Computational heat transfer analysis of liquid food in a heat exchanger with varying stirrer settings in a nonclassical continuum framework

Abstract

Rapid heat diffusion and stirring of food in channels and tanks for more desirable and safely regulated food delivery is of particular interest in food industry. In the present article, we investigate heat diffusion in a heat exchanger with varying stirrer settings in a nonclassical framework. Interestingly, the liquid food flows in all previous investigations are modeled using the classical continuous paradigm. Therefore, the purpose of this article is to offer a mathematical model that uses a nonclassical continuum framework to mimic the behavior of liquid food flows. This is influenced by the fact that during the stirring process, food particle microrotations affect the heat diffusion phenomenon, necessitating consideration of this in the modeling aspect of such studies. This non-Newtonian physical process is modeled based on the well-established theory of Cosserat continuum. The mathematical model presented here is taking into consideration a newly established constitutive relation by the author for the strain-based viscosity models in non-Newtonian mechanics. The applied constitutive relation incorporates the microrotational effects into the current rheology of rate-dependent viscosity model as a result of the kinematics at the macroscopic level. It offers a more practical method for examining the heat diffusion process in a heat exchanger. To the best of the author’s knowledge, this approach is first of its kind in analyzing heat diffusion process within non-Newtonian mechanics. The presented strain-based viscosity model is described in the form of PDEs along with prescribed boundary conditions. An in-house code is developed based on finite element method. The code is implemented using FreeFEM++. Liquid food flow in a heating process is analyzed numerically for heat transfer characteristics with varying Cosserat number and other physical aspects. Simulations are performed in a channel connecting a tank with different stirrer settings. Computed results are analyzed in a limiting case for accuracy and a strong agreement is achieved with the available solutions from the literature. Some interesting features of the liquid food flow and heat transfer are presented and discussed. It is observed that when liquid food particles rotate faster, the temperature difference between the walls also increases. The temperature difference between the top and bottom walls of the liquid food tank increases with faster speed of stirrers. Rise in the Cosserat number results in a dispersed vortices throughout the liquid food tank. The temperature differential between the liquid food tank’s top and bottom walls rises as a result of an increase in the microrotational motions of the food particles. Moreover, the microrotational motion of the liquid food particles rises with an increase in Cosserat number, enabling effective particle mixing.