The thermal analysis of collector storage walls is presented in Section 6.2.1, Chapter 6, where a diagram of the wall and the thermal gains and losses are given. The unutilizability concept, developed by Monsen et al. (1982), can also be applied in this case to determine the auxiliary energy required to cover the energy supplied by the solar energy system. Again here, two limiting cases are investigated: zero and infinite capacitance buildings. For the infinite thermal capacitance case, all net monthly heat gain from the storage wall, Qg, given by
Life cycle analysis is performed annually and the following are evaluated according to Eq. (12.10) to find the solar savings:
• Fuel savings.
• Extra mortgage payment.
• Extra maintenance cost.
• Extra insurance cost.
• Extra parasitic cost.
• Extra property tax.
 Extra tax savings.
As indicated before, not all these costs may be present in every case, depending on the laws and conditions in each country or region. Additionally, as already indicated, the word extra appearing in some of the items assumes that the associated cost is also present for a fuel-only system and, therefore, only the extra part of the cost incurred for the installation of the solar energy system should be included. The inflation, over the period of economic analysis, of the fuel savings is estimated by using Eq. (12.13) with (i) equal to the fuel inflation rate. The parasitic cost is the energy required to power auxiliary items, such as the pump, fan, and controllers. This cost also increases at an inflation rate over the period of economic analysis using Eq. (12.13) with (i) equal to the annual increase in electricity price.
Solar savings for each year are the sums of the items shown above, as shown in Eq. (12.10). Actually, the savings are positive and the costs are negative. Finally, the present worth of each year’s solar savings is determined using Eqs. (12.11) and (12.12). The results are estimated for each year. These annual values are then added up to obtain the life cycle savings, according to the equation: