Transient Analysis on the Onset of Thermal Instability in the Thermal Entrance Region of a Horizontal Parallel Plate Channel

A transient analysis on the onset of thermal instability in the thermal entrance region of a horizontal parallel plate channel, where the lower plate is heated isothermally, is presented. A novel time-dependent approach based on a three-dimensional linear stability theory is developed to determine the neutral stability position, where a disturbance neither grows nor decays with time. The range of parameters Pe=30, 40, 60, 80, and 100, and Pr=0.2, 0.7, 1.0, and 7.0 are covered in the study. One finds that increasing Prandtl number has a destabilizing effect on the flow for a fixed Peclet number along the streamwise direction. On the other hand, increasing Peclet number or Reynolds number tends to stabilize the flow. As the onset of thermal instability moves upstream, the critical Rayleigh number and the critical wave number are increased. The result shows a good agreement with the previous experimental investigations.