More Heat Transfer from Elephant Ears

Elephants use their ears for thermo-regulation. You might wonder how much of this provocative idea is true. Is there any validation? We shall detail now the quantitative validation procedure with experimental data support from the research literature [1].

A big African elephant weighs anywhere between 2000 kg to 4000 kg. A 4000 kg elephant needs to maintain a heat loss of 4.65 kW or more while moving and feeding (taken from [3]). This indicates that the elephant not only generates much energy but also must have an effective means of thermo-regulation to allow this excess energy to escape out as heat. Assuming most of this excess heat needs to be released from the pinna (ear region) of the elephant, this can happen through radiation and convection heat transfer to the surrounding air. The convection can either be natural or forced depending on whether the elephant ear flaps is stationary or swinging. Further, the flapping rate determines the forced convection to be laminar or turbulent. Let us analyze in detail.

The radiation heat transfer (loss) can be calculated as

$Q_R = \sigma \epsilon A (T_S^4 - T_a^4) \cdots (1)$

where, $\sigma = 5.67 \times 10^{-8} W/m^2K^4$ is the Stefan-Boltzmann constant and $\epsilon$ is the emissivity of the elephant ear surface taken to be equal to 0.96, the standard value for biological tissue (from [4]). The average surface area of the elephant ear, A, can be found once the average length and breadth of the elephant ear are measured. Further the average surface temperature of the elephant ear, $T_S(\deg C)$ and the ambient air temperature $T_a (\deg C)$ also should be measured before one can arrive at the radiation heat loss.

The convection heat loss can be calculated as

$Q_C = hA(T_S - T_a) \cdots (2)$

where h is the combined natural and forced convection heat transfer coefficient of the configuration, which needs to be determined. The rest of the symbols are as defined earlier.

In the case of natural convection heat transfer from the elephant ear, it can be calculated using the correlation

$Nu = h_{nc}L / k = 0.15Ra^{1/3} = 0.15\left(\frac{g\beta (T_S - T_a)}{\alpha \nu}\right)^{1/3} \cdots (3)$

where $Nu_NC$ is the non-dimensional form of the natural convection heat transfer coefficient and Ra is the non-dimensional Rayleigh number, which controls the magnitude and strength of natural convection. The above correlation is for turbulent natural convection (page 372, [5]), an assumption made due to the flapping of the elephant ear.

Other symbols are: k is the thermal conductivity of the elephant ear tissue (W/m.K); L is the characteristic length along which natural convection prevails (equal to 4A/p, where p is the perimeter of the elephant ear); g is the acceleration due to gravity $(m/s^2)$ ; $\beta$ is the coefficient of volumetric thermal expansion (1/K); $\alpha$ is the thermal diffusivity (m²/s) and $\nu$ the kinematic viscosity or momentum diffusivity ( $m^2/s$ ) of the surrounding air. The temperatures are as defined earlier and observe as before, they are the only required measurements. The rest of the properties are obtained at film temperature (simple average of the surface and ambient temperature) from standard data books.

The turbulent forced convection heat loss can be calculated by assuming the elephant ear as a heated flat plate undergoing turbulent forced convection cooling in the surrounding air. The forced convection heat transfer coefficient can be calculated using the correlation (page 357, [5])

$Nu = 0.037Re_L^{4/5}Pr^{1/3} = 0.037\left(\frac{UL}{\nu}\right)^{4/5}\left(\frac{\nu}{\alpha}\right)^{1/3} \cdots (4)$

where Re_L is the characteristic length based non-dimensional Reynolds number, a parameter that determines the flow to be laminar or turbulent and Pr is the Prandtl number, the ratio of the diffusivities defined earlier. Here only the average velocity of the flow, U (m/s), near the elephant ear needs to be measured. The rest of the properties are obtained as before at the film temperature of the configuration.

In summary, to determine the heat loss from the elephant ear, one requires measurement of the ear surface temperature, the ambient temperature and the velocity of air flow around the ear, while it is flapping. For instance, upon simplification the resulting heat transfer coefficients from Eq. (3) and (4) are $h_{NC} = 1.81(T_s-T_a)^{-3}$ for natural convection and $h_{FC} = 5.76V^{0.8}L^{-0.2}$ for forced convection. The velocity V can be calculated using V = L(N/60) where L is the arc length of the ear flapping and N is the number of flapping made in 1 minute. Using these relations we can find $Q_C$ the heat loss by convection given in Eq. (2), which when summed with $Q_R$ the heat loss by radiation given in Eq. (1), results in the total heat loss from the elephant ear flaps.

Experiments that measure the above required temperatures and velocity were conducted and reported in a research paper by Polly Phillips and Edward Heath in 1992 [1]. For four African elephants (Loxodonta Africana), they measured the ear (pinna) surface temperature using infrared thermography under ambient conditions varying between 18 °C and 32 °C. They also measured the velocities of turbulent air flow around the ears for each case. From reference [1], for <i>Mame</i>, an elephant weighing 2000 kg, height = 2.31 m, ear surface area = $15.9 m^2$ and having a standard metabolic rate of 0.8 W/kg, one set of the reported measured values of the parameters are as follows: V = 5 m/sec, $T_S = 33.97 \deg C$ and $T_a = 27.2 \deg C$ .

The convection correlations used in reference [1] have been improved in the last decade, as presented in our Eq. (3) and (4). However the major conclusions remain aligned with that of the original paper. So, using the experimental values from [1] in the procedure detailed above from Eq. (1) to (4), results in a total heat loss of Q = 76.21W from one side of one ear of Mame. For all the four sides of the two ears, this translates to about 325 W, twenty five percentage of the standard metabolic rate of 1643 W of Mame. Further, Polly Phillips and Edward Heath report in their paper [1] that using the flat plate model of the ear flap, for a wind velocity of 5 m/sec around the ear, when $T_S = 36 \deg C$ and the temperature gradient is $20 \deg C$ , the heat loss raises to 1500 W, about 91 percentage of 1643 W, the standard metabolic rate of Mame.

For an Asiatic elephant of the same size and metabolic rate but with only one third the ear size of the African elephant, the paper reports, loses only 544 W in similar situation, amounting to only 33 percentage of the standard metabolic rate.

In their subsequent research [6], the same authors show that the elephant ear adapts its temperature to the surrounding temperature by vaso-dilation, a thermo regulatory body mechanism by which the organism dilates the blood vessels to increase or decrease blood flow in a localized region. This ensures the favorable temperature gradient for the elephants to maintain their ear heat loss. In another 2001 paper [7], on a lighter vein, these authors use the simple flat plate convection heat transfer model of the elephant ear to analyze the usefulness of the ear size of Dumbo, the Disney elephant character.

Additional research material discussing the hotness of the savannah climate and the elephant adaptation and thermoregulation in other animals are provided in [8] and [6]. These research literature, [3] [6] and [8], provide quantitative support and substantiate well that the elephant ears serve as a thermo-regulatory mechanism, capable of transferring up to 100 percent of the heat loss requirement.

Related Article: Why do Elephants have Big Ear Flaps

Main Reference discussed:

Narasimhan, A. (2008). Why do elephants have big ear flaps? Resonance, 13 (7), 638-647 DOI: 10.1007/s12045-008-0070-5

References

Phillips, P. K., and Heath, J. E., Heat exchange by the pinna of the african elephant (Loxodonta africana), Comparative Biochemistry and Physiology Part A: Physiology, v. 101, 693-699, 1992. Abstract
Image adapted from pictures at elephant country web
Wright P. G., Why do elephants flap their ears? S. Afr. J. Zool. 19, 266-269., 1984.
Mohler F. S., Oscillating heat flow from the pinna of the ear of the rabbit (Oryctolagus cuniculus), Ph.D. thesis, University of Illinois, 1987.
Bejan, A., Convection Heat Transfer, 3rd edition, John Wily & Sons, NY, 2003.
Phillips, P. K., and Heath, J. E., Dependency of surface temperature regulation on body size in terrestrial mammals, Journal of Thermal Biology, Volume 20, Issue 3, , June 1995, Pages 281-289 Abstract
Phillips, P. K., and Heath, J. E., Heat loss in Dumbo: a theoretical approach, Journal of Thermal Biology, Volume 26, Issue 2, , April 2001, Pages 117-120. Abstract
Kinahan, A. A., Pimm, S. L. and van Aarde, R. J., Ambient temperature as a determinant of landscape use in the savanna elephant, Loxodonta africana, Journal of Thermal Biology Vol. 32, Issue 1, January 2007, Pages 47-58. Abstract

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More Heat Transfer from Elephant Ears

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