# Heat Transfer Performance of Fruit Juice in a Heat Exchanger Tube Using Numerical Simulations
## 1 Introduction
[PERSON] and [PERSON] [14] analysed laminar flow for a Power-Law of non-Newtonian fluid, obtaining correlation for the friction factor using boundary layer approximation. [PERSON] et al. [15] experimentally studied laminar steady-state heat transfer in a pseudoplastic fluid food, through circular and concentric annular ducts. In addition, they measured the rheological properties in the ranges of 9.3-49.4\({}^{\circ}\) Brix and 0.4-68.8\({}^{\circ}\)C. In their study, empirical equations for Nusselt number were obtained, which were useful for manufacturers to design double-pipe and triple tube heat exchangers. As a complementary activity to experimental activities and a prior step to the detailed designing of heat exchangers, computational fluid dynamic techniques (\(CFD\)) are a common tool for analysing heat exchanger performance. Few works have focused on studying non-Newtonian flow on pipe bends and coiled pipes [16; 17] using numerical simulations. However, some studies [18] have carried out experimental and numerical investigation of convective heat transfer in helically coiled tube heat exchangers, to study friction losses in a helical coil tube heat exchanger using laminar flow regime for a non-Newtonian fluid. In the cited study, the authors used water, glycerol-water mixtures, and diluted aqueous polymer solutions of Sodium Carboxy Methyl Cellulose and Sodium Alginate as non-Newtonian fluids. They developed innovative correlations for Nusselt number and friction factor for non-Newtonian fluids. Hence, Nusselt number was obtained as a function of one dimensionless number (M) [13], Prandtl number and coil curvature ratio, and the friction factor was obtained depending on the Dean number. [PERSON] and [PERSON] [18] compared the correlations obtained for Nusselt number and friction factor with previous studies, and they obtained good agreement between experimental and numerical results. Hence, the average correlated Nusselt number was approximately 6% higher than the one proposed by [PERSON] et al. [11]. Friction factor values obtained by [PERSON] and [PERSON] [14] were higher than the obtained in the proposed correlation. [PERSON] et al. [19] developed a numerical simulation of the mixed convection heat transfer from vertical helically coiled tubes in vertical helically coiled tube heat exchangers. They compared the numerical results with experimental data, finding that the heat transfer coefficient decreases as the tube diameter increases, considering the same coil pitch. [PERSON] and [PERSON] [20] numerically analysed the flow of non-Newtonian liquid trough elbows, considering a laminar non-Newtonian pseudoplastic fluid. They concluded that the pressure drop for the 45\({}^{\circ}\) elbow was higher than that of the 135\({}^{\circ}\) elbow when analysing the influence of the curvature on the flow mixing process, depending of the type of elbow. The aim of this work was to numerically simulate, with a non-Newtonian fluid in laminar regime, the heat transfer process in a tube with a curved elbow, similar to that used in double tube heat exchangers or in shell and tube heat exchangers with a U-tube bundle as the rear head. The rheological properties of the fluid were experimentally measured and the numerical model was previously validated with published correlations using water as heat transfer fluid (\(HTF\)).