Chato J C
J Biomech Eng. 1980 May;102(2):110-8. doi: 10.1115/1.3138205.
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 10(3) 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 anad 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.
单个血管、逆流的两个血管以及靠近皮肤表面的单个血管。对于单个血管，格雷茨数是控制参数。小动脉、毛细血管和小静脉的格雷茨数非常低，Gz < 0.4，并且充当完美的热交换器，其中血液迅速达到组织温度。格雷茨数超过10³ 的大动脉和大静脉与组织几乎没有热交换，血液离开它们时的温度接近进入时的温度。逆流平行血管之间的热传递受分离相对距离以及沿长度从动脉到静脉传递的质量影响最大。这两种效应具有相同的量级，而血流中的膜系数虽然显著但重要性较低。血管对其正上方皮肤温度分布以及向环境热传递的影响随着深度与半径之比的减小以及基于半径的毕奥数的减小而增加。这些效应的绝对大小与其他线性效应无关，例如内部热生成或叠加的一维热通量。
