The temperature evolution of a Newtonian fluid within an idealised scraped surface heat exchanger has been studied in a physically realistic parameter regime. To our knowledge, this is the first theoretical (non-numerical) study to attempt to address the phenomenon of “channelling” in a scraped surface heat exchanger that has included the effects of both three-dimensionality and heat transfer. The simultaneous inclusion of both multi-dimensional and thermal effects is complicated by the fact that the thermal problem necessarily involves advection, diffusion and dissipation. It is only through the use of asymptotic analysis and averaging methods that progress may be made.
A four-parameter model was studied which included material properties, geometrical variables of scraped surface heat exchangers and processing parameters. The analysis enables the key non-dimensional parameters that govern the industrial process to be identified and analysed. It it worth noting that the main assumptions of the study (namely laminar flow, large Péclet number, small aspect ratio and small reduced Reynolds number) hold for a very wide range of scraped surface heat exchangers. The analysis is therefore widely applicable to industrial processes involving scraped surface heat exchangers.
The solutions obtained compare well to a full numerical simulation, although the agreement is likely to improve markedly as the aspect ratio decreases. The asymptotic analysis that was used has the great advantage of leading to a numerical formulation that is markedly simpler than a full numerical simulation, and this allows the parametric dependence of the solutions to be investigated with ease. The asymptotics also allow the different flow topologies that result from different chamber leakage rates to be easily enumerated and explained.
A two-dimensional averaged model was then formulated and solved numerically, using “reconnection” boundary conditions that faithfully reflect the salient details of the flow inside an scraped surface heat exchanger and its effect on the heat transfer that occurs. The averaged model allows easy identification of regimes where undesirable “channelling” may occur.
Finally, the methodology that has been developed allowed a parametric study to be performed. This focused on predicting the onset of “channelling”. This allowed the identification of parameter regimes that resulted in dramatic changes in output temperature profiles. The effect of increasing blade through-flow and the associated dissipation, illustrated in Fig. 10, was also discussed.
In spite of the relative generality of the model presented, many further developments are possible. Key aims for the future include accounting for the dependence of viscosity on temperature and adding non-Newtonian effects (many foodstuffs processed in scraped surface heat exchangers are known to be pseudoplastic). It may also be possible to extend the analysis presented here to encompass multiphase materials (e.g. jams containing fruit segments or soups containing vegetable parts). Phase changes such as freezing may also take place in scraped surface heat exchangers (though these are usually considered to be undesirable) and it may be possible to use the methodology developed in this study to examine such scenarios.
It is also clear that, if more experimental data were to become available, comparison studies could be carried out to assess the accuracy of the results presented here. One reason why experimental data is inherently hard to gather is that, if any apparatus is added to the flow for the purpose of data collection, it is likely to be damaged by the scrapers.