UNSTEADY HYDRODYNAMIC AND THERMAL BOUNDARY LAYERS OVER A FLAT PLATE WITH UNIFORM INJECTION OR SUCTION

Abstract

A computational algorithm for calculating the unsteady compressible and turbulent hydrodynamic and thermal boundary layers over a porous flat plate with uniform suction or injection is developed in the present work. The mathematical modeling involves the derivation of the governing partial differential equations of the problem. These are the continuity, the momentum, the ( κ −ε ) turbulence model and the energy equations. Besides, the perfect gas law and the Sutherland' s law of molecular viscosity are also used. A proper initial and boundary conditions are specified to be used in the solution of the governing equations. A numerical solution of the governing equations is made by using the control volume approach, with non-staggered grid technique and modified SIMPLE algorithm. The numerical solution is capable of calculating the velocity and temperature distributions of the calculation domain, the kinetic energy and dissipation of turbulence, the local and average skin-friction and heat transfer coefficients and Nusselt number, and the hydrodynamic and thermal boundary layers thicknesses. All these parameters are calculated at the transient and steady states. The numerical results show that the developed algorithm is capable of calculating the flow field, properly and accurately. The results show that injection causess light decrease in the temperature inside the thermal boundary layer, a decrease in skin – friction coefficient, a slight increase in the Nusselt number, a decrease in hydrodynamic boundary layer thickness, an increase in thermal boundary layer thickness and an increase in the time required to reach the steady state. Suction almost causes reverse effects.