Studies of some problems in computational fluid dynamics

Abstract

In the present thesis, the solutions of some heat transfer problems in incompressible fluid mechanics are investigated. In cases, where the partial differential equations governing the flow and heat transfer problems are linear, these are solved by Laplace transform technique and the problems involving non-linear differential equations are solved numerically using shooting method. The thesis consists of seventeen problems with different physical situations. Chapter 1 : Title : Transient free convection flow past an infinite vertical plate with periodic temperature variation. Abstract : An exact solution to transient free convection flow past an infinite vertical plate whose temperature is fluctuating about a constant temperature is derived. The penetration distance of the leading edge effect is also derived. It is observed that the temperature decreases when wt (w-frequency, t-time) or the Prandtl number Pr increases. Also transient velocity and penetration distance decreases when wt, w or Pr increases. Chapter 2 : Title : Transient free convection flow of a viscous fluid past an infinite vertical plate with periodic heat flux. Abstract : An exact solution to the transient free convection flow past an infinite vertical plate in the presence of periodic heat flux superposed on the steady heat flux at the plate is presented. It is observed that the transition from conduction to convection takes place at a distance nearer and nearer to the leading edge when wt or frequency w or the Prandtl number is high. In case of flow of high Prandtl number fluids, when the frequency is high, the transition from conduction to convection may take place at the leading edge itself. Chapter 3 : Title : Free convective heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall : A numerical approach. Abstract : The problem of flow and heat transfer in a viscous incompressible fluid confined between a long vertical wavy wall and a parallel flat wall has been analysed by the...