Medical Physiology, 3rd Edition

Modes of Heat Transfer

Maintaining a relatively constant body temperature requires a fine balance between heat production and heat losses

If body temperature is to remain unchanged, increases or decreases in heat production must be balanced by increases or decreases in heat loss, resulting in negligible heat storage within the body. If the body is at constant mass, the whole-body heat-balance equation expresses this concept as follows:

(59-1)

All terms in the foregoing equation have the units kcal/hr.

Several physiological processes contribute to temperature homeostasis, including modulation of metabolic heat production, physical heat transfer, and elimination of heat. These processes operate at the level of cells, tissues, and organ systems. Let us discuss in order the terms in Equation 59-1.

Metabolism (M) is the consumption of energy from the cellular oxidation of carbohydrates, fats, and proteins. For an athlete, the useful work on the environment (W) might be the energy imparted to an iron ball during the shot put event. However, because of a long list of inefficiencies—the inherent inefficiency of metabolic transformations (see pp. 1173–1174) as well as frictional losses (e.g., blood flowing through vessels, air flowing through airways, tissues sliding passed one another)—most metabolic energy consumption ends up as heat production (H = M − W). Table 59-2 shows the fractional contributions of different body systems to total heat production under sedentary, resting conditions.

Under conditions of maximal exercise,  (see pp. 1213–1215) may correspond to a total energy expenditure (M in Equation 59-1) of 1300 kcal/hr for an endurance athlete. If 60% of this energy evolves as heat—so that the athlete does ~500 kcal/hr of useful work on the environment—the rate of heat production will be 1300 − 500 = 800 kcal/hr (~960 watts) for a brief period of time. This change is equivalent to changing from an 85-watt light bulb to a 1000-watt space heater. Unless the body can dissipate this heat, death from hyperthermia and heat stroke (Box 59-1) would ensue rapidly.

As body core temperature rises, excessive cutaneous vasodilation can lead to a fall in arterial pressure (see p. 576) and, therefore, to a decrease in brain perfusion. As T_core approaches 41°C, confusion and, ultimately, loss of consciousness occur. Excessive hyperthermia (>41°C) leads to the clinical condition known as heat stroke. High temperature can cause fibrinolysis and consumption of clotting factors and thus disseminated intravascular coagulation (DIC), which results in uncontrolled vascular thrombosis and hemorrhage. Heat-induced damage to the cell membranes of skeletal and myocardial muscle leads to rhabdomyolysis (in which disrupted muscle cells release their intracellular contents, including myoglobin, into the circulation) and myocardial necrosis. Cell damage may also cause acute hepatic insufficiency and pancreatitis. Renal function, already compromised by low renal blood flow, may be further disrupted by the high plasma levels of myoglobin. Ultimately, CNS function is affected by the combination of high brain temperature, DIC, and metabolic disturbances.

Virtually all heat leaving the body must exit through the skin surface. In the following three sections, we consider the three major routes of heat elimination: radiation (R), convection (C), and evaporation (E). As the heat-balance equation shows, the difference between heat production (M − W) and heat losses (R + C + E) is the rate of heat storage (S) within the body. The value of S may be positive or negative, depending on whether (M − W) > (R + C + E) or vice versa. A positive value of S results in a rise of T_core, such as during exercise, whereas a negative value of S results in a fall in T_core, as would occur shortly after entering very cold water.

Heat moves from the body core to the skin, primarily by convection

Generally, all heat production occurs within the body's tissues, and all heat elimination occurs at the body surface. Figure 59-1 illustrates a passive system in which heat flows depend on the size, shape, and composition of the body, as well as on the laws of physics. The circulating blood carries heat away from active tissues, such as muscle, to the body core—represented by the heart, lungs, and their central circulating blood volume. N59-2 How does the body prevent its core from overheating? The answer is that the core transfers this heat to a dissipating heat sink. The organ serving as the body's greatest potential heat sink is the relatively cool skin, which is the largest organ in the body. Only a minor amount of the body's generated heat flows directly from the underlying body core to the skin by conduction across the body tissues. Most of the generated body heat flows in the blood—by convection—to the skin, and blood flow to the skin can increase markedly during heat defense. There, nearly all heat transferred to the skin will flow to the environment, as discussed in the next section.

FIGURE 59-1 Passive or unregulated heat transfer. In the steady state, the rate of heat production by the body core must match the flow of heat from the core to the skin, and from the skin to the environment. Certain CNS commands that are not directly involved in temperature regulation can affect heat flow. Examples include CNS signals that initiate sweating in response to hypoglycemia, changes in blood flow patterns in response to a fall in blood pressure, and changes in metabolism in response to alterations in thyroid metabolism.

Contributed by Ethan Nadel

In the simplest analysis, the rate of heat transfer from any tissue to the blood depends on (1) the rate of tissue energy production, (2) the temperature of the tissue, (3) the temperature of the incoming blood, and (4) blood flow through the tissue.

Inactive skeletal muscle, for example, has a low blood flow and a correspondingly low rate of metabolism. The rate of O₂ consumption ()—a measure of metabolic rate—averages 1.5 to 2.0 mL of O₂consumed per minute for each kilogram of muscle tissue. Because the temperature of resting muscle (33°C to 35°C) is lower than that of the body core (37°C), heat flows from arterial blood to inactive skeletal muscle. A similar analysis shows that heat moves from a highly active tissue such as the liver (38°C) to the blood, which distributes the heat to the other tissues of the body core.

The body's greatest potential heat source is skeletal muscle, which has a relatively large mass and can increase its rate of heat production >100-fold. Because skeletal muscle has such potential, it is useful for modeling heat transfer and changes in tissue temperature (eFig. 59-1). The energy balance equation for skeletal muscle is as follows:

 (NE 59-1)

The three terms on the left describe all the heat that the muscle gains or loses. If they add up to a positive number, muscle temperature increases. In the steady state, these three terms add up to zero, and muscle temperature is stable.

During the onset of exercise, the heat produced by metabolism increases rapidly. If the three terms on the left side of Equation NE 59-1 sum to a very positive number (which implies a large energy excess), muscle temperature rises rapidly. However, the dramatic increase in the rate of warming is relatively short-lived because of two factors: (1) The increase in muscle temperature reverses the temperature gradient between muscle and the blood perfusing it, so that heat now flows from muscle to blood. (2) Muscle vascular resistance decreases and cardiac output increases rapidly (see p. 581), so that blood flow through the muscle increases proportionally with the intensity of exercise. These adjustments are relatively complete within a few minutes. Increases of up to 30-fold in blood flow account for a proportional increase in heat transfer from active muscle to blood.

As exercise continues, muscle temperature increases to a new steady-state level, which causes more heat transfer from muscle to blood. The result is an increase in core temperature as warm venous blood leaving the muscles enters the body core.

EFIGURE 59-1 Energy flows in muscle.

The transfer of heat from core to skin occurs by two routes:

(59-2)

Both the conduction and convection terms in the previous equation are proportional to the temperature gradient from core to skin (T_core − ), where  is the average skin temperature, usually obtained from at least four skin sites. The proportionality constant for passive conduction across the subcutaneous fat (the body's insulation) is relatively fixed. However, the proportionality constant for heat convection by blood is a variable term, reflecting the variability of the blood flow to the skin. The ability to alter skin blood flow, under autonomic control, is therefore the primary determinant of heat flow from core to skin. The capacity to limit blood flow to the skin is an essential defense against body cooling (hypothermia) in the cold. A side effect, however, is that skin temperature falls. Conversely, the capacity to elevate skin blood flow is an essential defense against hyperthermia. On very hot days when skin temperature may be very high and close to T_core, even high skin blood flow may not be adequate to transfer sufficient heat to allow T_core to stabilize because the temperature gradient (T_core − ) is too small.

Although most of the heat leaving the core moves to the skin, a small amount also leaves the body core by the evaporation of water from the respiratory tract. The evaporative rate is primarily a function of the rate of ventilation (see p. 675), which in turn increases linearly with the metabolic rate over a wide range of exercise intensities.

Heat moves from the skin to the environment by radiation, conduction, convection, and evaporation

Figure 59-2 is a graphic summary of the heat-balance equation (see Equation 59-1) for an athlete exercising in an outdoor environment. This illustration depicts the movement of heat within the body, its delivery to the skin surface, and its subsequent elimination to the environment by radiation, convection, and evaporation.

FIGURE 59-2 Model of energy transfer between the body and the environment.

Radiation

Heat transfer by radiation occurs between the skin and solid bodies in the environment. The infrared portion of the electromagnetic energy spectrum carries this energy, which is why infrared cameras can detect warm bodies at night. The exchange (gain or loss) of body heat with another object by radiation occurs at a rate that is proportional to the temperature difference between the skin and the object:

(59-3)

R is positive when the body loses heat and negative when it gains heat.

One may not be very aware of radiative heat fluxes to and from the body, particularly when the T_radiant differs from the ambient environmental temperature (T_ambient), which tends to dominate our attention. Indoors, T_radiant is the same as T_ambient because surrounding objects thermally equilibrate with one another. Outdoors, radiating bodies may be at widely different temperatures. The radiant heat load from the sun to the body on a cloudless summer day may exceed the RMR by a considerable amount. The radiant heat load from a fire or a radiant lamp can provide substantial warming of bodies in the radiant field. Conversely, on a winter evening, the radiant heat loss from the body to a cloudless, dark sky—which has a low radiant temperature—may exceed RMR. Thus, one may feel a sudden chill when walking past an uncurtained window. This chill is caused by the sudden fall in skin temperature owing to increased radiant heat loss. Radiation of heat from the body accounts for ~60% of heat lost when the body is at rest in a neutral thermal indoor environment. A neutral thermal environment is a set of conditions (air temperature, airflow and humidity, and temperatures of surrounding radiating surfaces) in which the temperature of the body does not change when the subject is at rest (i.e., RMR) and is not shivering.

Conduction

Heat transfer by conduction occurs when the body touches a solid material of different temperature. For example, lying on the hot sand causes one to gain heat by conduction. Conversely, placing an ice pack on a sore muscle causes heat loss by conduction. However, under most normal circumstances (e.g., when one is standing and wearing shoes or recumbent and wearing clothes), the heat gain or loss by conduction is minimal.

Convection

Heat transfer by convection occurs when a medium such as air or water carries the heat between the body and the environment. The convective heat loss is proportional to the difference between skin and ambient temperature:

(59-4)

C is positive when the body loses heat, and negative when it gains heat.

Whereas the radiative heat-transfer coefficient (h_radiative) is constant, the convective coefficient (h_convective) is variable and can increase up to 5-fold when air velocity is high. Thus, even when ( − T_ambient) is fixed, convective heat loss increases markedly as wind speed increases. In the absence of air movement, the air immediately overlying the skin warms as heat leaves the skin. As this warmer and lighter air rises off the skin, cooler ambient air replaces it and, in turn, is warmed by the skin. This is the process of natural convection. However, with forced air movement, such as by wind or a fan, the cooler “ambient” air replaces the warmer air overlying the skin more rapidly. This change increases the effective convective heat transfer from the skin, even though the temperature of the ambient air is unchanged. This is a process of forced convection, which underlies the wind chill factor.

Evaporation

Humans can dissipate nearly all the heat produced during exercise by evaporating sweat (see pp. 1215– 1216) from the skin surface. The evaporative rate is independent of the temperature gradient between skin and environment. Instead, it is proportional to the water vapor-pressure gradient between skin and environment:

(59-5)

E is positive when the body loses heat by evaporation and negative when it gains heat by condensation.

The evaporation of 1 g of water removes ~0.58 kcal from the body. Because the body's sweat glands can deliver up to 30 g fluid/min or 1.8 L/hr to the skin surface, evaporation can remove 0.58 kcal/g × 1800 g/hr or ~1000 kcal/hr. Thus, under ideal conditions (i.e., when ambient humidity is sufficiently low to allow efficient evaporation), evaporation could theoretically remove nearly all the heat produced during heavy exercise (see p. 1195). As with convection, increased air velocity over the skin increases the effective vapor-pressure gradient between skin and the overlying air because of the faster movement of water vapor away from the skin.

The efficiency of heat transfer from the skin to the environment depends on both physiological and environmental factors. If ambient humidity is high, the gradient of water vapor pressure between skin and air will be low, thereby slowing evaporation and increasing the body's tendency to accumulate excess heat during exercise. This phenomenon underlies the temperature-humidity index—or heat index. Conversely, if ambient humidity is low, as in the desert, net heat loss from the body by evaporation will occur readily, even when ambient temperature exceeds skin temperature and the body is gaining heat by radiation and convection.

When the body is immersed in water, nearly all heat exchange occurs by convection, because essentially no exchanges can occur by radiation or evaporation. Because of the high conductivity and thermal capacity of water, the heat-transfer coefficient (h_convective) is ~100 times greater than that of air, so that the rate of body heat exchange is much greater in water than it is in air. It is therefore not surprising that nearly all the deaths in the Titanic shipwreck disaster resulted from hypothermia in the cold Atlantic waters, rather than from drowning.

When heat gain exceeds heat loss, body core temperature rises

With a knowledge of the transfer coefficients—h_radiative (see Equation 59-3), h_convective (see Equation 59-4), and h_evaporative (see Equation 59-5)—and the gradients of temperature and water vapor pressure between the skin and environment, we can calculate the body heat fluxes (R, C, and E). Knowing M (computed from  by indirect calorimetry, see pp. 1011– 1012) and W (if any), we can use the heat-balance equation (see Equation 59-1) to calculate the rate of heat storage. From this value, we can predict the rate of change in mean body temperature:

(59-6)

We can verify the accuracy of this predicted rate of change in  N59-3 by comparing it to the  measured by direct thermometry, using a weighted average of the measured T_core and average T_skin.

Contributed by Ethan Nadel

It is difficult to make an accurate determination of mean body temperature (). An approximation is that mean body temperature is 0.67 T_core + 0.33  in cold conditions, and 0.9 T_core + 0.1  in warm conditions. T_core is measured directly from the rectum (or esophagus), and  is the average skin temperature.

The body has to deal with two types of heat load that tend to make its temperature rise. In the heat-balance equation (see Equation 59-1), the term (M − W) constitutes an internal heat load. Although the term (R + C + E) normally reflects a net heat loss from the body, it can also be a net heat gain by the body—an external heat load, which can occur if either the radiation (R) or convection (C) terms are heat gains rather than heat losses. Thus, if we stand in the sun and T_radiant exceeds  (see Equation 59-3), we experience a radiant heat load. If we stand in a hot sauna and T_ambient exceeds  (see Equation 59-4), we experience a convective heat load. Clearly, both internal and external heat loads can result in net heat storage and thus a rise in body temperature. Changes in environmental temperature (T_radiant and T_ambient) exert their influence from the outside, through the body surface. If, starting from relatively low values, T_radiant or T_ambient rises, at first the rate at which heat leaves the body decreases, so core temperature tends to rise. Further increases in environmental temperature produce a frank heat load rather than a loss.

For the athlete, all the terms of the heat-balance equation are important because dissipating the thermal load is essential for prolonging exercise. The clinician must understand these principles to treat thermally related illnesses. For example, excessive heat exposure can lead to heat exhaustion, in which T_core rises to as high as 39°C if the body cannot dissipate the heat load. Failure of the body's heat-defense mechanisms arises principally from dehydration (which reduces sweating) and hypovolemia (which reduces blood flow from muscle to core to skin). Heat exhaustion is the most common temperature-related abnormality in athletes. In more severe cases, excessive heat can lead to heat stroke (see Box 59-1), in which T_core rises to 41°C or more, due to impaired thermoregulatory mechanisms.

Clothing insulates the body from the environment and limits heat transfer from the body to the environment

Placing one or more layers of clothing between the skin and the environment insulates the body and retards heat transfer between the core and the environment. In the presence of clothing, heat transfer from a warmer body to a cooler environment occurs by the same means as without clothing (i.e., radiation, conduction, convection, and evaporation), but from the clothing surface rather than from the skin surface. The insulating effect of clothing is described by the clo unit. By definition, 1 clo is the insulation necessary to maintain a resting person at a thermal steady state in comfort at 21°C with minimal air movement. Obviously, clo units increase with a greater area of skin coverage by clothing, or with thicker clothing.