The Modelling of Photovoltaic, Solar Thermal, and Photovoltaic/Thermal Domestic Hot Water Systems

Solar heating of potable water has traditionally been accomplished through the use of solar thermal (ST) collectors. With the recent increases in availability and lower cost of photovoltaic (PV) panels, the potential of coupling PV solar arrays to electrically heated domestic hot water (DHW) tanks has been considered. Additionally, innovations in the SDHW industry have led to the creation of photovoltaic/thermal (PV/T) collectors, which heat water using both electrical and thermal energy. The current work compared the performance and cost-effectiveness of a traditional solar thermal (ST) DHW system to PV-solar-electric DHW systems and a PV/T DHW system. To accomplish this, a detailed TRNSYS model of the solar hot water systems was created and annual simulations were performed for 250 L/day and 325 L/day loads in Toronto, Vancouver, Montreal, Halifax, and Calgary. It was shown that when considering thermal performance, PV-DHW systems were not competitive when compared to ST-DHW and PVT-DHW systems. As an example, for Toronto the simulated annual solar fractions of PV-DHW systems were approximately 30%, while the ST-DHW and PVT-DHW systems achieved 65% and 71% respectively. With current manufacturing and system costs, the PV-DHW system was the most cost-effective system for domestic purposes. The capital cost of the PV-DHW systems were approximately $1,923-$2,178 depending on the system configuration, and the ST-DHW and PVT system were estimated to have a capital cost of $2,288 and $2,373 respectively. Although the capital cost of the PVT-DHW system was higher than the other systems, a Present Worth analysis for a 20-year period showed that for a 250 L/day load in Toronto the Present Worth of the PV/T system was approximately $4,597, with PV-DHW systems costing approximately $7,683-$7,816 and the ST-DHW system costing $5,238.

THE TRANSPORT OF HEAT BY FLOWING GROUNDWATER IN A DISCRETE FRACTURE

In typical theoretical or experimental studies of heat migration in discrete fractures, conduction and thermal dispersion are commonly neglected from the fracture heat transport equation, assuming heat conduction into the matrix is predominant. In this study analytical and numerical models are used to investigate the significance of conduction and thermal dispersion in the plane of the fracture for a point and line sources geometries. The analytical models account for advective, conductive and dispersive heat transport in both the longitudinal and transverse directions in the fracture. The heat transport in the fracture is coupled with a matrix equation in which heat is conducted in the direction perpendicular to the fracture. In the numerical model, the governing heat transport processes are the same as the analytical models; however, the matrix conduction is considered in both longitudinal and transverse directions. Firstly, we demonstrate that longitudinal conduction and dispersion are critical processes that affect heat transport in fractured rock environments, especially for small apertures (eg. 100 μm or less), high flow rate conditions (eg. velocity greater than 50 m/day) and early time (eg. less than 10 days). Secondly, transverse thermal dispersion in the fracture plane is also observed to be an important transport process leading to retardation of the migrating heat front particularly at late time (eg. after 40 days of hot water injection). Solutions which neglect dispersion in the transverse direction underestimate the locations of heat fronts at late time. Finally, this study also suggests that the geometry of the heat sources has significant effects on the heat transport in the system. For example, the effects of dispersion in the fracture are observed to decrease when the width of the heat source expands.