Heat transfer for Herschel-Bulkley fluids flowing through cylindrical ducts: the case for cooling with constant exchange coefficient

This work presents experimental and numerical results concerning heat trans fer for Herschel-Bulkley fluids, the consistency of which depends on temper ature. We have considered the flow through a horizontal cylindrical duct su bmitted to a wall cooling by an external counter current flow. According to the experimental conditions, the wall temperature may fall below the freez ing temperature of the non-Newtonian fluid, for some locations. The numeric al model shows that the Nusselt number, which characterizes the internal he at transfer, may be written as constant (Pe'/Z*)1/3. Z* corresponds to a di mensionless abscissa, Pe' being a particular Peclet number. This last param eter depends on the wall shear rate, determined for the inlet section, whic h indirectly takes into account the rheological properties. A very simple m odel predicting the wall temperature distribution has been developed. The e volution of this quantity allows us to distinguish roughly two zones along the duct. For the first zone, the temperature drop is abrupt and is mainly affected by the internal heat transfer coefficient. For the second zone, th e evolution is smoother, the external condition being prevalent. (C) 1999 E lsevier Science Ltd. All rights reserved.