Question

The air-conditioned room which stands in a ventilated basement measuring length, width, height 6m x 3m x 3m. one of the two 3m walls faces west and has a double glass window measuring 1.5 m x 1.5 m, mounted on a wall without external shading. There is no heat gain through the wall other than the wall facing west. Calculate sensible heat, latent heat, and total heat in the room. How much cooling capacity is needed?

Inside conditions: 25 Celsius drybulb, 50% RH
Outside conditions: 43 Celsius dry bulb, 24 Celsius wetbulb
U-Value for walls: 1.78 W / m ^ 2.K
U-Value for roof: 1,316 W / m ^ 2.K
U-Value for floors: 1.2 W / m ^ 2.K
Effective Temp.Difference (ETD) for walls: 25 Celsius
Effective Temp.Difference (ETD) for roof: 20 Celsius
U-Value for glass: 3.12 W / m ^ 2.K
Solar Heat Gain (SHG) for glass: 300 W / m ^ 2
Internal shading coefficient (SC) for glass: 0.86
Occupants: 4 (90W sensible heat / person) (40W latent heat / person)
Lamp load: 33 W / m ^ 2 of floor area
Equipment load: 600 W (Sensible) + 300W (latent)
Infiltration: 0.5 Air Changes per Hour
Barometric pressure: 101 kPa
CLF: 1

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Answer 1

Sol:

From the psychrometric chart,

For the inside conditions of dry bulb, 50 percent RH:

For the outside conditions of   dry bulb, wet bulb:

density of dry air = 1.095 kg / m3

External loads:

a) Heat transfer rate through the walls: Since only the west wall measuring 3m x 3m with a glass window of 1.5m x 1.5m is exposed; the heat transfer rate through this wall is given by:

(Sensible)

b) Heat transfer rate through the roof:

  (Sensible)

c) Heat transfer rate through the floor: Since the room stands on a well-ventilated basement, we can assume the conditions in the basement to be same as that of the outside (i.e., dry bulb and wet bulb), since the floor is not exposed to solar radiation, the driving temperature difference for the roof is the temperature difference between the outdoor and indoor, hence:

(Sensible)

d) Heat transfer rate through a glass: This consists of the radiative as well as conductive components. Since no information is available on the value of CLF, it is taken as 1.0. Hence the total heat transfer rate through the glass window is given by:

(Sensible)

e) Heat transfer due to infiltration: The infiltration rate is 0.5 ACH, converting this into mass flow rate, the infiltration rate in kg/s is given by:

minf = density of air x (ACH x volume of the room) / 3600

Sensible heat transfer rate due to infiltration, Qs,inf;

(Sensible)

Latent heat transfer rate due to infiltration, Ql,inf:

(Sensible)

Internal loads:

a) Load due to occupants: The sensible and latent load due to occupants are:

Qs,occ = no.of occupants x SHG = 4 x 90 = 360 W

Ql,occ = no.of occupants x LHG = 4 x 40 = 160 W

b) Load due to lighting: Assuming a CLF value of 1.0, the load due to lighting is:

Qlights = 33 x floor area = 33 x 18 = 594 W (Sensible)

c) Load due to appliance:

Qs,app = 600 W (Sensible)

Ql,app = 300 W (Latent)

Total sensible and latent loads are obtained by summing-up all the sensible and latent load components (both external as well as internal) as:

Qs,total = 300.38+473.76+388.8+706.9+151+360+594+600 = 3574.84 W (Ans.)

Ql,total = 16.4+160+300 = 476.4 W (Ans.)

The total load on the building is:

Qtotal = Qs,total + Ql,total = 3574.84 + 476.4 = 4051.24 W (Ans.)

Room Sensible Heat Factor (RSHF) is given by:

RSHF = Qs,total / Qtotal = 3574.84 W / 4051.24 W = 0.882 (Ans.)

To calculate the required cooling capacity, one has to know the losses in return air ducts. Ventilation may be neglected as the infiltration can take care of the small ventilation requirement. Hence using a safety factor of 1.25, the required cooling capacity is:

Required cooling capacity = 4051.24 x 1.25 = 5064.05 W      (Ans.)