A NEW ANALYTIC TECHNIQUE FOR 3-D HEAT-TRANSFER FROM A CYLINDER WITH 2 OR MORE AXIALLY INTERACTING ECCENTRICALLY EMBEDDED VESSELS WITH APPLICATION TO COUNTERCURRENT BLOOD-FLOW

A new approximate analytic solution technique is developed for treating the heat exchange between two or more axially interacting vessels which are eccentrically embedded in a cylinder. The cylinder exchanges heat by convection with the environment and has a non-uniform surface temperature due to the vessel eccentricity. The flow in the vessels can be either countercurrent or unidirectional. The solution is constructed by superposition of a new solution for a single embedded vessel which exactly satisfies the boundary conditions when the thermal conductivity of the fluid is equal to that of the cylinder material and is a very good approximation when these conductivities are not equal. Comparison with an exact solution for a single embedded vessel, when the conductivities are not equal, shows that the approximate solution results in very minor errors for a wide range of the governing parameters. As an application of the new technique the two-vessel solution is used to examine the countercurrent heat exchange in a human arm.