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Equivalency of Counter-Current Vessel Heat Transfer Formulations


 Models of counter-current blood vessel heat transfer have used one of two, different, previously unreconciled formulations, based either on: 1) an average vessel wall temperature difference, or 2) a bulk mean blood temperature difference. This paper shows that these two formulations are only equivalent when the four, previously undefined, “convective heat transfer coefficients” that are used in the bulk mean temperature difference formulation (two each for the artery and vein) have very specific, problem dependent relationships to the standard convective heat transfer coefficients. These bulk mean temperature difference formulation “convective heat transfer coefficients” are shown to be either: 1) arbitrary, user defined values, or 2) specific functions of a) the tissue conduction resistances, b) the standard convective heat transfer coefficients, and c) the independently specified bulk mean arterial, bulk mean venous and tissue temperatures. Thus, they are not true convective heat transfer coefficients, and must change values dependent on the blood and tissue temperatures, a dependence which significantly limits their usefulness.