Chieh, Sherman, authorNickerson, Everett C., authorSandborn, Virgil A., authorFluid Dynamics and Diffusion Laboratory, College of Engineering, Colorado State University, publisher2020-04-172020-04-171973-05https://hdl.handle.net/10217/204904CER72-73SC-ECN-VAS33.May 1973.Includes bibliographical references (pages 84-90).Circulating copy deaccessioned 2020.The mechanism of turbulent plane Couette flow with a negative temperature gradient was examined theoretically. First, the instability of fluid under various conditions was examined by utilizing linear and nonlinear numerical models. From the results, it was confirmed that constant shear has a stabilizing effect on the perturbations. It is shown that the neutral Rayleigh numbers, found from linear and nonlinear models, are almost identical for non-longitudinal rolls, but quite different for longitudinal rolls. The heat and momentum flux for the flow in a certain range of Reynolds numbers (Re≤500) and Rayleigh numbers (Ra≤500,000) were determined by integrating the Boussinesq equations numerically. In this range of Reynolds and Rayleigh numbers, the convection characteristic dominates the flow motion; hence the following occurs: a) Heat flux and momentum flux are linearly correlated; b) Both heat and momentum flux increase with the Rayleigh number, but decrease with an increasing wave angle; c) Heat flux increases as the Reynolds number decreases; d) Heat flux approximately follows the "one-thirds power law" to the Rayleigh number; and e) Heat flux attains its maximum at α= 0 (longitudinal roll). The nonlinear numerical model also shows that preferred mode of perturbation is a roll-type convection (α = 0); and the perturbation with a larger wave angle (α≠ 0) can exist only at smaller Rayleigh numbers for certain Reynolds number. The above conclusion confirms Chandra's (1938) laboratory results and Kuo's (1963) cloud-form assumption. A theoretical approach based on Malkus' upper bound hypothesis was also investigated. Accordingly, two inequalities were derived to express the upper bound on heat and momentum flux for heated plane Couette flow.technical reportsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.HydrodynamicsFluid mechanicsText