Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

A mathematical model of fluid flow in a scraped-surface heat exchanger

Duffy, B.R. and Wilson, S.K. and Lee, M.E.M. (2007) A mathematical model of fluid flow in a scraped-surface heat exchanger. Journal of Engineering Mathematics, 57 (4). pp. 381-405. ISSN 0022-0833

[img] PDF
SSHEpaper.pdf
Preprint

Download (1MB)

Abstract

A simple mathematical model of fluid flow in a common type of scraped-surface heat exchanger in which the gaps between the blades and the device walls are narrow, so that a lubrication-theory description of the flow is valid, is presented. Specifically steady isothermal flow of a Newtonian fluid around a periodic array of pivoted scraper blades in a channel with one stationary and one moving wall, when there is an applied pressure gradient in a direction perpendicular to the wall motion, is analysed. The flow is three-dimensional, but decomposes naturally into a two-dimensional "transverse" flow driven by the boundary motion and a "longitudinal" pressure-driven flow. First details of the structure of the transverse flow are derived, and, in particular, the equilibrium positions of the blades are calculated. It is shown that the desired contact between blades and the moving wall will be attained, provided that the blades are pivoted sufficiently close to their ends. When the desired contact is achieved, the model predicts that the forces and torques on the blades are singular, and so the model is generalised to include three additional physical effects, namely non-Newtonian power-law behaviour, slip at rigid boundaries, and cavitation in regions of very low pressure, each of which is shown to resolve these singularities. Lastly the nature of the longitudinal flow is discussed.