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Specifically: what are some biological structures that could help subvert the square-cube law's effects on animal overheating?

Bob is a really, really big land-based ambush predator that's normally sedentary but that puts on massive bursts of speed in order to catch his prey.

The problem with this is, like with many such things, the square-cube law. Specifically, big animals have issues dumping heat quickly, since they have more volume, and therefore, mass, relative to their surface area. Therefore, if Bob exerts himself for too long, Bob will overheat, and it won't be pretty.

When at rest, or going for a stroll, Bob doesn't produce enough heat to overheat himself. He might be warm to the touch, but he's doing fine in terms of body temperature. However, when Bob is running, fighting, or otherwise exerting himself, he can't dump heat quickly enough to stay alive. Sometimes, Bob has to do these things for a long, long time, because his prey has a tendency to run him down over the course of day-long periods if they believe he's responsible for any deaths in the area; as such, limiting activity to brief bursts is not an option. As such, please do not answer with this.

A common solution I've seen to this would be to make Bob less dense. However, Bob's prey is very good at fighting back with a wide variety of lethal weapons, and so Bob needs to be as dense as water, on average, in order to contain enough mass and therefore enough bodily structures to fight well and withstand damage long enough to heal. As such, please do not answer with a decrease in Bob's density, because Bob would rather not die, thank you very much.

Please note that I am referring to biological structures, not behavioral adaptations - "biological structures" in this sense include the brain, the blood cell, bones, and other such things, whereas "behavioral adaptations" are things such as "this animal is aggressive" or "this animal is nocturnal".

Additionally, please note that I am not interested in determining what evolutionary pressures might lead to this. Assume it's being built in a mad scientist's lab.

Good answers will will cite a biological structure/bodily feature/design adaptation/etc. capable of storing, rapidly dispersing, or otherwise mitigating heat that's also capable of existing under Earth-like conditions and that is compatible with Earthly biochemistry.

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    $\begingroup$ How big is "really really big" exactly? Xenomorph? T-Rex? Godzilla? $\endgroup$
    – Philipp
    Dec 13, 2021 at 15:15
  • $\begingroup$ @Philipp Hopefully, these answers will scale regardless. $\endgroup$
    – KEY_ABRADE
    Dec 13, 2021 at 16:45
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    $\begingroup$ This likely wouldn't work in anything with remotely hard science, but releasing the heat as some sort of fire breath could be cool $\endgroup$ Dec 13, 2021 at 21:08
  • $\begingroup$ @RedwolfPrograms You might be surprised. Thermal management on spacecraft is an engineering challenge since there's no air to moderate temperatures. As such, the heat transferred into gases expelled by thrusters is important to consider. As long as your fire breath doesn't come from some kind of exothermic process like combustion, it's totally viable... better yet, an endothermic process to absorb the heat, so ice breath? $\endgroup$
    – drmuelr
    Dec 14, 2021 at 0:16
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    $\begingroup$ @KEY_ABRADE basically no answer will scale very far, that is the totality of the square cube law. $\endgroup$
    – John
    Dec 14, 2021 at 22:43

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This builds off the answer by Lemming: Perhaps you could give Bob some gills, like fish, even though Bob is a land creature. The gills help aerate the internal organs with cool air (rapid moving air) on the inhale, and then expel heat from around the critical organs on the exhale. My thought behind this is that no matter how warm air is, when it is blowing across hot skin it has a cooling effect.

Perhaps the gills could be part of a secondary (involuntary) respiration system that kicks in on its own rather than being consciously performed (or even vice versa). The gills wouldn't lead to the lungs but rather a series of intercostal tubes that surround the organs expressly for the purpose of removing heat through rapid air movements. It provides the wicking effect of the rapid movement of air as well as the increased surface area presented by the other commenter.

https://www.livescience.com/34062-breeze-feel-cool.html

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  • $\begingroup$ "but rather a series of intercostal tubes that surround the organs expressly for the purpose of removing heat through rapid air movements." Water cooling is far more effective than air cooling for moving heat, so the animal's circulation system would be better for this. However, do like the idea of 'gill'-like structures as radiators. $\endgroup$
    – NPSF3000
    Dec 15, 2021 at 2:02
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Biological methods to reduce internal body temperature:

  • Increase surface area of skin, via cracks, and folds (mentioned elsewhere) like an elephant.

Folded, cracked elephant example

  • Use extrusions of the skin to increase surface area, and use them to pump blood through to cool blood. Elephants have this with their ears, but some elephants don't need this, so have smaller ears. Lets compare the african and asian elephants.

Asian elephant, smaller ears, left, African elephant large ears left

  • Use internal openings, wet from internal moisture, to cool off. Many, if not most mammals, use this method of "Wet" cooling off in dry weather with their tongues, and the inside of their mouths.

dog with tongue out

  • Even plants attempt to cool off with this method, though it does appear like sweating, it is more so that holes inside leaves open, rather than water is excreted out.

transpiration

  • Use externally wet methods of cooling off, ie sweat glands what humans do. Requires mostly exposed skin for this to work.

sweating skin

  • Light coloration can be used to reflect radiated energy instead of absorbing it and turning it into heat.

fennic fox leapord gecko

  • With mammals near the equator, usually this coloration applies to the fur, often what happens is this coloration is tied into the environment, so not completely white. The skin of the animal however is still very dark. The production of melanin is used to block UV radiation, preventing skin cancers. You'll find many animals with dark noses and even tongues because of this melanin issue, even in hot environments. It's common knowledge that this applies to humans, but it also applies to dogs like the Xolo breed dog of Mexico, which actually tan like we do. This isn't so much a heat adaptation, but an equatorial adaptation

Xolo pup, next to adult

  • Lower metobolic rate, to decrease internally produced body temperature. The metobolic rate of elephants for example, is much lower than that of small animals like mice:

two graphics with body mass and metobolic rate

  • Use ectothermy, to derive your temperature mostly from the outside world. Reptiles do this, and have created some truly massive predators that weren't dinosaurs, but traditional basal reptiles and basal archosaurs (snakes, turtles, crocadilimoprhs) were able to achieve massive sizes. Ectothermy, cold-blooded ness, is where body temperature is mostly determined by the environment (though, even ectotherms, at very large sizes, will start having internal dynamics with increasing body temperature with out adaptation). During the period directly after the fall of the dinosaurs (paleocene), the largest animals on earth weren't birds, or mammals, they were reptiles, reptiles at sizes bigger than they had ever been even during the Mesozoic (reign of the dinosaurs). The temperature of the earth was very hot, hotter at some points than it was during the age of the dinosaurs, and certainly hotter than today. This, in combination with niches opening up, enabled massive reptiles to prosper, like titanaboa, Carbonemys, and various extremely large crocodilians like Euthecodon.

  • Use of Mesothermy. Mesothermy is basically anything in-between ecto and endothermy. One hypothesis for why Sauropods were able to get so big is their use of mesothermy. While many dinosaurs were likely endotherms, albeit with possibly lower metabolisms like the African Elephant, at the sizes Sauropods reached, they would have cooked themselves. However, despite being so large, Sauropod babies were extremely small comparatively, "no larger than geese", their parents were "10000 times heavier" than they were. At those sizes, baby sauropods would likely not have had ectothermy, as they'd otherwise be relegated to the same niches as similar sized reptiles, though even more vulnerable. What's more, is that dinosaur babies grew extremely fast. They couldn't afford to be slow lumbering beasts, these babies had to eat a lot and eat fast. Hypothesis have been thrown out that the smaller babies had different metabolic characteristics than adults, and that adults metabolism wouldn't have matched either ectothermy or endothermy. The idea that traditionally ecto/endo/thermic animals could achieve something different than strict cold/warm bloodedness or transition has been seen in naked mole rats, which have transitioned to a mostly ectothermic lifestyle, and some monitor lizards which have developed a somewhat ectothermic+ strategy.

Added Thoughts

A few things I thought off the top of my head that I didn't exactly feel like would fit here, but I think are worth mentioning.

  • While sort of behavioral, licking is used to cool off, particularly with mammals. Dogs, Cats, Kangaroos, they will lick themselves in order to cool off, though I think this may go against the spirit of the question, not only due to the behavioral nature, but also because this is a temporary measure against heat. It's not really something constant or passive, as the animal can't exactly hunt while this is happening.

  • Op mentions density as a method by which you could produce less heat, but not an ideal answer. I'm not sure this mechanism would reduce heat in exactly. However lower density animals are a real thing, namely as a hypothesis in non avian dinosaurs (backed up by or modern avian dinosaurs and marks left on bones) and seen in avian dinosaurs, birds, even large birds. Birds have a series of airsacs inside them, which help support their body, and are hypothesized to have been at least one of the aspects that allowed some dinosaurs to get so large, though in the case of flying birds, this is accompanied by much less dense bones. This however, alone, isn't a measure to "reduce internal body temperature", in fact, since air is an insulator, one might hypothesize these airsacs would do more to insulate internal body-parts than cool things down. However, this lower density can reduce energy exerted, thus may indirectly reduce heat.

Dinosaur vs bird airsacs

  • Along the same lines, certain body plans are going to be better at certain actions than others, in terms of energy efficiency etc... Bipedalism is a much more efficient plan for certain types of movement, one of those being endurance running. Humans are currently the best ultra long distance animals on the planet in hot climates (longer than 30 miles), sled dogs may rival or beat them in cold climates, ostriches beat them in medium (they can run very fast for a surprisingly long time and distance, measured in miles, not feet, not like a cheetah). So perhaps this creature would benefit indirectly interims of heat with a bipedal stance, something similar to modern large birds, or theropod dinosaurs, the largest theropod dinosaurs were around the 5 -> 10 metric tonne range, many over 10 meters long. I'm not sure if that mass is big enough, they would be well above human size.

  • It may also be worth pointing out, that while airconditioners aren't (yet ;) ) a biological adaptation, the way they work may be inspiration for a hypothetical biological adaptation. Modern airconditioners are usually two way, they cool things one direction, reverse the flow, they heat things up. This is because air conditioners work via a series of compression and heating of a special chemical inside the airconditioner by:

  1. passing normal air over a liquid refrigerant (usually with a fan of some sort, which heats the refrigerant up, causing it to turn into a gas.

  2. Compressing this gas, making it "hotter" and pushing this gas into a different location, normally outside.

  3. Because the refrigerant gas is compressed, it is much hotter, even than outside ambient temperatures on hot days. This means it is still possible to cool this "heated" air.

  4. Air from outside then condenses as it cools down outside, back into a liquid

  5. this liquid is then pushed back inside, but now is depressurized, where it can be heated once again.

  • Maybe the animal in question could some how produce a refrigerant that has the properties that make this possible and cool itself. It would however expend a tremendous amount of energy doing so (as air conditioning does today). It's unclear how realistically these concepts could be applied to an animal.
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    $\begingroup$ A white colour is a better reflector but a blackbody is a perfect radiator, so I think black would be a better choice in order to dump more heat via radiation into the environment $\endgroup$
    – Jay
    Dec 13, 2021 at 1:25
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    $\begingroup$ @Jay I'm not sure that's how that works, that seems like it has more to do with the non visible spectrum properties of the material, and isn't supported by what we see with wildlife. Indeed, polar bears, despite having white fur for camouflage, are black underneath, while many animals in hot climates still aren't black outside of more exposed skin areas near the face and feet, and are actually quite pale when shaved. $\endgroup$
    – Krupip
    Dec 13, 2021 at 1:56
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    $\begingroup$ @Dakkaron Colour does affect radiation rate. See also en.wikipedia.org/wiki/…. A good absorber is automatically a good emitter. But due to the sun any effects of increasing radiation will be overpowered by increased absorption of sunlight. Houses in the mediterranean area are often white due to this reason. If you left out a black and a white tile out at night with exposure to the night sky the black tile would cool of much quicker. $\endgroup$ Dec 13, 2021 at 13:19
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    $\begingroup$ One can pretty much be white in visible light and near infrared (where the most of the solar energy comes) and black in the far infrared (where one radiates when heated to temperatures compatible with life). $\endgroup$
    – fraxinus
    Dec 13, 2021 at 17:08
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    $\begingroup$ (re: the comments) whether you want to radiate or absorb heat, i.e. to be light or dark in colour, depends on whether you're warmer or cooler than your environment. If Bob lives in a cool environment then it would want to be dark, at least in the IR band, to radiate its heat away. If it lives in a hot environment it might want to be light to avoid absorbing even more heat from sunlight, but then it will have an even greater need for other methods of staying cool. $\endgroup$
    – N. Virgo
    Dec 14, 2021 at 3:08
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Well now, this is an easy one.

Simply increase your surface area. This can easily be done, just look at elephants and their ears. Since I'm to assume this creature will not have come about through evolution and will be built in a mad scientist's lab, I can simply say that bob will either:

(1) Have huge ears. Design them in a way that won't be a detriment or will have him trip, aight?

(2) Have many large ears, all over his body. Great for detecting prey and pinpointing sounds!

(3) Have a large amount of flaps that are not ears, but have the express purpose of cooling down bob as he exerts himself and they flap all over the place. Passive air cooling for the win!

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    $\begingroup$ And then put middle-sized ears on the large ears, small ears on the middle-sized ears, tiny ears on the small ears, and so on, to produce a fractal surface, to which the square-cube law doesn't apply. $\endgroup$ Dec 12, 2021 at 22:08
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    $\begingroup$ You could also use a sail on the back instead of ears, similar to the en.wikipedia.org/wiki/Dimetrodon $\endgroup$
    – Dakkaron
    Dec 13, 2021 at 11:30
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Allen's Rule

Nobody seems to have mentioned the easy answer yet...

Allen's Rule is the simple, natural subversion of the square-cube law in organisms. Where square-cube refers to objects which scale up isometrically (i.e. proportionally), Allen's Rule deals with allometric (i.e. non-proportional) scaling in organisms, specifically for the sake of heat rejection/retention. The rule states:

... animals adapted to cold climates have shorter limbs and bodily appendages than animals adapted to warm climates. More specifically, it states that the body surface-area-to-volume ratio for homeothermic animals varies with the average temperature of the habitat to which they are adapted (i.e. the ratio is low in cold climates and high in hot climates).

Wikipedia further explanations:

Allen's rule predicts that endothermic animals with the same body volume should have different surface areas that will either aid or impede their heat dissipation.

...

Because animals with low surface area-to-volume ratios would overheat quickly, animals in warm climates should, according to the rule, have high surface area-to-volume ratios to maximize the surface area through which they dissipate heat.

Consider the following illustration using building blocks:

Eight cubes arranged 3 ways: a 2x2x2 cube, a 1x2x4 slab, and a 1x1x8 tower

You can readily see that the surface area increases as the shape becomes longer, and more slender, while maintaining the same mass. This is shown via the surface-area-to-volume ratio, as mentioned above; large numbers more readily dissipate heat. The cube has the lowest ratio of 3, and while the slab is an improvement at 3.5, the tower is a staggering 4.25 -- a whopping 42% more surface area than the cube!

It's a little hacky, but this one simple trick can make a major difference in surface available for rejecting heat. This can be combined with the methods mentioned by others, such as skin texture, to amplify the effectiveness of each individual approach.

Of course, this is a double-edged sword. A lanky body will provide entirely passive cooling; it will help stay cool during physical exertion, but it will also cool off at all other times, as well. Bob the gigantic animal will almost certainly need a method to actively control his heat loss while in a sedentary state. The right approach is probably to use Allen's rule to get most of your cooling, and the active physiology mentioned by others to regulate based on conditions.

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  • $\begingroup$ Hum... According to this answer, Bob is a giant ananconda $\endgroup$ Dec 15, 2021 at 18:08
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It's not necessary to prevent overheating of the body if you can keep the brain within tolerable limits. Canines use this fact to their advantage by having a structure known as a rete mirabile (Latin for "wonderful net.")

A rete mirabile is a complex of arteries and veins lying very close to each other, found in some vertebrates, mainly warm-blooded ones. The rete mirabile utilizes countercurrent blood flow within the net to act as a countercurrent exchanger. (Wikipedia)

One predatory behavior of canines is to run down their prey until the prey succumbs to heat exhaustion and can run no further. The canine's body tends to become about as hot as the prey's body, but the rete mirabile in the canine's neck serves to keep the brain a few degrees cooler than the body.

Blood in a canine is cooled by air flow and evaporation in the nose, muzzle and tongue. When this blood returns toward the heart through veins, it enters the rete mirabile in the neck, where it is divided into many small veins and venules. Blood from the heart that is flowing toward the brain in arteries likewise enters the rete mirabile in the opposite direction, and likewise is divided into smaller arteries and arterioles. The close proximity of a tangle of veins and arteries with blood flowing in opposite directions forms an effective countercurrent heat exchanger. The result is a canine brain several degrees cooler than the overheated body, sufficiently cool to continue the chase until the prey succumbs to overheating.

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Increase thermal mass.

Early in the morning, before the sun comes up, Bob takes a long drink and fills up with a couple of cubic meters of water. Water has a high specific heat capacity and will absorb a lot of energy before increasing its temperature. Over his long day of shucking and jiving Bob heats up his onboard thermal mass, using the cool water to absorb his excess heat.

If the water in him gets hot then he needs new water. He dumps his hot water then stops and drinks a new load of water. It might not be as cool as it was in the early morning but it is still cooler than Bob; it will do.

The water is heavy. But Bob is strong and that is not an issue. Also, the added mass actually lets him hit harder than he would on an empty stomach.

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    $\begingroup$ This is not true. The cooling effect of water absorption is very minor compared to the heat it absorbs by evaporating (read: sweating). The specific heat of water is about 4 joules/gram/per degree celsius. If your glass of water is 20 degrees cooler than body temperature it can absorb 80 joules per gram of water. The heat absorbed by evaporating water is about 2200 joules per gram . Over 200x times as much. At rest a human produces about 80 joules of heat every second. Drinking glasses of water is not the main method of cooling humans down. $\endgroup$ Dec 13, 2021 at 13:38
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    $\begingroup$ To bring @AccidentalTaylorExpansion's point home: if I guzzle 2 kg of ice water (roughly the capacity of my stomach) at almost freezing temperature (0°C), it takes a measly 74 Calories to heat it to my body's internal temperature of 37°C. That's slightly more than the Calories I burn by walking 1 km (65 kcal). The same amount of water evaporated as sweat is equivalent to rejecting 1,150 Calories, about 16x as much as using thermal mass alone (not 200x). $\endgroup$
    – drmuelr
    Dec 14, 2021 at 0:49
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    $\begingroup$ @drmuelr Nice to see such a sophisticated answer. Most would have used the usually-quoted figure for the heat of vaporization of water (~540 cal/g), which is at the boiling point (100 C @ 1 bar). You, on the other hand, knew the heat of vaporization is actually higher if the water is at 37 C (~575 cal/g), and used that figure instead. $\endgroup$
    – theorist
    Dec 14, 2021 at 7:01
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    $\begingroup$ @drmuelr Thanks for correcting me! I didn't know the heat of evaporation goes up with temperature so I overstepped my bounds a bit. The 200x time figure is just plain wrong my brain wasn't working at the time. If I use a difference of 37°C as well I get that it takes about 150 joules to heat per gram of water which would give ~14x times increase (using the wrong heat of evaporation at 100°C) $\endgroup$ Dec 14, 2021 at 10:56
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    $\begingroup$ @drmuelr - I too appreciate some math. I got on my high horse and did it all and got an answer orders of magnitude higher. Then I remembered that kilocalories goes by its nickname. And to clarify: I did not mean this system was a better way to cool than sweating. But Dutch already offered "sweating!" so I came up with this, $\endgroup$
    – Willk
    Dec 14, 2021 at 13:15
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Built-in radiators

Bob's powerful muscles have a very rich blood supply to meet their massive energy needs. Fortunately for Bob, blood, being mostly water, is an excellent coolant, and, conveniently, when his muscles' heat generation is greatest, their energy needs - and, thus, their blood flow - are also at a peak. After oxygenating and feeding his muscles, the blood carries waste heat into a network of venous plexi under his skin, allowing it to be easily convected and radiated away. The blood then flows back to the heart and lungs and thence to the muscles again, cooled back down and ready to carry away more waste heat.

The dense networks of small vessels do increase venous resistance considerably, making it harder to get blood back to the heart; fortunately for Bob, he's evolved auxiliary hearts to force blood through the plexi when they're needed for cooling. When Bob is inactive, the sphincter muscles surrounding the small veins distributing blood throughout the plexi constrict, shunting blood into a few larger, low-resistance channels and reducing the load on Bob's hearts.

This could be easily combined with @Willk's suggestion, by adding another set of venous cooling plexi in the walls of the gut to transfer heat from Bob's coolant blood into the tremendous thermal mass of cold water stored in the stomach.

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Endothermic reaction
Bob creates chemicals within itself on demand he mixes these chemicals in a unique organ, and circulates its blood around it to cool its blood. The reaction of these chemicals creates an Endothermic reaction Cool bonus creates ammonia gas.

Solid barium hydroxide reacted with solid ammonium thiocyanate produces barium thiocyanate, ammonia gas, and liquid water. This reaction gets down to -20°C or -30°C

If you don't like this particular endothermic recipe, others are easily discovered.

Peltier Device
Bob either has implanted or grows a Bio-Thermoelectric cooling organ to cool his blood. To cool the device before it overheats it's self the Peltier can be constructed as a tube. water can be expelled though the tube and exhausted as steam.

Thermoelectric cooling uses the Peltier effect to create a heat flux at the junction of two different types of materials. A Peltier cooler, heater, or thermoelectric heat pump is a solid-state active heat pump which transfers heat from one side of the device to the other, with consumption of electrical energy, depending on the direction of the current. Such an instrument is also called a Peltier device, Peltier heat pump, solid state refrigerator, or thermoelectric cooler (TEC) and occasionally a thermoelectric battery. It can be used either for heating or for cooling,1 although in practice the main application is cooling. It can also be used as a temperature controller that either heats or cools.

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Can Bob change shape?

Maybe while fighting, Bob is kind of dense and compact. Afterwards, when Bob needs to cool down his body extends to become longer and skinnier (increasing surface area to volume).

Also, perhaps various protrusions emerge, helping shed heat. (The only example I can think of from the natural world is the way male genitalia in some species such as whales and horses are tucked inside mos of the time). A lot of emerging protuberances like this could help.

Also, you don't mention the terrain, but perhaps there are mud puddles or ponds that Bob can wallow in, similar to water buffaloes or hippos.

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    $\begingroup$ So in other words, Bob is a blob? $\endgroup$
    – barbecue
    Dec 14, 2021 at 18:59
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    $\begingroup$ @barbecue Maybe he is a spring! $\endgroup$ Dec 15, 2021 at 0:55
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Sweating is an effective way of dispersing excess heat. Horses sweat, human sweat, and both are optimized for running.

And if you ever got sick after standing still after a good sweat, you have proven on yourself how good sweat is at cooling.

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All the solutions offered thus far—and there are many good ones—focus on either thermal dissipation or thermal avoidance (dissipating thermal energy, or keeping it from building up in the first place).

But what about simply increasing Bob's thermal tolerance?

I.e., make Bob an extremophile, specifically a hyperthermophile. Alter Bob's proteins, lipids, nucleic acids, and other biological molecules, as well as his organelles, cells, tissues, organs and organ systems, so that he can withstand extremely high internal temperatures.

Doing so will enable him to sustain longer periods of intense activity, since it will take longer to reach his maximum temperature limit. It will also allow the level of activity that Bob can sustain continuously to be much higher, since the hotter Bob gets, the faster he can dissipate thermal energy. I.e., in addition to allowing a longer period at max intensity, the intensity he can sustain at steady-state will be higher.

Essentially, you'd be scaling up the adaptations made by existing hyperthermophiles—like the single-celled methanogen Methanopyrus kandleri, which can grow at temperatures of up to $122 ^{\circ}C$—to the vastly more complicated scale of of tissues, organs, and organ systems.

One of the adaptations used by Methanopyrus kandleri is high concentrations of cyclic 2,3-diphosphoglycerate, which helps keep proteins from denaturing (think of cooked egg whites) at high temperatures. See: https://en.wikipedia.org/wiki/Methanopyrus

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Lots of people here have mentioned surface area. What about a heatsink and fins? Some people think that's what the stegosaurus plates were for. Some folks think that's a load of hoo-ha, but it's at least debated, and therefor plausible.

Suppose you grant Bob many thin, bladelike protrusions which are hard and reasonably thermally conductive? Maybe as he's running, he realizes much happiness and relief from the convection cooling of wind against his hyper-functional fully-weaponized heat fins? Maybe he thinks the journey is almost as important as the destination.

You do you, Bob! Live large! We love ya, big guy!

https://blogs.scientificamerican.com/tetrapod-zoology/the-stegosaurus-plate-controversy/

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Selective cooling

Although this example seems to be recently rebutted the idea of selective cooling might still be applicable: Oryx and similar antilopes adapted to hot and dry environments were thought to use a special network of capillaries in the nose to cool to the brain, in order to reduce sweating and therefore saving water.

Bob might be able to use any of the mentioned cooling mechanisms to selectively cool the brain and or other vital organs, in order to prevent the effects of a heat stroke. The rest of the body might be more robust against raised temperatures and function as a heat sink which would prolong the timeframe Bob would have available at max speed before the heat buildup starts to lead to exhaustion.

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  • $\begingroup$ @MTA beat me to it, I just came back to post the answer I started writing earlier and didn't see their answer in time $\endgroup$
    – Tanque
    Dec 13, 2021 at 16:11
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Bob has weird lungs. When he's sedentary, he breathes like a normal animal - filling up his lungs, exchanging gas, and then emptying them. However, when he's running, his lungs act more like the air intake on a car.

He locks his mouth open cartoonishly wide, revealing a windpipe the size of a basketball. And he has a second huge windpipe on his back (or perhaps his back is just somewhat permeable to gas), creating a wind tunnel. He gallops along at 15 miles per hour, forcing hundreds of litres of air through his body every second. The hot blood in his lungs, pumped through heatsink-like structures, is cooled by the wind, and exchanges gasses with it as it blows past.

This does come with limitations of course - bob must run to cool down (unless it's windy), so he can't fight for too long in one place. He also can't run with too much of a tailwind - he might need to zigzag or tack to get the airflow he needs. But I think that's neat, so whatever.

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There is an excellent answer on pretty much every thing biological. There is a mention of shape shifting. Let's go Sci-Fi! (And also full-retard.)

This is a brief version of a well-know sci-fi "explanation" of shape shifters. All the vampire, werewolf, or robot transformations can fit this scheme. I have read it in Russian fiction by someone, who calls them "Gray Zone", if it matters, but it seems to be older.

Hammer space for a shape shifter

Bob has access to a personal space cavern. Also, Bob has two bodies. A "combat" body, large, heavy, prone to die from overheating. Bob uses this body only for the actual attack and other combat situations.

Everyday life of Bob happens in another body, much lighter, more capable to sustain heat.

Should a combat body be needed, Bob shape shifts. Basically, he switches his everyday body for combat body. The shift is immediate. The other body is waiting in hammer space, let's freeze or slow-down the time there.

So, Bob does not need to care for cooling his combat body, as long as it is not used for too long.

Bob has now a weakness, too. If there is an attack he does not anticipate, but it is strong to kill the everyday body immediately, Bob dies.

Well, at least it's somewhat original...

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Subvert the square-qube law by not following it. Bob the giant animal may be a very long snake or centipede. When eating well, he may grow bigger still – but only by getting even longer. So surface area go up with volume, and cooling does not become harder.

An extremely long Bob may have problems, as a single mouth can't feed kilometers of body. If this becomes an issue, he grows more heads at regular intervals. This also solves the problem of breathing, the problem of controlling large amounts of body parts, and the problem of defending distant parts. The first head is biggest and do the thinking, the rest are just followers managing their segment of the body.

In cold weather, Bob looses heat through his large surface. But then he rolls up like ball of string, minimizing exposed surface.

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A slow, majestic, giant octopus

Think out of the box. An octopus shape may come in handy, to overcome square cube law, that is to increase Bob's surface.. Bob would swim, or crawl around, low energy creature don't produce much heat.. Say 24 feet tall, starfish shaped, about 250 feet wide ? span 750 meters ? I see no real issue with that. As long as it moves slowly..

No agile predator

The size contest would never be won by a land predator. Its agility and energy consumption requires a lot of heat to be transferred out, which is the root problem here.

So this is no real answer for predator Bob. But it's too big for a comment, so I leave it in

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Maybe increase Bob's locomotive efficiency so there isn't so much waste heat in the first place. This would also help him to maintain a quick pace over long periods of time.

Without resorting to wheels, his gait at speed would have to be a natural oscillation of his limbs, maintained by spring-like structures and requiring only minimal muscle input at constant speed. He would need to have evolved specialized springy ligaments that are connected across joints in parallel to the muscles.

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What if Bob grew horns, like longhorns, hollow and full of spongy material that circulates blood. But what if those horns are made of iron or aluminum, like the shells of certain mollusks. This would give him a weapon and essentially a natural high-efficiency heat sink

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  • $\begingroup$ This -I would just make the animal mostly out of metal. Then the strength is higher and dissipation is faster. $\endgroup$
    – axsvl77
    Dec 15, 2021 at 15:07
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In a word, chemistry. You could have Bob extract from its food the necessary chemicals to produce an endothermic reaction, and then poop the exhaust.

In alternative, you could imagine a very efficient biological heat sink, such as metal spikes; some molluscs can incorporate high concentrations of iron into the points of their teeth.

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Why make it complicated, when Bob could just install a solar sail on his back to increase surface area and cool (or heat!) his body when required, just like the Spinosaurus in the back:

Spinosaurus

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Bob creates chemicals which when combined cause a strong endothermic reaction - ie it absorbs heat energy. Bob stores these in internal "tanks" for use when needed. The resultant compound(s) can then be reconverted with time.

Examples of endothermic reactions are the solution of any of ammonium chloride, ammonium nitrate, barium hydroxide in water.

Here is an example of two solids combining endothermically (Ammonium Chloride and Barium Hydroxide).

It happens that dissolving Ammonium Chloride in water appears to be a potentially very useful system. NH4CL is very soluble in water - a several molar solution can be made, but to go gentle on Bob's internals we may wish to limit ourselves to a 1 molar solution, or less. As shown below, it seems likely that 10 kg of water and NH4Cl would provide very adequate for a behemoth sized Bob to use occasionally.

NH4CL does not REACT with water, it just dissociates into NH4 and Cl ions in solution. Bob could conceivably have a liquid NH4Cl tank and a dry(ish) powder reservoir and use suitable internal processes to dehydrate the solution and save the solid product for later use.

Enthalpy of solution for NH4Cl is 14.78 kJ/mol 1 mol ~= 51 grams. So about 295 kJ / kg
1 kWh = 3.6 MJ so 1 kWh of cooling requires about 3.4 kg of NH4Cl. 1 kWh = 3,600 kW-seconds, <- drag racer or 360 kW for 10 seconds, <- small battle tank or 36 kW for 100 seconds. <- car highway cruising

Even allowing for inefficiencies of heat distribution and other 'mere details' it looks like say 10 kg of ammonium chloride and water would serve Bob's needs in times of duress,


Related:

Niven, Pournelle & Barnes in "Legacy of Heorot " had "Grendell" - a creature with a super-oxygenated "speed" mode with similar cooling issues. To kill it you trigger it into speed mode while far from water. That doesn't help you cool Bob but a read may help you scope the problems.

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