# Heat Transfer Performance of Fruit Juice in a Heat Exchanger Tube Using Numerical Simulations
## 1 Introduction  
In the food industry, it is important to determine the flow properties of fluid foods and their behaviour because it is related to the power requirements for the pumping and sizing of pipes during processing. In these cases, it is a key aspect to determine the rheological properties when selecting the equipment and type of processing, and to understand the flow pattern and the heat transfer performance. Most fluid foods used in the industry are non-Newtonian, where the fluid viscosity is not uniform and depends on the shear rate and temperature gradient. To characterise the flow behaviour of such fluids, several mathematical models can be used, such as the Power-Law model, the Cross model, the Bingham model, the Carreau model or the Herschel-Bulkley model [1]. In fluid foods, such as juices, the most common mathematical method is the Power-Law model. Several studies have focused on analysing the rheological properties of fluid foods. [PERSON] et al. [2] analysed the rheological behaviour of two different redcurrant juices using three models (Newtonian model, Power-Law model and Herschel-Bulkley) to define the relationship between shear stress and shear rate. They concluded that, for redcurrant juices containing pectins, the Power-Law model better described their rheological behaviour. Other studies, such as that by [PERSON] et al. [3], modelled the rheological behaviour of pomelo juice concentrates for a temperature range between 6 and 75 \({}^{\circ}\)C. Theyobtained good results using the non-Newtonian Power-Law model. [PERSON] and [PERSON] [4] studied the rheological behaviour of sour-cherry juice, as well as the effect of soluble solids concentration and temperature on flow behaviour. In their study, they used Power-Law model and exponential model to study the effect of concentration on the viscosity. [PERSON] et al. [5] experimentally compared smooth and helically corrugated tubes in the laminar and transitional flow regimes in a shell and tube heat exchanger, and used the Power-Law model to define the rheological behaviour of two pseudoplastic fruit pureses. In engineering applications, mainly in the food industry, many processes use high viscosity fluids. In these cases, the flow regime tends to be laminar, typically associated with low heat transfer coefficients. Moreover, in many industry applications that use heat exchangers, energy costs account for a high percentage of the total operation and maintenance costs. In this regard, methods to enhance heat exchanger tubes are essential in many of such applications. These methods can be defined as either active or passive [6; 7]. One of the key aspects is improving heat transfer performance for more efficient use of these devices, with it being important to analyse flow behaviour and heat transfer performance in heat exchangers. Some studies have experimentally reported that curved tubes as a passive heat transfer technique are commonly used in many industrial applications, such as nuclear industries, heat recovery systems or food processes [8; 9]. In this case, these devices promote secondary flow, which helps improve heat transfer performance in comparison to a straight smooth pipe. [PERSON] and [PERSON] [10] analysed the effect of curvature on heat transfer for fully developed turbulent flow in curved pipes. They reported a significant increase in heat transfer rate in comparison to a straight pipe, considering wall heat flux boundary condition. Other works [11] have carried out experimental studies to analyse heat transfer and pressure drop in helical and spiral coils using non-Newtonian fluids. In this regard, [PERSON] [12] proposed correlations to predict turbulent Nusselt number and friction factor for viscous Power-Law fluids in helical coils. [PERSON] and [PERSON] [13] studied pressure drop for several pseudoplastic polymer solutions, obtaining a correlation to calculate friction factor as a function of the curvature ratio.