Analytical solutions to non-uniform surface heat transfer with volumetric sources in magnetohydrodynamic duct flow

[+] Author and Article Information
Michael J. Bluck

Mechanical Engineering Dept. Imperial College, London

ASME doi:10.1115/1.4042776 History: Received April 22, 2018; Revised January 07, 2019


This article considers the convective heat transfer processes in fully developed laminar magnetohydrodynamic (MHD) flows in rectangular ducts of the kind proposed in some nuclear fusion blanket designs. Analytical solutions which incorporate the non-uniformity of peripheral temperature and heat flux and the effect of volumetric heating, are developed as functions of magnetic field strength and duct aspect ratio. A distinct feature of these MHD problems, not yet addressed in the literature, is that unlike the conventional characterisation of heat transfer by a Nusselt number, it is necessary to generalise the concept to vectors and matrices of Nusselt coefficients, due to the extreme anisotropy of both the flow and heating. The new analytical results presented here capture more complex heat transfer behaviour than non-MHD flows and in particular chracterize the importance of aspect ratio. The importance of these new results lie not only in the improved understanding of this complex process, but also in the provision of characterisations of convective heat transfer which underpin progress toward systems scale simulations of fusion blanket technology which will be vital for the realisation of practical fusion reactors.

Copyright (c) 2019 by ASME
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