# Heat

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```					                    WP3 Food quality and safety
T6 Animal welfare-environment-food quality interactions:
production consequences.
WP3T6L1EE Heat exchange in cowshed
Heat and humidity balance in the cowshed

Cowshed air exchange calculations can be based on the heat and humidity balance.
Separate components of heat balance must be determined to find out total energy
losses
In livestock housing the main heat sources are animals.
Energy is consumed to heat the ventilation air and compensate for the heat losses
through boundaries and vaporization. Total, sensible or latent heat can be the basis
for heat balance formula.
Sensible heat balance of cowshed can be found with the following formula:
qv  q s  q p  q a  qo  0                      (1)

where qv - sensible heat gain, W,
qs -capacity of continuously powered equipment, W
qp - heat losses through the building boundaries, W
qa - heat losses due to vaporization from wet surfaces, W
qo - heat loss due to ventilation, W

Sensible heat gain qv

Livestock produce various quantities of metabolic heat (total heat production qk)
depending on the type of animal, its body weight, production and environmental
conditions. A portion of heat is dissipated in the form of sensible heat qv (non-
evaporative heat) and the rest as latent heat ql (evaporative heat).
Emission rates are described in normatives, e.g. the normatives suggested by the
International Commission of Agricultural Engineering (Commission Internationale du
Geine Rural, CIGR).
Total heat production rate (qk, W) for dairy cow is found on the basis of average
feeding level at 20 ºC.
5 3                    (2)
qk  5.6m         1.6 10 t  22 p,
0.75

where m – body mass, kg
t – number of gestation days
p – daily milk production, kg
Total heat output rate might be adjusted according to the air temperature.

k k  4 10 5 (20   ) 3  1                      (3)
 - real air temperature, °C.
For a 650 kg cow with milk production of 25 kg/day and 140 days of gestation, the
total heat production is shown in figure 1.
2500
Total heat production, W

2000

1500

1000

500

0
-7    -1   4     10   16    21       27
Environmental temp, °C

Figure 1. Total heat production of 650 kg cow.

If the environmental temperature is higher than +10 °C sensible heat rate (q                               v   in
watts) is found from the total heat output rate qk with the following ratio:

qv  qk 0.8  1.85 10 (  10 )
7        4
                       (4)

2000
Sensible heat production, W

1500

1000

500

0
-7    -1     4        10    16       21    27
Environmental temp, °C

Figure 2. Sensible heat loss in the cowhed.
Latent heat rate (ql in watts) is:
ql  qk  qv                                                                                       (5)

Considering that 680 W·h/kg (2450 kJ/kg) is used to vaporize 1 kg water, the emitted
amount of vapour from one animal w (kg/h) is found according to the following ratio:
w  1.47 10 3 ql                                           (6)
Sensible heat and latent heat are the critical components of the heat and moisture
balance. Sensible heat is useful in cold weather and a problem in hot weather. Latent
heat must be removed from the building in cold weather and can be useful in hot
weather.
Heat losses through building boundaries, qp W
Heat transfers from a high-temperature body to a low-temperature body. Heat
exchange takes place by means of conduction, convection and radiation.
Heat exchange through enclosures takes place mainly by conduction, which is
specific for solid opaque bodies.
Convection takes place in gases (e.g. air) and fluids and occurs at the boundary
surface.
Heat exchange by radiation is possible in the environments transparent for infra-red
Heat transfer (q) through multi-layer enclosure can be calculated with the following
formula:
s  v
qF
1            1
 i                                             (7)
s       i  v
where F – area of enclosure, m2
s – indoor air temperature , °C
v – outdoor air temperature, °C
2
άs – heat transfer coeff. from indoor air to wall, W/(m K)
2
άv – heat transfer coeff. from wall to outdoor air , W/(m K)
δ – thickness of structural component, m
 – thermal conductivity of structural component, W/(mK)
1             1
 i          is the reciprocal value of thermal conductance (U-value) and is
s       i  v
known as thermal resistance (R –value, (m²K)/W). Cowsheds are called either
insulated or uninsulated. Insulated cowshed have multilayer boundaries which have
significant thermal resistance (R-value) that uninsulated cowsheds conversely do not
have.               1       2      3
 10 cm 12,5 cm 10 cm                               <1 cm

v=5 ºC                     s=7 ºC
1                        s=15 ºC

3
v=-2o ºC                                           =0,9          W/(m·K)

= 0,5     0,04    0,9    W/(m·K)             R= 0,07        0,13   m2·K/W
0,01
R= 0,07 0,2     3,13   0,11 0,13 m2·K/W
Rtot=0,07+0,2+3,13+0,11+0,13=3,64 m²K/W         Rtot= 0,07+0,01+0,13=0,21m²K/W

Figure 3. Temperature change in wall: 1 – masonry wall, 2 – heat insulation, 3–
concrete wall,  – thermal conductivity, 1 –outside surface temperature, 3 – inside
surface temperature, v – outside temperature, s – inside temperature, R –
thermal resistance
Example 1
Heat losses through the boundaries in insulated and uninsulated cowshed
Building 30*88 m, roof area 2735 m², walls area 708 m² (Figure 4)
a) insulated:
qroof=2735*(15-(-20))/3.64=26298 W
qwalls=708*(15-(-20))/3.64=6808 W
b) uninsulated:
qroof=2735*(7-5)/0.21=26047 W
qwalls=708*(7-5)/0.21=6743 W

a)

b)

Figure 4. Heat losses through the boundaries in insulated (a) and uninsulated (b)
cowshed (pay attention to the differences of ambient and indoor temperatures).

Heat loss due to ventilation, qo W

Heating and humidifying are the processes occurring in the cowshed (Figure 5 and
6).
Sensible heat loss qo due to ventilation can be found by the formula
qo= qv3 – qv1,                                                     (8)
where
qv3 – enthalpy of warmed air (W or kJ)
qv1- enthalpy of ingoing air (W or kJ)
qv3 – qv, expresses the amount of sensible heat added to ventilation air in kJ
Figure 5. Moisture pickup by ventilation air exchange in livestock building.

Figure 6. Heating and humidifying process in building (Esmay and Dixon, 1986).

It is very convenient to use psychometric chart for calculations of enthalpy (Figure 6)
or any other component of heating and humidifying process. Enthalpy is an energy
content of water or an air water vapoure mixture (Esmay and Dixon, 1986).
Note! The values of enthalpy are relative. It is 0 kJ/kg at 0°C and 0% of RH. Minus
sign does not indicate at any deficit of enthalpy.
1 kg of outside air with temperature -20°C and RH 80% has enthalpy qv1= -18.8 kJ.
(see point 1 at figure 6). Heating to temperature 15°C needs 16-(-18.8)= 34.8 kJ of
sensible heat (point 3 at Figure 6). During the heating process specific volume of air
increases from 0.717 to 0.817 m³/kg, humidifying to 15°C and 80% of RH 36.7-
16.0=20.7 kJ (point 2 at Figure 6).
Ventilation rates

For the calculation of ventilation rates sensible and latent heat must be discussed
separately.

Ventilation rate Vair, sensible heat (l/s) for removing sensible heat can be
calculated by the formula:
Vair, sensible heat = (qo/(qv3-qv1))*v,                              (9)
where v – specific volume of air in m³/kg

Ventilation rate Vair , latent heat (l/s) for removing latent heat can be calculated by
the formula:
Vair , latent heat= (ql/(qv2-qv3))*v,                                  (10)
where qv2-qv3 - the latent heat difference between ambient and indoor air (kJ)

Example 2:

There are 300 cows in a cowshed described in example 1. Total heat production of
cow at 15°C is about 1300 W (Figure 1). Sensible heat production per cow is 800 W
(Figure 2) and latent heat production ql= 1300-800=500W.

Ventilation rate for removing sensible heat can be calculated by formula 9.

v = 0.827m³/kg at 15°C and 80% RH (also found in the psychometric chart).

As qs and qa do not have significant value, sensible heat available for ventilation
can be found by the formula:
qv= qv-qp                                                    (11)

qp=26298+6808=33106 W (Figure 4)

qv=300*800-33106=206894 W

Vair, sensible heat=206894/(16.0-(-18.8)*0.827=4917 l/s
4917/300= 16.4 l/s*cow

Ventilation rate based on humidity (latent heat) balance
Latent heat production in the cowshed is ql =300*500=150000 W and according to
formula 10
Vair , latent heat=150000/(36.8-16.0)*0.827=5963 l/s.
5963/300 = 19.9 l/s*cow.
Ventilation rate necessary for removing water vapour exceeds the ventilation rate
available from sensible heat and extra heating is needed at the outside temperature
of -20°C. If no supplemental heat is available condensation will build-up in the
cowshed.
By using formulas 9, 10 and 11 ventilation curves for different ambient temperatures
can be drawn (Figure 7). Indoor conditions considered in example 1 and 2 show that
ventilation is optimal at the ambient temperature -12...-13°C, when both ventilation
rates are approximately the same. Removing sensible heat will cause a problem in
warm and hot weather. In that case evaporative cooling a process of converting
sensible heat to latent heat may be used.

40000

35000

30000
Ventilation l/s

25000
sensible heat
20000
latent heat
15000

10000

5000

0
-20   -15   -10   -5    0      5    10
ambient temp °C

Figure 7. Ventilation curves for sensible and latent heat.

Humidity balance can also be expressed through the amount of water vapour.
The amount of water vapour of ambient (incoming) and indoor (outgoing) air can be
found in the psychometric chart. Formula 6 is the basis for calculating the water
vapour production by cattle.

Literature

Aerial Environment in Animal Housing. CIGR Working Group Report Series nr. 94.1.
Climatization of Animal Houses. Report of Working Group CIGR, Commission Internationale du Gėnie
Rural. Aberdeen, 1984.
Esmay, M. L. and Dixon, J. E. 1986. Environmental Control for Agricultural Buildings. The AVI
Publishing Company, Inc, Westport, Connecticut
Livestock Housing. Edited by C. M. Wathes, D. R. Charles. CAB International, 1994, 428 p.
Liiske, M. 2002. Sisekliima. Tartu: EPMÜ, 188 p.

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