The mathematical model available in the literature to calculate the skin temperature required to determine the heat loss from the body of an average cow under different environmental and skin-wetness conditions is complex and iterative. This paper presents a simplified methodology, which can be used for quick and accurate estimation of the skin temperature as well as heat loss without a detailed understanding of heat and mass transfer and fluid flow concepts. Multiple linear regression (MLR) is first used to predict the skin temperature which can subsequently be used to compute various forms of heat losses from the body of the cow. It is found that the skin temperature predicted by the correlation obtained from MLR is accurate except for a few combinations of environmental and skin-wetness conditions where in the maximum error is found to be 8·9%. However, skin temperature of a cow can be more accurately calculated using a set of simple linear relationships proposed in this paper. In addition to this, simple correlations are also presented for the calculation of convective heat and mass transfer coefficients, boundary layer thickness, and latent heat of vapourisation. The use of the proposed correlations for calculating skin temperature is illustrated through an example. It is found that the skin temperatures, and total heat losses under different environmental and skin-wetness conditions predicted by the proposed methodology agree very closely with those available in the literature.

Notation

A_f

cross-sectional area of fur, m²

A_s

surface area of the cow, m²

A_t

total area (fur and air), m²

C_o

concentration of water vapour in the turbulent layer, kmol m⁻³

C_skin

concentration of water vapour on the skin surface, kmol m⁻³

D

mass diffusive coefficient of water, m²s⁻¹

d_h

hair diameter, m

f_eff

coefficient of effective radiant area

f_fur

ratio of fur surface area to skin surface area, %

H_R

relative humidity, %

h_c

convective heat transfer coefficient which has been corrected for the areal porosity of the hair coat, W m⁻² K⁻¹

h_m

convective mass transfer coefficient, m s⁻¹

h_r

coefficient of radiant heat transfer, W m⁻² K⁻¹

j

total mass flux of water vapour, kmol m⁻¹ s⁻¹

K₁

coefficient of linear correlation

K₂

coefficient of linear correlation

k_air

thermal conductivity of air, W m⁻¹ K⁻¹

k_eff

mean effective thermal conductivity of the fur layer normal to the skin surface, W m⁻¹ K⁻¹

k_fur

thermal conductivity of fur layer, W m⁻¹ K⁻¹

k_x

thermal conductivity of the fur layer along the horizontal direction, W m⁻¹ K⁻¹

k_y

thermal conductivity of the fur layer along the vertical direction, W m⁻¹ K⁻¹

l_c

coefficient

P_aamb

actual vapour pressure in the air at ambient temperature, Pa

P_samb

saturation vapour pressure at ambient temperature, Pa

P_sskin

saturation vapour pressure at skin temperature, Pa

Q_conv

convective heat loss, W

Q_evap

evaporative heat loss, W

Q_rad

radiant heat loss, W

Q_sensible

sensible heat loss, W

Q_total

total heat loss, W

R

universal gas constant, kJ kmol⁻¹ K⁻¹

r²

coefficient of determination

T_amb

ambient air temperature, °C

T_mrt

mean radiant temperature, °C

T_skin

skin temperature, °C

V_o

air velocity, m s⁻¹

W

weight of the cow, kg

β

skin-wetness level, %

λ

latent heat of vapourisation at the skin-surface temperature, kJ kg⁻¹

δ₁

thickness of fur layer, m

δ₂

thickness of a thin film of air layer above fur layer, m

ρ_h

fur density, hairs m⁻²

ε

radiant emissive coefficient of animal skin

Article Outline

Nomenclature

1. Introduction

2. Methodology

3. Results and discussion

4. Conclusions

Acknowledgements

Appendix A. Illustrative example

A.1. Example

A.2. Solution

A.2.1. Interpolation for intermediate wetness at the lower relative humidity

A.2.2. Interpolation for intermediate wetness at the higher relative humidity

A.2.3. Interpolation for intermediate relative humidity at the same wetness

References