Building Energy Analysis

Net Heating Load - I During winter, the major sources of heat gain/loss into/from a building are shown below. The net heat loss out is called the heating load. Based on an energy balance, the net heat load out is: Qnet,out = (Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration + Qground)out – (Qsolar + Qpeople + Qelectricity)in

Net Heating Load - II To maintain the interior of the building at a steady temperature, the furnace must provide enough heat to the space, Qfurnace, to balance the net energy loss from the space, Qnet,out. Because furnaces are not 100% efficient, some of the energy supplied to the furnace, Qnatural gas, is lost in the exhaust, Qexhaust. The building energy balance can be written as under:

Net Heating Load - III In this case, an energy balance on the house gives: Qfurnace – Qnet,out = (dE)house = 0 (if the house temperature remains constant, i.e. Steady State) It follows that: Qfurnace = Qnet,out Efficiency is defined as: In the case of a furnace, the useful output is Qfurnace and the required input is Qnatural gas. Thus, the efficiency of a furnace is: η furnace = Qfurnace / Qnatural gas   The efficiencies of furnaces have improved over the years from about 65% to 95%. The efficiency equation can be rearranged to determine the natural gas energy use consumed by the furnace. Qnatural gas = Qfurnace / η furnace

Example – Heating Load Consider a building has the following average loads in winter: Qpeople = 13,000 Btu/h, Qsolar = 3,000 Btu/h, Qelec = 3,000 Btu/h, Qwalls = 20,000 Btu/h, Qwindows = 15,000 Btu/hr, Qdoors=1,500 Btu/hr, Qceiling = 12,500 Btu/hr, Qinfiltration = 15,000 Btu/hr, Qground = 5,000 Btu/hr. A) Calculate the Qnet,out of the building. B) The furnace of this building operates 1,000 hours over the winter and is 80% efficient. Natural gas costs $10 /MBtu. Calculate the cost of fuel for the furnace over a winter.

Solution Qnet,out = (Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration + Qground)out – (Qsolar + Qpeople + Qelectricity)in Qnet,out = (20,000+15,000+12,500+1,500+15,000+5,000)Btu/hr – (3,000+13,000+3,000) Btu/hr Qnet,out = 50,000 Btu/hr Qfurnace = Qnet,out = 50,000 Btu/hr Qnatural gas = Qfurnace / η furnace = 50,000 Btu/hr /0.80 = 62,500 Btu/hr Qnatural gas, yr = Qnatural gas x HPY = 62,500 Btu/hr x 1,000 hr/yr = 625,00,000 Btu/yr Cnatural gas, yr = Qnatural gas,yr x Cng = 62.5 MBtu/yr x $10 /MBtu = $625 /yr

Net Cooling Load - I During summer, the major sources of gain into a building are shown below. Note that ground losses/gains in the summer are typically small and are here assumed to be negligible. The net heat load into a building is called the cooling load. Based on an energy balance, the net heat load in is: Qnet,in = (Qsolar + Qpeople + Qelectricity + Qwalls + Qwindows + Qceiling + Qdoors + Qinfiltration)in

Net Cooling Load - II To maintain the interior of the building at a steady temperature, the air conditioner must remove enough heat from the space, Qac, to balance the net energy gain to the space, Qnet,in. In this case, an energy balance on the house gives:  Qnet,in – Qac = dE = 0  It follows that:  Qac = Qnet,in

Net Cooling Load - III To pump heat “uphill” from the cool space to the hot outdoors, electric air conditioners require electrical energy Welec. As before, efficiency is defined as: For an electric air conditioner, the useful output is Qac and the required input is Welec . Thus, the efficiency of the air conditioner is: η ac = Qac / Welec The efficiency equation can be rearranged to determine the electricity consumed by an air conditioner. Welec = Qac / η ac

Net Cooling Load - IV The efficiency of air conditioners is measured in several ways. The coefficient of performance (COP) is a non-dimensional measure of steady state efficiency at a single set of operating conditions. The COP of typical air conditioners is about 3, which means that an air conditioner removes 3 units of heat from a space for every unit of electrical work it consumes. Air conditioner efficiency varies with the temperature of the air returned to the air conditioner and the temperature of the outdoor air to which heat is rejected. The average efficiency rating of air conditioners over a season is reported as the Seasonal Energy Efficiency Rating (SEER) with units Btu/Wh. The electricity consumed by an air conditioner can be calculated using either COP or SEER with proper attention to units. Welec = Qac / η ac = Qnet,in / COPac = Qnet,in / SEER