Warming Hemocoels

Watch bees at a hive entrance on a cold morning. Lethargic bees beat their wings slowly and stiffly. Insects balance the heat they absorb and produce against the large quantities they must lose to the environment, but at early morning start-up, a little sun helps. Insects control heat gain or loss or thermoregulate depending on need. Contracting muscles release heat. About ninety-four percent of a muscle's energy degrades into heat; only the remaining six percent produces mechanical force.

Hemocoels distribute heat by conductive cooling or warming. Suppose for a moment the hemocoel were a connected tubular system supplied by a pump. For any given rate of flow, tubes of large diameter would present less resistance and strain to the pump, but a large tube linking a heat source to a heat sink would be inefficient, as it would make poor thermal contact with the muscular generators of heat. Giving the tubes smaller diameters might improve thermal contact and heat exchange, but the increased resistances of all the small tubes together would strain the pump.

So the pump tubular system of vertebrates is a compromise, employing tubes of large bore to carry blood over the greater distances but tubes of smaller bore to cover the remainder. Linking large arteries and veins to capillary beds satisfies Murry's Law. Murry's law states that for a system of tubes containing laminar flows, the minimum volume for any given drop in pressure occurs when the sum of the cubed radii of the smaller tubes at a branch point of a vessel equals the cubed radius of the larger tube leading to or from the branch. This balance equalizes shear stresses in the tubes. For many fractal systems, tube lengths are approximately proportional to their radii, so the sum of the areas of the tubes at each level of the hierarchy conveys approximately the same volumes. Circulating blood resides for almost equal times at each level (Folkov and Neil, 1971).

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