Natural convection in a horizontal fluid-superposed porous layer heated locally from below is studied in this thesis. This problem occurs in numerous engineering and geophysical systems, such as fibrous and granular thermal insulations, water reservoirs, grain storage installations, solid-matrix heat exchangers, solidifying castings, and post-accident cooling of nuclear reactors. In nature, thermal circulation in lakes, shallow coastal areas and other reservoirs occurs in a system having a fluid layer superposed on top of a porous matrix that is heated locally at the base. In spite of its fundamental nature, there are virtually no studies in the literature pertaining to this problem. To address this shortcoming, the fundamental aspects of this problem are studied in this work.
The goal of the thesis is to study how free convective heat transfer in a composite layer with a localized bottom heat source is affected by parameters such as the size of the heat source, the fluid-to-porous layer height ratio, the Darcy number, the aspect ratio, the solid-to-fluid conductivity ratio, and the fluid Prandtl number. To that end, two particular aspects of the problem are studied: (a) the steady-state and transient flow and temperature fields, and (b) measurement and prediction of the overall heat transfer characteristics of the system. A numerical approach has been used to study the development of the temperature and flow fields in the system and predict overall heat transfer rates. A one-domain formulation, which uses a single set of governing equations to model fluid flow and heat transfer throughout the entire composite domain, is used. To solve the governing equations, a control volume based numerical solution technique is used. Results show that the nature of convective motion in a composite system with a localized bottom heat source is identical to that observed when the base is uniformly heated. A cellular flow pattern is observed with flow penetration occurring from the overlying fluid layer to the underlying porous layer. Penetration, however, is significant only near the fluid-porous layer interface. The overall heat transfer coefficients are found to depend strongly on the heater length, height ratio, and the fluid-to-porous layer conductivity ratio, while the effects of the aspect ratio and the fluid Prandtl number are not very significant. The effect of the Darcy number is moderate up to Darcy numbers of 10<super>-3</super> beyond which there is a sudden increase in heat transfer coefficients Experiments are performed to validate the numerical solutions and develop empirical Nusselt-versus-Rayleigh number correlations. Experiments are conducted in a cubical chamber with 3 mm DIA glass beads as the porous layer and distilled water as the saturating fluid. Two different heater lengths and three different height ratios are investigated. Experimental results confirm the numerical predictions that the Nusselt number increases with a decrease in the heater length and an increase in the height ratio. However, significant numerical differences are seen when experimental and numerical results are compared. The most likely reason for the observed discrepancy is the implementation of the one-domain model for the numerical solution. This discrepancy calls into question the results of prior numerical studies for the fully heated bottom which have used a one-domain formulation and emphasizes the necessity of validation via experiment.
University of Minnesota Ph.D. dissertation. December 2010. Major: Mechanical Engineering. Advisor: Francis A. Kulacki. 1 computer file (PDF); xxii, 184 pages, appendices A-D.
Natural convection in horizontal fluid-superposed porous layers heated locally from below..
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