## 12.2 Introduction

In the present module, we will calculate the exchange of heat between an animal and its physical environment. This is a problem of considerable biological importance. An organism’s energy balance is crucial to its survival. If it loses heat faster than it takes it or other forms of energy in, then eventually its temperature will drop to that of its surroundings. On the other hand, if the organism takes in heat faster than it gets rid of it, eventually it will become overheated. In both cases, the temperature extremes to which the organism is subjected may be outside the range in which it is able to function effectively or even to survive.

Moreover, it is clear that there is a good deal of variation in temperature regimes to which animals are adapted. Few tropical mammals and birds can survive prolonged periods of freezing weather. On the other hand, animals like sheep and polar bears may not be able to withstand high ambient temperatures, especially in combination with exposure to sunlight. Every animal has a preferred range of body temperatures. How it manages to maintain its body temperature within this preferred range is largely determined by its ability to control the factors which affect its heat balance.

For this reason, it is exceedingly important to identify the factors which determine an animal’s temperature and to understand the relative magnitude of their contributions. How important is sweating as a cooling process? Is a layer of fat as effective as one of feathers or fur in preventing bodily heat loss? Is there a relationship between body size and heat loss, and if so, how large must a warm-blooded aquatic animal be if it is to survive, say, in the waters surrounding Antarctica? It is only by carefully calculating the contributions of sweating, insulation, body size, ambient temperature, radiation, wind, humidity, and other factors to an animal’s heat balance that we can make useful answers to these questions.

Accordingly, it is the objective of this module to provide the reader with some of the intellectual equipment they will need to calculate the heat balance of an organism. Our approach will be to develop a mathematical model that represents the energy balance of an animal, to discuss briefly the theory of some of the components of the model (e.g., heat conduction, convection, and absorption and emission of radiation), and to apply these theories by working out the details of the energy budget of a familiar animal. Since the principles are perfectly general, the techniques developed here may be used for any organism, plant or animal, or the reader may even wish to apply them to such practical problems as determining the effect of additional insulation on his yearly household fuel bill or the practicality of attempting to capture solar energy in Seattle, Chicago, or New York!

An animal can exchange heat with its environment by absorption or emission of radiation, by evaporation of water from its surface, and by conductive or convective exchanges of heat with its surroundings. Moreover, heat moves from the animal’s body through its layers of insulation (fat and fleece) by the process of conduction. We will confine our attention to the equilibrium or “steady state” case, in which rates of heat loss and gain are equal. A solution to the more complicated situation, in which the rate at which the organism gains or loses heat changes in response to changing environmental conditions, is available in the computer model of Vera et al. (1975).

If we assume that the animal is in thermal equilibrium with its environment, our analysis boils down to an identification of all sources of energy loss and gain. Our assumption of thermal equilibrium, which greatly simplifies the analysis, is not entirely unrealistic. Thermal equilibrium implies that the total energy gained by the animal equals total energy lost. If an animal is to maintain its body temperature within a relatively narrow range, it cannot afford to gain or lose substantial amounts of heat. If it finds itself out of thermal equilibrium, it must make suitable adjustments. These may include moving into the shade or increasing its rate of energy loss by panting or sweating if heat gains are excessive or increasing rate of metabolism in case heat losses are very great. Having made these adjustments successfully, the animal returns to its “average” state of equilibrium. Any prolonged, substantial departure from this state constitutes a crisis which, of course, may terminate in the animal’s death.

To fix our ideas, we choose an unshorn domestic sheep as our study organism. The sheep is convenient because it is a familiar animal which has been thoroughly studied by a number of veterinary scientists (e.g., Blaxter, 1962; Brockway, McDonald and Pullar, 1965; Joyce, Blaxter and Park, 1966). In addition, the energy balance of the sheep has been studied by Priestley (1957), Monteith (1973), Porter and Gates (1969), and Vera et al. (1975). Experimental work by Walsberg et al. (1978) and theoretical studies have shown that under certain environmental conditions it becomes important to take into consideration the penetration of radiation and wind into the wool. These complications are not included in the present model, which must therefore be considered only a first approximation to a more correct approach. In the present module, we adopt the general method of analysis put forward by Porter and Gates, but in may details we follow Priestley and, in some cases, Monteith.