## Estimation of the body surface area and its impact on the heat transfer by convection in sheep: A computational way

journal contribution

posted on 08.08.2017, 17:00 by Bruno Rodrigo Simão, Alex Sandro Campos Maia, Patric André Castro, Gustavo André Bernado Moura, Vinicius de França Carvalho Fonsêca: The aim of this work it was to validate the 3D
modeling to obtain the body surface area of animals, and determine the impact
on the rate of heat transfer by convection in Corriedale sheep when include
legs and head in the standard cylindrical model. Five shorn Corriedale sheep weighing
between 29 and 105 kg (two breeders, one young male and two young females) were
used. A regression equation, standard cylindrical model, hand instrument and 3D
modeling were used to obtain surface area. Data were analyzed by least-squares
methods and a non-linear regression was applied with geometric adjust in a
power function. Pearson correlation was tested. Coefficients were highly significant (p<0.01). Body
surface area and weight presented high (r = 0.99) correlation. From the power function (allometric equation)
adjusted in the regression equation, the coefficient “b” assumed the following
values 0.5025, 0.6122 and 0.6391 and the coefficient “a” 0.171, 0.1117 and
0.1045 for Bennett’s equation, 3D modeling’s and instrument’s equation,
respectively. Coefficients differences between the present investigation and
Bennett’s work can be explained by the intraspecific relationship and range of
body weight considered, once he used Merino sheep from 23 to 63 kg and we
worked with corriedale sheep from 29 to 105 kg. Considering an animal of 63 kg,
Bennet’s equation presented an underestimate value to the body surface area over
the 7.3 % and 8 % when compared with hand
instrument’s and 3D Model’s, respectively. Furthermore, this error increases at
least 3% if we considered a 100 Kg Corriedale sheep. At this condition, 3D model with hand
instrument presented less than 1% of the difference. The use of simple
horizontal cylinder causes an underestimated on the rate of heat flow by
convection because legs and head can represent 35 %, on average, of the total body
surface area in a Corriedale sheep of 100 Kg. Thus, 3D modelling seems to be
the best way to obtain the animal surface area, and certainly, appears as a
tool to improve research involving heat and mass transfer and animal breeding.