# Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity

Smith, Andrew and Wilson, Stephen and Duffy, Brian and Hall-Taylor, N. (2010) Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity. Journal of Engineering Mathematics, 68 (3-4). pp. 301-325. ISSN 0022-0833

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## Abstract

Scraped-surface heat exchangers (SSHEs) are extensively used in a wide variety of industrial settings where the continuous processing of fluids and fluid-like materials is involved. The steady non-isothermal flow of a Newtonian fluid with temperature-dependent viscosity in a narrow-gap SSHE when a constant temperature difference is imposed across the gap between the rotor and the stator is investigated. The mathematical model is formulated and the exact analytical solutions for the heat and fluid flow of a fluid with a general dependence of viscosity on temperature for a general blade shape are obtained. These solutions are then presented for the specific case of an exponential dependence of viscosity on temperature. Asymptotic methods are employed to investigate the behaviour of the solutions in several special limiting geometries and in the limits of weak and strong thermoviscosity. In particular, in the limit of strong thermoviscosity (i.e., strong heating or cooling and/or strong dependence of viscosity on temperature) the transverse and axial velocities become uniform in the bulk of the flow with boundary layers forming either just below the blade and just below the stationary upper wall or just above the blade and just above the moving lower wall. Results are presented for the most realistic case of a linear blade which illustrate the effect of varying the thermoviscosity of the fluid and the geometry of the SSHE on the flow.

#### ORCID iDs

Smith, Andrew, Wilson, Stephen ORCID: https://orcid.org/0000-0001-7841-9643, Duffy, Brian ORCID: https://orcid.org/0000-0003-2687-7938 and Hall-Taylor, N.;
• Item type: Article 29073 DateEventDecember 2010Published scraped-surface heat exchanger , thermoviscosity , temperature-dependent viscosity, asymptotic methods, Mathematics, Science, Engineering(all), Mathematics(all) Science > MathematicsScience Faculty of Science > Mathematics and Statistics Pure Administrator 07 Mar 2011 23:24 11 Nov 2021 01:56 https://strathprints.strath.ac.uk/id/eprint/29073