Abstract

Thermally driven flows in a two-dimensional rectangular cavity filled with a fluid-saturated porous medium are considered when the applied temperature difference is perpendicular to the gravity vector. The flow depends on two non-dimensional parameters, the Darcy-Rayleigh number A and the cavity aspect ratio h (height/length). The motion is generated by maintaining the vertical sidewalls of the cavity at different constant temperatures and attention is focussed on the limit of large aspect ratio, h— oo . Use of asymptotic and numerical methods leads to an excellent correlation with existing results for the heat transfer across the cavity, and a prediction of the conditions needed to minimize the heat transfer.

The basic problem for h>> and finite Darcy-Rayleigh numbers, A, is formulated in Chapter 2, leading to a nonlinear end-zone problem which is studied in detail in Chapters 3-5. Asymptotic methods are used to solve the problem analytically for small A in Chapter 3 and for large A in Chapter 4. Numerical solutions for finite values of A are obtained in Chapter 5. Convective effects become important throughout the slot when A is of order h and solutions for the main core flow in this regime are considered in Chapter 6. A position of minimum heat transfer is identified. Properties of the flow near the ends of the slot are considered in Chapter 7 and the results are related in the limit as A/h— oo to existing theories for high Darcy-Rayleigh number flow in finite aspect-ratio cavities.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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