## Exercises

6.1 A building has a peak heating load equal to 18.3 kW and a peak cooling load of 23.8 kW. Estimate the seasonal heating and cooling requirements if the heating degree days are 1240°C-days, the cooling degree days are 980°C-days, the winter indoor temperature is 23°C, and the summer indoor temperature is 25°C. The design outdoor temperature for winter is 2°C, and for summer, it is 39°C.

6.2 Estimate the overall heat transfer coefficient of a wall that has the following layers:

Outside plaster, 2 cm. Brick, 20 cm. Air gap, 2 cm.

Polyurethane insulation, 3 cm. Brick, 10 cm. Inside plaster, 2 cm.

6.3 Estimate the overall heat transfer coefficient of the wall in Exercise 6.2 by replacing the 10 cm inside brick with the same thickness of medium-density concrete.

6.4 Estimate the overall heat transfer coefficient of the wall in Exercise 6.2 by replacing the air gap and polyurethane with 5 cm polyurethane.

6.5 Estimate the U value of a pitched roof that has a ceiling U value = 1.56 W/m2-K, area of 65 m2, and a roof U value = 1.73 W/m2-K. The slope angle of the roof is 35°.

6.6 A building has a south-facing thermal storage wall with night insulation of Rins = 1.35 m2-K/W, applied for 6 h. Estimate the monthly heat transfer through the wall into the indoor space with and without night insulation for the month of January. The following data are given:

Uo = 6.3 W/m2-K. w = 0.31 m. k = 2.2 W/m-K. hA = 8.3 W/m2-K. Ht = 11.8 MJ/m2-K. (to) = 0.83.

 Tr = 21°C. Ta = 3°C. Aw = 25.1 m2

6.7 A house has a south-facing window of 1.8 m height, located in 35°N latitude. The overhang is wide enough so as to neglect the side effects and its length is 0.9 m located 0.6 m above the top surface of the window. Estimate the shading fraction for a vertical window facing due south and a window in the same direction and tilted 10° from vertical at 11 am and 2 pm on July 17.

6.8 A building with a south-facing window with height = 2.5 m_and width =_5 m is located in an area where KT = 0.574, hss = 80°, Rb = 0.737, H = 12.6MJ/m2, and Fw = 0.705. The ground reflectance is 0.3. Estimate the mean monthly area-average radiation received by the window when there is no shading and when an overhang with a gap of 0.625 m, extension 0.5 m on both sides of the window, and projection of 1.25 m is used.

6.9 A solar space and hot water heating system has a collector with FrUl = 6.12 W/m2-°C and an area of 20 m2. The flow rate in a collector-storage heat exchanger of antifreeze and water is 0.02 kg/s-m2, the heat exchanger has an effectiveness equal to 0.73. What is the ratio FR/FR if the cp of water is 4180 J/kg-°C and that of antifreeze is 3350 J/kg-°C?

6.10 A room is maintained at a temperature of TR = 22°C and has a (UA) = 2850 W/°C. The ambient temperature is 2°C and the storage tank temperature is 75°C. Estimate the space load, domestic water heating load, and rate of auxiliary energy required for the following conditions:

Heat exchanger effectiveness = 0.75.

Flow rate of air side of heat exchanger = 0.95 kg/s.

Environmental temperature at the space where storage tank is located = 18°C.

(UA) of storage tank = 3.4 W/°C. Mass flow rate of domestic water = 0.15 kg/s. Required domestic water temperature = 55°C. Make-up water temperature = 14°C.

6.11 A liquid solar heating system has a 16 m2 collector and is used to preheat the city water, which is at a temperature of 12°C. If the tank is fully mixed and the capacitance of the collector side of the heat exchanger is 890 W/°C and the storage side is 1140 W/°C, estimate the final temperature in the storage tank at 3 pm and the energy balance of the system for the following parameters and conditions of the system:

Heat exchanger effectiveness = 0.71.

Storage tank capacity = 1100 L.

Initial tank water temperature = 40°C.

Environmental temperature at the space where storage tank is located = 18°C.

The meteorological conditions and load flow rate are given in the following table.

 Hour I, (MJ/m2) Ta (°C) Load flow rate (kg) 9-10 0.95 13 160 10-11 1.35 15 160 11-12 2.45 18 80 12-13 3.65 22 0 13-14 2.35 23 80 14-15 1.55 21 160

6.12 Using the data of the previous problem, estimate the effect of increasing the effectiveness of the heat exchanger to 0.92 and the city mains water temperature to 16°C. Each modification should be considered separately and the result should be compared to those of the previous problem. In every case, the energy balance should be checked.