An idealized solar pond measures 100 m ×100 m ×1.2 m. The bottom 20 cm (the storage layer) has an effective absorptance a = 0.7. The 1.0 m of water above (the insulating layer) has a transmittance t= 0.7, and its density increases downwards so that convection does not occur. The designer hopes to maintain the storage layer at 80 ᵒC. The temperature at the surface of the pond is 27 ᵒC (day and night).
(a) Calculate the thermal resistance of the insulating layer, and compare it with the top resistance of a typical flat-plate collector.
(b) Calculate the thermal resistance of a similar layer of fresh water subject to free convection. Compare this value with that in (a), and comment on any improvement.
(c) The density of NaCl solution increases by 0.75 g/liter for every 1.0 g of NaCl added to 1.0 kg H2O. A saturated solution of NaCl con tains about 370 g NaCl per kg H2O. The volumetric coefficient of thermal expansion of NaCl solution is about 4x10-4/K. Calculate the minimum concentration C of NaCl required in the storage layer to suppress convection, assuming the water layer at the top of the pond contains no salt. How easy is it to achieve this concentration in practice?
(d) Calculate the characteristic time scale for heat loss from the storage layer, through the resistance of the insulating layer. If the temperature of the storage layer is 800C at sunset (6 p. m.) what is its temperature at sunrise (6 a. m.)?