A number of apparently disparate problems from engineering, meteorology, geophysics, fluid mechanics and applied mathematics are considered under the unifying heading of natural convection. After a review of the mathematical framework that serves to delineate these problems, the heuristic approach to Benard and Rayleigh convection is discussed with special attention to buoyancy and surface tension. Then consideration is given to some aspects of scaling, and the nondimensionalization of equations to a given problem. The thermohydrodynamic description of a Newtonian fluid is presented, and the Boussinesq--Oberbeck model. This is followed by a treatment of the linear stability problem, and a description of the basic ideas of Landau and Hopf concerning the bifurcation of secondary solutions. Quantitative, though approximate, estimations are given for quantities belonging to the nonlinear steady convective regime: flow velocity and temperature distribution. Higher-order, though steady, bifurcations are discussed, as well as the transition to turbulence, along with such time-dependent phenomena as relaxation oscillations. The paper concludes with an Appendix showing a simple application of the Leray--Schauder topological degree of a mapping.

Convective instability: A physicist's approach

Performance analysis of photovoltaic-thermal collector by explicit dynamic model

Comparative study of the performances of four photovoltaic/thermal solar air collectors.

http://web.mit.edu/hemond/www/docs/performance_design_optimization.pdf

Performance and design optimization of a low-cost solar organic Rankine cycle for remote power generation

Energy-efficient production of water from desert air has not been developed. A proof-of-concept device for harvesting water at low relative humidity was reported; however, it used external cooling and was not desert-tested. We report a laboratory-to-desert experiment where a prototype using up to 1.2 kg of metal-organic framework (MOF)-801 was tested in the laboratory and later in the desert of Arizona, USA. It produced 100 g of water per kilogram of MOF-801 per day-and-night cycle, using only natural cooling and ambient sunlight as a source of energy. We also report an aluminum-based MOF-303, which delivers more than twice the amount of water. The desert experiment uncovered key parameters pertaining to the energy, material, and air requirements for efficient production of water from desert air, even at a subzero dew point.

L. Konicek

Papers

Free convective heat transfer across inclined air layers

Correlation equations for free convection heat transfer in horizontal layers of air and water