Abstract
The physical mechanism of Tollmien-Schlichting wave and heat transfercharacteristic in the fully developed region between horizontal parallelplates are analysed theoretically by a direct numerical simulation. In thisinvestigation, a direct numerical scheme is developed to study the temporalamplification of a two-dimensional disturbance in plane Poiseuille flow.Transient non-linear equations are applied in a region of a wavelengthmoving with the wave propagation speed. The complex amplitude involved inthe perturbation functions is considered as the initial input of thenon-linear stability equations. The growth and decay of disturbance withtime are presented, and the neutral stability curves is in good agreementwith the existing solutions. In the subcritical regime usingfinite-amplitude approach, the neutral stability curves shift toward lowerReynolds number, and the critical conditions as a function of the initialmagnitude A0 of the disturbance is presented. The friction factor increaseswith the increase in the Reynolds number in the supercritical regime. This thesis also investigates numerically the effect of asymmetricheating on wave instability and thermal convection in a horizontal parallelplate channel. The lower plate and upper plate are at two differenttemperature levels. By the linear stability theory, the critical Reynoldsnumber decreases due to the heating of the lower plate and increases due tothe heating of the upper plate. The result of linear theory shows thevariation of critical Rec with the varying Grashof number for Pr = 0.7 and7. By using a direct numerical simulation on the amplification of a 2-Ddisturbance, the thesis also studies the flow and heat transfercharacteristics in the post-critical regime with the effect of asymmetricheating. The numerical results show the non-linear and time-periodicbehavior of the streamlines, vorticities, velocity vectors, and isotherms. Subsequently, one attempt is to explore the effect of nonlinear basictemperature distribution due to the constant wall heat flux on the wavestability. The modified Grashof number Gr* characterizes the effect ofconstant wall heat flux. Gr* > 0 indicates the heating and Gr* < 0 standsfor the cooling of the channel. The governing parameters are Gr*, Pr and Re.By the linear stability theory, the critical Reynolds number alwaysincreases with the increase in the magnitude of Gr* for both heating andcooling. The boundary condition of the wall heat flux tends to stabilize theflow. For a fixed Gr*, the effect of axial temperature gradient becomessignificant for a small Pr. The T-S wave moves upward due to expandedreverse flow near the lower plate as Gr* > 0 and moves downward due toexpanded reverse flow close to the upper plate as Gr* < 0. This means thatthe axial temperature gradient can enlarge the effect of adverse temperaturegradient in the gravitational direction. The effect of axial temperaturegradient decreases with the increase in the Reynolds number because thebuoyancy force is suppressed by the inertia force. The friction factors andthe Nusselt numbers at the upper plate and the lower plate in thepost-critical regime are exhibited.