Heat transfer to individual blood vessels has been investigated in three configurations: a single vessel, two vessels in counterflow, and a single vessel near the skin surface. For a single vessel the Graetz number is the controlling parameter. The arterioles, capillaries, and venules have very low Graetz numbers, Gz < 0.4, and act as perfect heat exchangers in which the blood quickly reaches the tissue temperature. The large arteries and veins with Graetz numbers over 103 have virtually no heat exchange with the tissue, and blood leaves them at near the entering temperature. Heat transfer between parallel vessels in counterflow is influenced most strongly by the relative distance of separation and by the mass transferred from the artery to the vein along the length. These two effects are of the same order of magnitude, whereas the film coefficients in the blood flow are of significant but lesser importance. The effect of a blood vessel on the temperature distribution of the skin directly above it and on the heat transfer to the environment increases with decreasing depth-to-radius ratio and decreasing Biot number based on radius. The absolute magnitude of these effects is independent of other linear effects, such as internal heat generation or a superimposed one-dimensional heat flux.

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