Combined Forced and Free Convection in Stratified and Unstratified Flows

Citation

Robertson, Grant Earl (1975) Combined Forced and Free Convection in Stratified and Unstratified Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/47d4-nd32. https://resolver.caltech.edu/CaltechTHESIS:10062021-232305217

Abstract

The laminar, steady, horizontal flow past a hot or cold two-dimensional body is examined; the fluid is unbounded, diffusive, and viscous. The presence of significant ambient stable temperature (or density) stratification, or significant buoyancy-induced convection, or both, is considered. A detailed understanding of the fundamental structure of such flows is obtained by developing effective analytical and numerical solution procedures.

Chapter 2: This chapter considers the general problem of stably stratified, Oseen flow at large distances upstream and downstream of a body which is represented as a line sink of horizontal or vertical momentum, or as a line heat source or heat dipole. The analysis is focused on the general properties of the horizontal velocity component, as well as on explicit calculation of the horizontal velocity profiles and disturbance streamfunction fields for varying degrees of stratification. For stable stratifications, the flow fields for all four types of singularities exhibit the common feature of multiple recirculating rotors of finite thicknesses, which leads to an alternating jet structure. both upstream and downstream for the horizontal velocity component and to lee-waves in the overall flow. Self-similar formulae for the velocity, temperature, and pressure at very large distances upstream and downstream are also derived and compared with the Oseen solutions

Chapter 3: The simultaneous forced and free convection flow of a neutrally- or stably-stratified fluid past a hot or cold horizontal flat plate is investigated by numerically solving the full equations of motion and thermal energy subject only to the Boussinesq approximation. The solutions span the parameter ranges 10 ≤ Re ≤ 100, 0.1 ≤ Pr ≤ 10, -2.215 ≤ Gr/Re^5/2 ≤ +2.215, and O ≤ Ri ≤ 6.325, where Re, Pr, Gr, and Ri are based on the overall plate length ℓ and the ambient free stream fluid properties evaluated at the plate level. For all degrees of stratification a hot plate causes an acceleration of the boundary flow near the plate surface relative to the corresponding forced convection flow, thereby increasing both the local skin friction and heat transfer coefficients. On the other hand, the boundary flow adjacent to a cold plate is decelerated and the local skin friction and heat transfer rate are decreased. This deceleration effect is enhanced by either further cooling or increasing the amount of ambient stratification, Ri, leading to boundary-layer separation in some cases. When the effect of the ambient stratification dominates that of local heating or cooling, the boundary-layer displacement increases for decreasing Ri, due to the buoyancy restoring force lessening, thus diminishing the drag. The dimunition in the drag, for the same decrease in Ri, lessens (increases) by slightly heating (cooling) the plate. When the effect of local heating or cooling dominates that of the ambient stratification, the drag is diminished by increasing Ri. A wave-structure exists only for stably-stratified fluids, with the amplitudes and wavelengths of the waves being decreased for increasing Ri.

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