Laminar heat transfer to blood flowing in a circular duct

Abstract

Entrance-region heat transfer to blood steadily flowing in a pipe is studied. It is assumed that the non-Newtonian behaviour of blood can be expressed both by the Casson equation and the more complex law suggested by Merrill and Pelletier [ J. Appl. Physiol. 23, 179–182 (1967)]. The possible presence of a thin cell-free plasma layer at the wall is accounted for. The velocity distribution is determined analytically and a solution of the energy equation is obtained by a finite-difference method, for the two cases: (a) the uniform wall temperature, and (b) the uniform wall heat flux. Results are presented for the yield number Y ( = 2 Rτ y / σu m ) = 1, 5, 10 and 20 and the non-dimensional marginal layer thickness D ( = σ/ R) = 0,0.0002, 0.01 and 0.1.