Abstract
In the century since Graetz first formulated the partial differential equations which are fundamental to understanding the heat exchange of fluids flowing through pipes, substantial efforts have been, and continue to be, made to develop theoretical approaches to solve the “Graetz-problem” because it is fundamental to so many important engineering processes. In the absence of explicit theory, most approaches continue to incorporate one or more simplifying assumptions to achieve numerical solutions. We now report that Magnetic Resonance Imaging (MRI) can provide simultaneously spatial maps of the distribution of both the temperature and flow velocities of an opaque fluid whose complex rheology is temperature dependent, during its flow through a vessel which has a temperature gradient. Thereby it can provide both objective assessment and validation of computational models for the Graetz problem, as well as direct information about specific systems.
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