Heat Load Calculations

Building Specs

Building location: Jacksonville, FL
Building area: 2,420 sf
Occupants allowed: 92
Infiltration loss: 1 – 2 ACH (air changes per hour) is typical
Outdoor air required: 15 – 25% of ventilation air
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Breathing zone

3″ – 72″ from the floor
24″ from the walls or AC equipment
Humidity: 30% – 35% (< 20% or > 60% is problematic)
Inside design temperature: 70 – 72˚F (cooling set point)
T_o = 92.8˚F (1% cooling DB)
T_o = 28.6˚F (99.6% heating DB)
ASHRAE Climatic Design Conditions

Rough Estimation

20 cfm/person (common minimum design standard) and a reheat system
The estimated cooling load is 0.25 – 0.35 tons per 100 sf of total building area

Q = 2,420 sf x 0.35 tons / 100 sf = 8.47 tons

Cooling Load

Q_dot = U x A x (T_i – T_o) or more accurate Q_dot = U x A x (CLTD)
Cooling Load Temperature Difference gives ~15% error
T_i = 70˚F
T_o = 92.8˚F
∆T = 22.8

Roof

A = 2,420 sf with 3′ attic air space
R = 1.79 (1/2” acoustical ceiling tile)
R = 30 (9-1/4” R-19 insulation)
U = 0.03
CLTD = 28 (L- light construction &; ∆T=95˚C)

Q_roof = 0.03 x 2,420 x 28 = 2,130 btuh

Doors

Glass door in the front (west wall)
Qty (2) 1-¾” insulated metal doors in the back (east wall)
A = 80” x 36” = 20 sf
U = 0.40 (Btu/hr-sf-°F)
CLTD = 16 (light construction &; 95˚C)

Q_doors = U x A x #_doors x CLTD = 0.40 x 20 x 2 x 16 = 1,220 btuh

Concrete Slab

4” thick slab = 0.333’
∆T = 5˚F
Slab edge of N & S walls have zero heat transfer
U_slab_face = 0.05
U_ slab_edge = 0.81
A_slab_face = 2,420 sf
A_ slab_edge = 0.333’ x (41’ x 2) = 27.33 sf

Q_slab = (0.05 x 2,420 + 0.81 x 27.33) x 5 = 715 btuh

Exterior Walls

Zero heat transfer from N & S facing walls

East wall

Height is 128” & length is 41’
Made of 12” concrete block, ¾” plywood, ½” sheetrock, 1″ stucco
R = 0.33 (7.5 mph wind outside)
R = 0.68 – 0.69 (inside vertical air film)
R = 4.76 (1” stucco)
R = 2.04 – 2.56 (12” LW (light weight) block)
R = 1.08 (3/4” plywood)
R = 2.22 (1/2” sheetrock)
CLTD = 16 (light construction & 95˚C)
Area of East wall = 128’ x 41” = 200 sf
A_wall = (12’ x 200’) – A_windows – A_E_door = 2,400 – 80 – 60 = 2,260 sf
U_total = 1/R_tot = 0.09
Q_E_wall = 0.09 x 2,260 x 16 = 3,255 btuh

West wall

U_total = 1/R_tot = 0.09
Area of West wall = 24” (above window) x 41’ + 16.5” x 104” x 3 (between windows) = 82 + 36 = 118 sf
Q_W_wall = 0.09 x 118 x 16 = 170 btuh

Q_wall_tot = 3,255 + 170 = 3,425 btuh

Windows

Solar radiation through glass
3 – 5 hours of peak sun per day
Q_fes = (A_s x SHGF + A_sh x SHGF_sh) x SC
Q_fs = Q_fes x CLF (space cooling load)
SHGF = Maximum Solar Heat Gain Factor, Btu/hr-ft² (use latitude 32˚N & June)
SHGF_sh = Shaded Solar Heat Gain Factor (East/West & May)
A_s = Unshaded Area of Window Glass
A_sh = Shaded Area of Window Glass
SC = Shading Coefficient
SL = Shade Line = Shade Line factor x shadow width beneath edge of the overhang
SCL = Solar Cooling Load (SCL = SHGF x CLF, where CLF takes into account time lag)
GLF = Glass Load Factor (GLF = SCL x SC)

Aluminum frame single-pane glass door & windows

U = 1.27 Btu/hr-sf-°F
Area of door = 72” x 104” = 52 sf
Area of window = 66” x 104” = 48 sf
6 windows
Area_tot = 52 + (48 x 6) = 340 sf
CLTD = 16 (light construction & 95˚F)

Q_windows = 1.27 x 16 = 6,910 btuh (less accurate)

Width of the overhang = 101”
SLF = 0.8 | SL = 0.8 x 101” = 81”
A_s = (1 – (81/104) x 340) = 75 sf
A_sh = 340 – 75 = 265 sf
SHGF = 1,169 Btu/sf-day / 8 hours = 146
SHGF_sh = 142 W/m ² x 0.0929 m²/sf x 3.41 Btu/h-W = 45
SC = 0.50 (blinds or translucent roller shade for single pane)
0.25 for white shades, 1.0 for no shades

Q_windows = (75 x 146 + 265 x 45) x 0.50 = 11,440 btuh (more accurate)

Lighting

Q = 3.412 x W x BF x CLF
3.412: converts watts to btuh
W: lighting capacity
BF: Ballast Factor (heat loss in the ballasts of fluorescent lights)
CLF: Cooling Load Factor (heat storage in the lighting fixtures)
Fluorescent lights
Qty (25) 4’X2’ fixtures with qty (4) 48” T12 lamps, 32 W per bulb, BF = 0.92
Qty (6) 2’X2’ fixtures with qty (2) 24” T12 u-shaped lamps, 32 W per bulb, BF = 0.94
CLF (1.0 is often used)

Q_lighting = 3.412 x [(25 x 4 x 32 W x 0.92 x 1.0) + (6 x 2 x 32W x 0.94 x 1.0)] = 11,270 btuh

Occupants

Qs = qs x n x CLF | Ql = ql x n
Qs & Ql = Sensible and Latent heat gains, btuh
qs & ql = Sensible and Latent heat gains per person, btuh-person
n = Number of People
CLF = Cooling Load Factor (capacity of a space to absorb and store heat is 0.91 – 1.0)
Activity type: office work
Activity level: moderate
Sensible heat gain is 250 btuh-person
Latent heat gain is 200 btuh-person

Q_occupants: 450 btuh-person x 92 people = 41,400 btuh

Equipment

Qty (59) computers (21” monitors) 30 W at idle & 130 W continuous
Fridge (15 ft³) = 150 W
Laser Printer is 70 W
Coffee maker is 2,590 btuh
Qty (2) 50” tv (Westinghouse) = 151.3 kWh/yr
Any other office equipment = 25% nameplate
Q = 3.41 x (59 computers x 130 W) = 26,150 btuh (21” monitors)
Q = 3.41 x (1 computer x 110 W) = 375 btuh (15” monitor)
Q = 2 x 151.3 kWh/yr x 0.3895 [(btuh) / (kWh/yr)] = 120 btuh (tv)
Q = 3.41 x 150 W = 510 btuh (fridge)
Q = 3.41 x 70 W = 240 btuh (laser printer)
Q = 2,590 btuh (coffee maker)
Q = 2,185 btuh (8 head soda machine)

Q_equipment_undiversified = 32,170 btuh

Q_equipment_diversified = 32,170 x 0.60 = 19,300

Q_l+s_r = 9,800 + 2,130 + 1,220 + 715 + 3,425 + 11,440 + 11,270 + 41,400 + 19,300 = 100,700 btuh

Ventilation

Rp: 5 cfm/person
Pz (no. of people): 92
Ra: 0.06 cfm/ft²
Az (floor area): 2,420 ft²
Ez (distribution effectiveness): 1.00
V_bz_dot = Rp x Pz x Ra x Az (ventilation rate, breathing zone outdoor air)
Voz_dot = V_bz_dot / Ez (zone outdoor airflow)
Voz = (5 x 92 + 0.06 x 2,420) / 1.0 = 605 cfm

Ventilation Air Cooling Load

engineeringtoolbox.com/cooling-heating-equations-d_747.html
Load on the coil due to leakage in the return air duct and the return air fan is negligible

Sensible heat in a cooling process of air

h_s = 1.08 x V_oz x ∆T | ρ = 0.075 lbm/ft³
T_o = 92.8˚F (dry-bulb) | T_i = 70˚F (dry-bulb) | ∆T = (T_o – T_i) = 22.8
h_s = 1.08 x 605 ft³/min x 22.8 = 14,900 btuh

Latent heat due to moisture in the air, in a humidification process of air

h_l = 4,840 x V_oz x dw_lb
dw_lb = humidity ratio difference (lb water/dry air)
T_wb = 25.4˚C = 77.7˚F (mean coincident wet bulb)
dw_lb = 0.0206
h_l = 4,840 x 605 ft³/min x 0.0206 = 60,320 btuh
h_t = h_s + h_l = 14,900 + 60,320 = 75,220 btuh

Q_t = Q_l+s_r + h_t = 105,740 + 76,395 = 182,135 btuh / 12,000 = 15.18 tons

Alternative method

h_t = 4.5 x V_oz x dh
dh = h_o – h_i (enthalpy difference)
h_o = 45.5 (using psychrometric chart at T_db = 92.8˚F & dw_lb = 0.0206)
h_i = 22 (using psychrometric chart at T_db = 70˚F & RH = 30%)
h_t = 4.5 x 605 x (45.5 – 22) = 63,980 btuh

Q_t = Q_l+s_r + h_t = 100,700 + 63,980 = 156,850 btuh / 12,000 = 13.07 tons