TY - JOUR

T1 - Heat and fluid flow in a scraped-surface heat exchanger containing a fluid with temperature-dependent viscosity

AU - Smith, Andrew

AU - Wilson, Stephen

AU - Duffy, Brian

AU - Hall-Taylor, N.

PY - 2010/12

Y1 - 2010/12

N2 - 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.

AB - 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.

KW - scraped-surface heat exchanger

KW - thermoviscosity

KW - temperature-dependent viscosity

KW - asymptotic methods

UR - http://www.scopus.com/inward/record.url?scp=78149497340&partnerID=8YFLogxK

UR - http://www.ingentaconnect.com/content/klu/engi/2010/00000068/F0020003/00009403#aff_1

U2 - 10.1007/s10665-010-9403-y

DO - 10.1007/s10665-010-9403-y

M3 - Article

VL - 68

SP - 301

EP - 325

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 3-4

ER -