Cooling Load Calculations
Cooling Load Calculations
LEARNING OUTCOME:
   1. Explain the general procedure required to calculate the heat gain and
      cooling load for the space to be air-conditioned in designing an air-
      conditioning system.
   2. Define and differentiate heat gain, cooling load and heat extraction
      rate.
2. Cooling Load
   The rate at which heat energy must be removed to maintain the
   temperature and humidity at the design values. It is taken as the
   sum of the heat gain and the system heat loads. The cooling load
   will generally differ from the heat gain since some of the heat gains
   such as solar radiation are absorbed by the structure and the
   contents and do not appear as cooling load until sometime later.
   Recommended for summer: 20-24OC, 50-60% RH and 4.6-7.6 m/min air movement within the living
   zone. Source: PME Code 2012 edition, item 8.a page 53.
Add all of the sensible and latent loads discussed in item number nine,
the room sensible heat, RSH and the room latent heat, RLH are now
determined. Equate the two such as:
                                RSH              RSH
                  RSHF =                  =
                                RTH           RSH + RLH
               i)    Simple wall,
                                                x
                          Outside                               Inside
                          air film                              air film
QST
to ti
                                                                      Homogeneous Material
                                                                            Non-homogeneous Material
                                                                      AΔt
               QST = UAΔt = UA(to - ti) =
                                                                       RT
                                     1
                          U =
                                     RT
x1 x2
                     to
    Outside                                                     ti
    air film                                                                 Inside
                                               a                             air film
                          C          K1                 K2
QST
     QST = UAΔt
                     1                           1
            U =               =
                     RT           1 + 1 + x1 + 1 + x2 + 1
                                  fo  C   k1   a   k2   fi
Example:
Determine the heat transmission gain through a 12.0 m x 6.0 m external
wall with a cross section shown. Inside temperature is 24OC and
outside temperature is 34OC. The wall has a 1.5 m x 2.0 m flat glass
window.
                                                                                             Face
                                                                        Air space            Brick
           12.0 m
to = 34OC
           Window   1.5 m
                                         6.0 m
                                                     Plaster
                                                                                                            Q ST
                                                               Tile
                                                                      Air space
                                          IPE Laboratory-Air Conditioning System Design
                     Aw Δt
       QSW =
                       R TW
  4. a = 6.9 w/m2-k - for air space at 10 cm. thickness & assume 32OC mean temperature.
                 1 =      1
         R =                           = 0.145 m2-k/w
                 a   6.9 w/m2-k
7. fi = 8.5 w/m2-k - for still air w/ vertical orientation and horizontal heat flow direction.
            Aw Δt
QSW =
              RTW
             AG Δt
QSG =
               RTG
          1    x    1
RTG =        + kG +
          fo        fi
Where fo and fi have the same values with that of the wall.
AG = 2 x 1.5 = 3 m2
             (3 m2)(34-24) k
QSG   =
              0.238 m2-k/w
QSG = 126.05 w
                                          IPE Laboratory-Air Conditioning System Design
                       W
                 12:00 MN
                                            30O           E
                    6:00 PM                              12:00 NN
                                          2:00 PM
N ln2
                                                P•                       Parallel
                                                         β
                                                     Ф
                                                             S
                                                     H
ln1
                                  l     d
                   o                                                        x
                           h
                                                 •A
        y
      Latitude angle, l is the angular distance north (+) or south (-) from
the earth’s equator to a point on the earth’s surface.
                                                sinh
               Tan ϕ =
                                     sinl cosh + cosl tand
For values of d, use Table 17.5 page 579, Refrigeration and Air Conditioning by C. P.
Arora
                    Sunray
                                            Glass
                                                          Absorbed solar heat
                                                                   Inward flow
          Outward flow                                             of absorbed
          of absorbed                                              radiation (4%)
          radiation (8%)
QSG = (SHGFmax)(R)(A)
               R     = Solar Factor
                       - Used to adjust        the value of SHGF for other types of glass or internal
                               shading device.
                           -   Table 17-8, page 601 by Arora
Sun Ray
                                                     External
                                                     Shading
                                                                    Window
                                                                     Glass
                                                                             y
 δ
                                                                                 Sunlit
                      w
                                                                                 Area
               x
                                             E
               w
x ψ D
Sunlit Area
     x
               Elevation View of the Window
                       Not Drawn to Scale
                 y
    Tan ϐ =                            Eq. 1, see isometric view.
                 w
                 D
     Cos δ =                           Plan view.
                 w
                                             IPE Laboratory-Air Conditioning System Design
                            D
              w        =                            Eq. 2
                           Cos δ
From Eq. 1,
y = w Tan ϐ Eq. 3
                              Tan ϐ
              y        = D                             Solve for y in meters.
                              Cos δ
                                                                                -
                  Where: δ = ϕ + ψ
                           (+) -   If the outer side of the window glass is opposite sides of south.
                           ( ) -   If the outer side of the window glass is same side of south.
                                   x
                  Tan δ      =
                                   D
Example:
A window 2.4 m x 1.5 m is recessed 300 mm from the outer surface of
the wall facing 10O west of south. Other data are to be considered:
   Design month-------------------------------------- March 21
   Condition/Location-------------------------------16O35’35” North latitude
   Solar time`                                        3:00 PM
   Glass specifications:
     Thickness      ------------   6 mm
     Type ---------------------    Heat absorbing
     Internal Shading        ---   Medium Venetian blinds.
Estimate the sunlit area and the solar heat gain.
                                             IPE Laboratory-Air Conditioning System Design
Solution:
             From Table 17.5 page 579 by Arora, for the month of March
             21, d = 0O21” = 0.35O
ϐ = 42.79O = 43O
                                      sinh
            Tan ϕ =
                        sinl cosh + cosl tand
                                       Sin45
            Tan ϕ =
                       Sin16.6cos45 + cos16.6 tan0.35
ϕ = 73.62O = 74O
D E
                                  δ
                              ϕ
δ = ϕ - ψ = 74O - 63O
             δ = 64O
                                  IPE Laboratory-Air Conditioning System Design
y = 0.638
x = 0.615 m
A = (L - x)(h - y)
QSG = (SHGF)(R)(A)
R = (0.94)(0.75)(0.65)
R = 0.46
                    Convected
                                                         Absorbed solar heat
        Sunray
                                                                      Conducted
       Radiated
Reflected
QOW = Solar heat gain through opaque surfaces including heat gain due
      to temperature difference of outside and inside air with outside
      and inside film coefficients.
QOW = UwA(CLTD)
Example:
Calculate the solar heat gain through an opaque wall 22m x 15 m
made up of 100mm concrete block with 50mm insulation (blanket &
batt mineral fiber) facing SW with solar time 2:00 PM. Outdoor
maximum and minimum daily range recorded are 38OC and 20OC. The
room is to be maintained at 24OC temperature.
38OC 24OC
                Concrete
                                          Insulation
                 block
From MRII Tables and Charts, page 93, average density of concrete block at
200 mm thickness is 2100 kg/m3. At 100 mm, density is (100/200 x 2100) is
1050 kg/m3.
m = 105 kg/m2
Table 18.9, Page 602 by Arora 3rd Ed., at SW, 2:00 PM, m = 105 kg/m2,
MRII Tables and Charts, page 93, for concrete block, 200mm thickness,
R = 0.37 m2-k/W
                       0.37(100mm)
             R1 =                    = 0.185 m2-k/W
                         200mm
                                            IPE Laboratory-Air Conditioning System Design
Table 4-4, page 68, RAC by Stoecker, for mineral fiber, 75-90 mm or an
average of 82.5 mm thickness,
R = 1.94 m2-k/W
                       1.94(50mm)
              R2 =                     = 1.176 m2-k/W
                         82.5mm
For outside air film, cooling season, 3.4 m/s wind velocity,
Ro = 0.044 m2-k/W
Ri = 0.12 m2-k/W
             RT = Ro + R1 + R2 + Ri = 1.525 m2-k/W
                         1            1
              Uw =              =
                         RT         1.525
Uw = 0.6557 W/m2-k
A = 22 x 15 = 330 m2
Qsw = 3,894.85 W
QFlrs = FPtEF
QRoofs = URAR(RETD)
                     (L x W x H)(NC)
          V   =
                          3600
          L = Room length, m
          W = Room width, m
                                       IPE Laboratory-Air Conditioning System Design
                   H = Room height, m
                   NC = a + b(vel) + c(to – ti) = number of air changes
                        vel = outside wind velocity
                            = 3.40 m/sec for summer average value
                        a, b and c --- Infiltration constants, use Table 4-
                                         5, page 70 by Stoecker.
Example:
Determine the heat gain from the occupants doing light works for an
office building 150m x 70m. Working time is 8 hrs.
                           Floor Area, m2
          N    =
                     Space occupied per person
A = 150 x 70 = 10,500 m
N = Number of motors
QOL = (qLP)(N)
               N     =           Number of occupants
                         -        The same as in QOS
3. Ventilation standard VO
               N     =           Number of occupants
                                 - The same as in QOS