Theory and Experiment for the Effect of Vascular Microstructure on Surface Tissue Heat Transfer—Part II: Model Formulation and Solution

TLDR: A closed form analytic solution for the boundary value problem coupling the three layers is obtained in terms of numerically evaluated integrals describing the detailed vascular geometry, a capillary bleed-off distribution function and parameters describing the shunting of blood to the cutaneous layer.

Abstract: In this paper the conceptual three-layer representation of surface tissue heat transfer proposed in Weinbaum, Jiji and Lemons [1], is developed into a detailed quantitative model. This model takes into consideration the variation of the number density, size and flow velocity of the countercurrent arterio-venous vessels as a function of depth from the skin surface, the directionality of blood perfusion in the transverse vessel layer and the superficial shunting of blood to the cutaneous layer. A closed form analytic solution for the boundary value problem coupling the three layers is obtained. This solution is in terms of numerically evaluated integrals describing the detailed vascular geometry, a capillary bleed-off distribution function and parameters describing the shunting of blood to the cutaneous layer. Representative heat transfer results for typical physiological conditions are presented.