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

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

Mathematical model of eyring fluid in a scraped surface heat exchanger

“…Rodrigues et al (2009) explored the work in a laboratory based SSHE and obtained qualitative match with numerical techniques extracted through lattice Boltzman discretisation techniques. Smith et al (2010) studied the heat transfer mechanism by using Newtonian fluid in SSHE. They explored the flow with temperature dependent viscosity.…”

“…LAT describes the flow of fluid in a geometry in which one dimension is very small in comparison to others. In case of SSHE, different gaps are considered very small i.e., the aspect ratio being of order 10 -1 , the appropriately reduced Reynolds number being of order 10 -2 , so that LAT can be used to study the flow [Duffy et al (2007), Smith et al (2010)] The governing equations using LAT i.e., the values of constant integration and are determined by using Mathematica. While finding these constants of integration in each region after using boundary conditions we have obtained four sets of roots in which three are extraneous.…”

Heat transfer analysis of scraped surface heat exchanger

“…After the heat exchanger reaches a steady state of production, Keep the temperature gradient inside it not changing with time, Steady heat transfer occurs in the heat exchanger, in this article, the process of margarine production is taken as an example to analyze and study the model [5].…”

“…There are mainly three ways of heat transfer in the scraper type refrigerator, they were the composite heat conduction of the barrel wall of grease 3  ,Thermal conduction between scraper and grease boundary film 4  ,Heat transfer between grease film and inside of barrel wall 5  ,In the course of work, The scraper is tightly bonded with the inner barrel wall under the influence of centrifugal…”

Flow of Second Grade Fluid in a Scraped Surface Heat Exchanger

“…Smith et al . () studied the steady nonisothermal flow of a Newtonian fluid with temperature‐dependent viscosity in SSHE. Härröd () provided detail of experimental and theoretical work on SSHEs published in 1986 and Rao and Hartel ().…”