平板クエット流れの粘性による加熱-感温流体に対する級数解-

概要

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The problem of the interaction between viscous heating, heat transfer and flow in Couette rheometers is investigated. Series solutions, up to 4th order in the Brinkman number (Br), are developed for planar Couette flows of materials whose viscosity and thermal conductivity can be expressed as polynomial functions of temperature with arbitrary coefficients. The derived solutions are validated by extensive comparison to existing closed-form results and to numerical solutions and are found to be highly accurate for a practical range of (Br). The presented solutions provide valuable insight into the functionality of the relevant dependencies, something that is lost in purely numerical solutions. Based on these results, the distribution of velocity, shear rate and temperature, as well as their sensitivity on material and process parameters are investigated. Finally, corrections for viscosity measurements in Couette viscometers, which account for viscous heating and temperature-dependent material properties, are derived.
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