**1. Introduction**

In general, physiological processes are basically isothermal and isobaric. Several mechanisms contribute to keep constant pressure in systems such as blood vessels, among them diameter distribution and peristaltic motion. In this, it is to be understood that pressure constancy refers to time-averaged or extreme values.

Many pathologies make the human body develop fever, which raises temporarily body temperature. It is common practice to use, in some cases, medicines that restore, albeit for a given period of time, normal temperature. Fever is not the only cause of body heat-transfer. This process also occurs with body adjustment to changes in ambient temperature, physical exertion, metabolism acceleration due to food ingestion, drug effects, and others. During these body changes, blood and other fluid vessels undergo heat-transfer processes that pose considerable difficulties to physical modeling. Some pertinent variables are fluid composition, vessel elasticity, peristaltic motion in some cases, unsteadiness, and complex vessel geometry.

Heat-transfer in tube-flow has been investigated for several decades. One main practical driving force for such studies is the need to understand and design efficient heat-transfer equipment, widely used in several industrial areas. Models of simple tube-flow heat-transfer problems are now textbook´s standard contents.

These include laminar Newtonian steady flow in round tubes with simple boundary condi‐ tions. More recently, as it is reviewed in the next section, Newtonian and non-Newtonian flows in tubes of geometry other then circular have been modeled and analyzed. One important finding as to this chapter´s objective is the effect of the interplay between tube geometry and non-linear viscoelasticity.

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Such coupling leads to the development of secondary flows, or helicoidal flows, that increase the transversal transport capacity of the flow, a phenomenon that can be applied, or related, to heat-transfer enhancement, or to other transversal transport processes, such as crosssectional transport of particles immersed in the fluid.

Especially in blood flow, cells and other components introduce viscoelasticity [1, 2] that becomes relevant in smaller blood vessels. The understanding of its effect on the flow charac‐ teristics may become very relevant in cases such as heart arteries, and when artificial implants affect the blood flow. Also blood plastic effects appear is smaller vessels due to the aggregation of red blood cells at low shear rates, which develop a yield stress to be overcome for the flow to ensue.

Drawing on the above results, in this chapter it is presented a summary of relatively new analytical findings that may be useful for the better understanding of heat-transfer and complex flow phenomena in vessels that share some characteristics with biological vessels, particularly when these work under abnormal conditions. Also it is analyzed the effect of geometry in energy dissipation. This chapter is closely related to [3].
