Paper Number “87” PRESSURE WORK EFFECTS IN UNSTEADY CONVECTIVELY DRIVEN FLOW ALONG A VERTICAL PLATE

This paper revisits the classical problem of convectively driven one-dimensional (parallel) flow along an infinite vertical plate. We consider flows induced by an impulsive (step) change in plate temperature and by a sudden application of a plate heat flux. Provision is made for pressure work and vertical temperature advection in the thermodynamic energy equation, processes that are generally neglected in previous onedimensional studies of this problem. In a statically stable environment these additional processes provide a simple negative feedback mechanism: warm air rises, expands and cools relative to the environment, whereas cool air subsides, compresses and warms relative to the environment. Exact solutions of the viscous equations of motion are obtained by the method of Laplace transforms for the case where the Prandtl number is unity. The pressure work and vertical temperature advection are found to have a significant impact on the structure of the solutions at later times. NOMENCLATURE p c – specific heat at constant pressure (=const); g – gravitational acceleration ; -2 ( 9.81 m s ) p – pressure t – time T – temperature (T is its deviation from the environmental value) ' w – velocity component along the plate; W – non-dimensional velocity along the plate; x – direction normal to the plate; z – direction along the plate; – buoyancy parameter; – molecular thermal diffusivity (=const); – non-dimensional temperature perturbation; – kinematic viscosity coefficient (=const); – non-dimensional time; – non-dimensional x coordinate. INTRODUCTION The transient natural convection flow of a viscous fluid adjacent to vertical surfaces is a fundamental problem in fluid mechanics and heat transfer, with significance for a variety of engineering applications [1]. The simplest form of this problem is one-dimensional transient convective flow adjacent to an infinite vertical plate, first considered in [2] for an impulsive change in plate temperature. Authors of [3][6] have obtained analytic solutions to this problem for a variety of temporal variations in plate