagndic Flows in Comergent-Divergent Challllels and [he Laminar Unsteady flow of a Viscous Fluid away from a Plane Stagnation Point, which belong to two different realms. Initially we havc discussed some basic topics in order (0 study the problems and the appro~imation meth.ods. Firs(/y, wc have studied thc location and naturc of dominant singularity in the complex plane for laminar unsteady flow of a viscous fluid at a plane stagnation point_ Thc series ~~pansion with 44 terms in time of the shear stress is inveMigated with High-ordcr difTerential approximant to determine the poles in thc complex plane using algebraic programming language MAPLE. The scries-improvement techniqucs are employed to impro\-e its convergencc propertics_ It is ohserved that lhe performance of High-order differcntial Jppl'Oximant i~ bettcr than that of Padc' approximant and Drazin-Tourigny approximant. "inally, we have studied the two-dimensional, 5leady, nonlinear now or an lllcompressibJe conducting viscous fluid in Convergent-Divergent Channels under thc influence of an e"ternaily ~pplicd homogeneous magnetic ficld by means of Hermi/e - Pade' approximation especially differentwl approximate mcthod. We have obt~illed the series related to similarity parameter~ by using algebraic programming language MAPLE. The serie~ is then analy~ed by appro~imate methods to show the dominatmg singularity behavi()r of the flow and the eritieal relationship among the parametcrs of (he solution_