# Heat Transfer Characteristics in Vertical Tubular Baffle Internal Reboiler through Dimensional Analysis

Title: Heat Transfer Characteristics in Vertical Tubular Baffle Internal Reboiler through Dimensional Analysis
Yuana Susmiati, Bambang Purwantana, Nursigit Bintoro, Sri Rahayoe

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Susmiati, Y., Purwantana, B., Bintoro, N., Rahayoe, S., 2022. Heat Transfer Characteristics in Vertical Tubular  Baffle Internal Reboiler through Dimensional Analysis. International Journal of Technology. Volume 13(3), pp. 508-517

884
 Yuana Susmiati 1. Doctoral student of Agricultural Engineering, Faculty of Agricultural Technology, Universitas Gadjah Mada, Jl. Flora 1, Bulaksumur, Yogyakarta, 55281, Indonesia 2. Departemen of Renewable Energy Bambang Purwantana Departement of Agricultural and Biosystem Engineering, Faculty of Agricultural Technology, Universitas Gadjah Mada, Jl. Flora 1, Bulaksumur, Yogyakarta, 55281, Indonesia Nursigit Bintoro Departement of Agricultural and Biosystem Engineering, Faculty of Agricultural Technology, Universitas Gadjah Mada, Jl. Flora 1, Bulaksumur, Yogyakarta, 55281, Indonesia Sri Rahayoe Departement of Agricultural and Biosystem Engineering, Faculty of Agricultural Technology, Universitas Gadjah Mada, Jl. Flora 1, Bulaksumur, Yogyakarta, 55281, Indonesia
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Abstract

Heat transfer in shell and tube heat exchangers is in general described in terms of the relationships of Nuselt, Prandtl, and Reynold dimensionless numbers. One of the parameters of heat exchanger performance is convective heat transfer coefficient (h), and mathematical model can predict it. This study aimed to find out the relationship of the parameters that affected the performance of vertical tubular baffle internal reboiler during ethanol distillation. The mathematical model was developed by a dimensional analysis with the ?-Buckingham method. Several influencing parameters during the distillation process were identified to develop a mathematical model. The study was carried out on the distillation process of low-concentration ethanol, i.e., 10%, 20%, 30% using internal reboilers with different tube sizes, i.e., diameters of 1.27 cm, 2.54 cm, 3.81 cm and height of 4 cm, 6 cm, 8 cm, to obtain the value of h observation. Based on the results of the study, a heat transfer model was obtained, i.e.,, where Nu, Re, D, L, T, Cp, v, ?, and k,  are respectively Nuselt, Reynold, tube diameter, tube height, temperature, heat capacity, velocity, mass density, and thermal conductivity of the fluid (material).  This model can be used to determine h prediction, and the result is following h observation with equation y = 0.98x and R² = 0.99. Based on the results of the study, it is known that differences in material concentration, diameter, and height of the reboiler tube affect the value of h.

Dimensional analysis; Internal reboiler; ?-Buckingham method

Introduction

A distillation process is determined by the type of heat exchanger (reboiler) that serves to heat and evaporate the distilled solution. The temperature in the reboiler is determined by the types of the reboiler and it affects the distillation productivity (Bhanvase et al., 2007 and Foletto, 2015). In general, small-scale distillation uses an internal reboiler, i.e., a heat exchanger located in the bottom column of the distillation equipment and submerged in the distilled solution (Bell et al., 2011).
The types of heat exchangers used as internal reboilers include stub in U-tube bundle reboiler (Voigt & Nj, 2013), calandria (Bhanvase et al., 2007), and vertical helical coil (Ghorbani et al., 2010). A design and test of another type of heat exchanger with different shapes and directions of fluid flow were developed by (Susmiati et al., 2019) named vertical tubular baffle. This study showed that the geometry (diameter, height, and the number of tubes) in this type of heat exchanger affects the heat transfer coefficient. As explained by (Abd & Naji, 2017) the heat transfer coefficient in a heat exchanger can be increased by increasing the tube length. (Lei et al., 2017) also stated that different baffle shapes in a shell and tube heat exchanger produce different heat transfer coefficients, i.e., louver baffle is higher than segmental baffle.

A vertical tubular baffle heat exchanger as a reboiler in an ethanol distillation process has been carried out by (Susmiati et al., 2021) and it was found that different reboiler geometries produced different distillation ethanol concentrations. This shows that different geometries lead to other heat transfer coefficients, thus leading to different productivity of the distillation process. This is in line with (Parhi et al., 2019) and (Badi et al., 2021), who stated that increasing the productivity of distillation equipment can be carried out by optimizing reboiler heat input.
The characteristics of a heat exchanger's performance include heat transfer rate, heat transfer coefficient, pressure drop coefficient, and friction factor. The heat transfer coefficient in a heat exchanger can be determined based on the Nuselt number (Kim et al., 2017). A study on heat transfer in spiral heat exchangers with different impellers was done by (Rosa et al., 2017) showing that the overall heat transfer coefficient is a function of the Nusselt (Nu), Reynolds (Re), Prandtl (Pr) numbers,  and wall temperature (Vi) i.e.,  on a pitched blade turbine impeller and   on Ruston turbine impeller.
The relationship among the Nuselt, Prandtl, and Reynold dimensionless numbers can be used to predict the convective heat transfer coefficient in a heat exchanger. The heat transfer model of a heat exchanger can be developed by a dimensional analysis as conducted by (Lin et al., 2007) on the characteristics of heat transfer in corrugated channels of a plate heat exchanger. (Nakla, 2011) also developed a heat transfer model on film boiling using dimensional analysis to calculate the effect of diameter on heat transfer coefficient. Dimensional analysis is useful to explain a phenomenon that is found in a process and described as a mathematical model (Pexton, 2014).
Several parameters affect the performance of a vertical tubular baffle internal reboiler in an ethanol distillation process, i.e., fluid temperature (T), viscosity (µ), and mass density (?) of fluid, diameter (D), and height (L) of reboiler tube. For the development of the instrument, it is important to have a model that describes the heat transfer process and the relationship between the influencing parameters, thus helping the scale-up and engineering processes.  The relationship among these parameters can be expressed in an equation of Nuselt, Prandtl, and Reynolds dimensionless numbers with dimensional analysis. This study aimed to develop a mathematical model of heat transfer in a vertical tubular baffle internal reboiler using dimensional analysis and the Buckingham method.

Conclusion

The heat transfer in the vertical tubular baffle internal reboiler during the ethanol distillation process can be described in the form of a relationship of various influencing parameters and  was obtained, where Nu, Re, D, L, T, Cp, v, ?, and k,  are respectively  Nuselt, Reynold, tube diameter, tube height, temperature, heat capacity, velocity, mass density, and thermal conductivity of the fluid (material).  The mathematical model can be used to determine the convective heat transfer coefficient (h) and its validity reaches 99%. The highest convective heat transfer coefficient was obtained in the experiment with a reboiler that was 1.27 cm in diameter and 8 cm in height, and a 10% material concentration, i.e., 196.19 J/m2soC.

Acknowledgement

The author would like to express her gratitude for the research funding through the program of Final Project Recognition (RTA) of Universitas Gadjah Mada in 2019. The author would also like to thank the technicians and managers of the Laboratory of Energy and Agricultural Machinery, Faculty of Agricultural Technology, Universitas Gadjah Mada, for the completion of this research

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