Question

How does heat exchange occur across the walls of capillaries? Specifically, how are certain veins/arteries/capillaries cooler or warmer than other ones? How does the body regulate that to make certain parts hotter or cooler?

Answer 1

Heat exchange across the walls of capillaries and also other blood vessels occurs for a conformation of homeostasis. Occurs via 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.

a)With the increase of the imposed heat flux, the heat transfer coefficient increases to a maximum value and then decreases afterwards.

b)As the imposed heat flux is increased, the liquid-vapor interface moves towards the heated surface. The critical heat flux is reached when the vapor film expands to cover the whole area of the heated surface. Under this situation, both the wall and the outlet temperatures would increase sharply with the advance of time.

c)The height of the porous structure is shown to have a large effect on the critical heat flux, but it has a small effect on the maximum value of the heat transfer coefficient.