This study used the proportional nodes method, a novel curve fitting approach to correlate data for dynamic viscosity of ammonia-water solution. The approach integrates polynomial equations, generated at various temperatures, with those calculated at selected mole fraction nodes. These nodes are scaling factors that account for variations in dynamic viscosity at different temperatures at selected mole fractions. The accuracy of the polynomial equations ensures a high degree of fitting accuracy. The proportional nodes, computed systematically, were integrated into a robust and highly accurate polynomial model to generate correlations that fit the data for the surface. This model exhibited minimal average percentage differences between predicted and actual viscosity values (±0.2614293 for temperature range, 273.15K to 303.15K and ±1.11 for temperature range, 303.15K to 423.15 K), indicating a high level of predictive accuracy. The proportional nodes method offers a significant contribution to both academic research and industry. It provides a more precise and adaptive model for predicting the dynamic viscosity of ammonia-water solution, which is critical for optimizing and designing various industrial applications, including refrigeration systems.
correlations, proportional nodes, curve fitting, dynamic viscosity, ammonia-water solution
S. N. Mumah. Corresponding author. Director, Centre for Renewable Energy & Chief Lecturer, Department of Chemical Engineering, Kaduna
Polytechnic, Kaduna, Nigeria, E-mail: mumahsndoyi@kadunapolytechnic.edu.ng
H.F. Akande. Chief Lecturer, Department of Chemical Engineering, Kaduna Polytechnic, Kaduna, Nigeria. E-mail: hassan.akande@kadunapolytechnic.edu.ng
S. Alexander. Lecturer, Department of Marketing, Kaduna Polytechnic, Kaduna, Nigeria. E-mail: astephen@kadunapolytechnic.edu.ng
K.Y. Mudi. Chief Lecturer, Department of Chemical Engineering, Kaduna Polytechnic, Kaduna, Nigeria. E-mail: m.kehinde@kadunapolytechnic.edu.ng
O. Olaniyan. Chief Lecturer, Department of Civil Engineering, Kaduna Polytechnic, Kaduna, Nigeria. E-mail: dejoolaniyan@kadunapolytechnic.edu.ng
F. Samuel. Lecturer, Department of Chemical Engineering, Kaduna Polytechnic, Kaduna, Nigeria. E-mail: francissamuel@kadunapolytechnic.edu.ng
Abbas, A., Ayub, Z. H., Ismail, T., Ayub, A. H., Li, W., Khan, T. S., and Ribatski, G. (2021). Experimental study of ammonia flow boiling in a vertical tube bundle: Part 1 – Enhanced dimple tube. International Journal of Refrigeration. https://doi.org/10.1016/j.ijrefrig.2021.07.012
Ahmed, Z., Saleem, S., Nadeem, S., and Khan, A. U. (2020). Squeezing Flow of Carbon Nanotubes-Based Nanofluid in Channel Considering Temperature-Dependent Viscosity: A Numerical Approach. https://doi.org/10.1007/s13369-020-04981-x
Ahmadi, M., Gharyehsafa, B. M., Farzaneh-Gord, M., Jilte, R., Kumar, R., and Chau, K. (2019). Applicability of connectionist methods to predict dynamic viscosity of silver/water nanofluid by using ANN-MLP, MARS and MPR algorithms. Engineering Applications of Computational Fluid Mechanics. https://doi.org/10.1080/19942060.2019.1571442
Bakhtiari Manesh, P., Shahbazi, K., and Shahryari, S. (2019). Application of Grid partitioning based Fuzzy inference system and ANFIS as novel approach for modeling of Athabasca bitumen and tetradecane mixture viscosity. Petroleum science and technology. https://doi.org/10.1080/10916466.2018.1471488
Barkhordar, A., Ghasemiasl, R., and Armaghani, T. (2021). Statistical study and a complete overview of nanofluid viscosity correlations: a new look. Journal of Thermal Analysis and Calorimetry. https://doi.org/10.1007/s10973-021-10993-y
Banerjee T., H. Firouzi, and A. O. Hero (2015). Non-parametric quickest change detection for large scale random matrices. IEEE International Symposium on Information Theory (ISIT), pp. 146–150, June 2015. http://arxiv.org/abs/1508.04720.
Banerjee, T. and A. O. Hero (2016). Quickest hub discovery in correlation graphs,” Signals, Systems and Computers, 2016 50th Asilomar Conference on. IEEE, pp. 1248-1255.
Bergman, T. L., Lavine, A. S., Incropera, F. P., and DeWitt, D. P. (2011). Fundamentals of Heat and Mass Transfer (7th ed.). John Wiley and Sons.
Bhattacharjee, S., Mishra, R. B., Malkurthi, S., and Hussain, A. (2022). Numerical Modelling of Differential Pressure Sensor System for Real-Time Viscosity Measurement. Students Conference on Engineering and Systems. https://repository.kaust.edu.sa/bitstream/10754/685582/1/SCES_2022_final_manuscri pt.pdf
Cardona, L. F., Rojas, R. E., and Valderrama, J. O. (2019). Correlation and prediction of ionic liquid viscosity using Valderrama-Patel-Teja cubic equation of state and the geometric similitude concept. Part I: Pure ionic liquids. Fluid Phase Equilibria. https://doi.org/10.1016/J.FLUID.2019.04.031
Cheng, N. S. (2008). Formula for the viscosity of a glycerol-water mixture. Industrial and Engineering Chemistry Research, 47(9), 3285-3288.
Cheraghian, G., Sajadi, S., Sharifpur, M., Alanazi, A. K., Khetib, Y., and Melaibari, A. (2021). Applying Artificial Neural Network and Response Surface Method to Forecast the Rheological Behavior of Hybrid Nano-Antifreeze Containing Graphene Oxide and Copper Oxide Nanomaterials. Sustainability. https://doi.org/10.3390/su132011505
Conde-Petit, M. (2006). Thermophysical Properties of NH3/H2O Mixtures for the Industrial Design of Absorption Refrigeration Equipment. A formulation for Industrial Use. M. Conde Engineering, Zurich, Switzerland
Dolomatov, M., Aubekerov, T. M., Koledin, O., Kovaleva, E. A., Akhtyamova, K. R., and Vagapova, E. V. (2020). QSPR model for the forecast of dynamic viscosity of arenas by the topological characteristics of molecules. https://doi.org/10.37952/ROI-JBC- 01/20-62-6-1
Eberhard, U., Hansjoerg J. Seybold, Marius Floriancic, Pascal Bertsch, Joaquin Jiménez-Martínez, José S. Andrade Jr. and Markus Holzner (May 2019). Determination of the effective viscosity of non-newtonian fluids flowing through porous media, Frontiers in Physics, Volume 7, https://doi.org/10.3389/fphy.2019.00071
Habibi, Mohammad Reza; Amini, Meysam, Arefmanesh, Aref, Ghasemikafrudi, Esmaeil (2019). Effects of Viscosity Variations on Buoyancy-Driven Flow from a Horizontal Circular Cylinder Immersed in Al2O3-Water Nanofluid, Iranian Journal of Chemistry and Chemical Engineering, Vol. 38, No. 1, pp 212-232
Holman, J. P., and Gajda, W. J. (2001). Experimental Methods for Engineers (7th ed.). McGraw-Hill.
Incropera, F. P., and DeWitt, D. P. (2002). Introduction to Heat Transfer (4th ed.). John Wiley and Sons
Irani, M., A. Masoud, M. Babak (2019). Curve fitting on experimental data of a new hybrid nano antifreeze viscosity: presenting new correlations for non-Newtonian nanofluid, Physica A, 531 (2019), 10.1016/j.physa.2019.04.073
Jaadi., Z. (Oct. 2019). Everything you need to know about interpreting correlations Towards Data Science; https://towardsdatascience.com/eveything-you-need-to-know-about- interpreting-correlations-2c485841c0b8
Jayeoba, O., and Okoya, S. (2019). Analytical solutions for the flow of a reactive third-grade fluid with temperature-dependent viscosity models in a pipe.
Jouenne, S., G. Heurteux (2020). Online Monitoring for Measuring the Viscosity of the Injected Fluids Containing Polymer in Chemical Eor. Presented in SPE Conference at Oman Petroleum & Energy Show 2020 in Muscat, Oman Society of Petroleum Engineers
Kumar, A., and Gardas, R. L. (2010). Viscosity of aqueous ammonia solution at high pressures. Journal of Chemical Engineering Data, 55, 3983-3986.
Kumari, M., M. Kumar, M.S. Barak (2021). Wave propagation characteristics at the welded interface of double-porosity solid and double-porosity dual-permeability materials, Waves Random Complex Media, 31 (6), pp. 1682-1707, 10.1080/17455030.2019.1698789
Lide, D. R. (2005). CRC Handbook of Chemistry and Physics (86th ed.). CRC Press.
Narayana, M., Udawattha, D. S., and Wijayarathne, U. P. L. (2019). Predicting the effective viscosity of nanofluids based on the rheology of suspensions of solid particles. Journal of King Saud University – Science. https://doi.org/10.1016/J.JKSUS.2017.09.016
Ma, C., Zhiyue Gao, Jie Yang, Lin Cheng and Tianhao Zhao (2022). Calibration of Adjustment Coefficient of the Viscous Boundary in Particle Discrete Element Method Based on Water Cycle Algorithm Water 2022, 14(3), 439; https://doi.org/10.3390/w14030439
Manesh, P. B., Khalil Shahbazi & Salman Shahryari (2019) Application of Grid partitioning based Fuzzy inference system and ANFIS as novel approach for modeling of Athabasca bitumen and tetradecane mixture viscosity, Petroleum Science and Technology, 37:14, 1613-1619, DOI: 10.1080/10916466.2018.1471488
Melaibari, Ammar, Yacine Khetib, Abdullah K. Alanazi, Goshtasp Cheraghian, Mohsen Sharifpur and Goshtasp Cheraghian (October 2021). Applying Artificial Neural Network and Response Surface Method to Forecast the Rheological Behavior of Hybrid Nano-Antifreeze Containing Graphene Oxide and Copper Oxide Nanomaterials, Sustainability 13(20):11505
Miyara, A., Alam, M. J., Yamaguchi, K., and Kariya, K. (2019). Development and Validation of Tandem Capillary Tubes Method to Measure Viscosity of Fluids. https://doi.org/10.11322/TJSRAE.18-47_EM_OA
Motulsky, H., and Ransnas, L. (1987). Fitting curves to data using nonlinear regression: A practical and nonmathematical review. FASEB Journal, 1(5), 365-374.
Mumah, S.N. (2021). Introduction of a novel curve fitting approach: The use of Proportional Nodes. Unpublished Research and Innovation Report. Kaduna Polytechnic, Kaduna, Nigeria
Mumah, S.N., Akande, H.F., Mudi, K.Y., Olaniyan, I.O. and Samuel, F. (2021). Correlations for Liquid and Vapour Dynamic Viscosities for Ammonia-Water Solution. Nigerian Research Journal of Engineering and Environmental Sciences. 6(2) 2021 pp. 596-606
Petricioli L., Humski L., Vrani M., and Pintar D. (February 25, 2020). Data Set Synthesis based on known Correlations and Distributions for Expanded Social Graph Generation. IEEE ACESS. 10.1109/ACCESS.2020.297086
Qinghua Yang (2017). Regression. Springer International Publishing AG 2017; L.A. Schintler, C.L. McNeely (eds.), Encyclopedia of Big Data, 10.1007/978-3-319- 32001-4_174
Rahmanifard, Hamid, Paiman Maroufi, Hamzeh Alimohamadi and Ian D. Gate (February 2021) The application of supervised machine learning techniques for multivariate modelling of gas component viscosity: A comparative study, Fuel 285:119146, DOI: 10.1016/j.fuel.2020.119146
Rajiv, B., Ram Natarajan and Daqun Zhang (2019). Two-stage estimation of the impact of contextual variables in stochastic frontier production function models using Data Envelopment Analysis: Second stage OLS versus bootstrap approaches, European Journal of Operational Research, 278(2), pp 368-384
Razmara, N., Namarvari, H., and Meneghini, J. R. (2019). A new correlation for viscosity of model water-carbon nanotube nanofluids: Molecular dynamics simulation. Journal of Molecular Liquids. https://doi.org/10.1016/J.MOLLIQ.2019.111438
Rezaei S, Harandi A, Moeineddin A, Ahmad Moeineddin, Bai-Xiang Xu and Stefanie Reese (2022). A mixed formulation for physics-informed neural networks as a potential solver for engineering problems in heterogeneous domains: comparison with finite element method. Computer Methods in Applied Mechanics and Engineering, Volume 401, Part B, 115616
Rojas, R. E., Cardona, L. F., and Valderrama, J. O. (2019). Correlation and prediction of ionic liquid viscosity using Valderrama-Patel-Teja cubic equation of state and the geometric similitude concept. Part I: Pure ionic liquids. Fluid Phase Equilibria. https://doi.org/10.1016/J.FLUID.2019.04.031
Shahryari, S., Bakhtiari Manesh, P., and Shahbazi, K. (2019). Application of Grid partitioning based Fuzzy inference system and ANFIS as novel approach for modeling of Athabasca bitumen and tetradecane mixture viscosity. Petroleum science and technology. https://doi.org/10.1080/10916466.2018.1471488
Stanovich, K. (2007). How to Think Straight About Psychology. Boston, MA: Pearson.
Takahashi, T., and Lin, M. C. (2019). A Geometrically Consistent Viscous Fluid Solver with Two‐Way Fluid‐Solid Coupling. Computer graphics forum (Print). https://doi.org/10.1111/cgf.13618
Thol, M., Richter, M. (2021). Dynamic Viscosity of Binary Fluid Mixtures: A Review Focusing on Asymmetric Mixtures. Int J Thermophys 42, 161. https://doi.org/10.1007/s10765-021-02905-x
Udawattha, Dilan S., Mahinsasa Narayana, and Uditha P. L. Wijayarathne (July 2019), Predicting the effective viscosity of nanofluids based on the rheology of suspensions of solid particles, Journal of King Saud University – Science, Volume 31, Issue 3, pp 412-426
Valderrama, J., Luis Fernando Cardona and Roberto E. Rojas (May 2019). Correlation and prediction of ionic liquid viscosity using Valderrama-Patel-Teja cubic equation of state and the geometric similitude concept. Part I: Pure ionic liquids, Fluid Phase Equilibria, 497, DOI: 10.1016/j.fluid.2019.04.031
Wahab, Hafiz Abdul, Hussan Zeb, Saira Bhatti, Muhammad Gulistan, Seifedine Kadry and Yunyoung Nam (2020).Numerical Study for the Effects of Temperature Dependent Viscosity Flow of Non-Newtonian Fluid with Double Stratification, Applied. Sciences. 2020, 10(2), 708; https://doi.org/10.3390/app10020708
Wietecha, T., and Kurzydło, P. (2019). Determination of the dynamic viscosity coefficient of the Stokes viscometer – construction of a measuring set in the Physical Laboratory of the State Higher Vocational School in Tarnów. Science Technology and Innovation. https://doi.org/10.5604/01.3001.0013.2885
Zare, Y., Sang Phil Park and Kyong Yop Rhee ((2019). Analysis of complex viscosity and shear thinning behavior in poly (lactic acid)/poly (ethylene oxide)/carbon nanotubes biosensor based on Carreau–Yasuda model, Results in Physics, 13, 102245, pp 1-8
Cite this article:
Mumah, S.N., Akande, H.F., Alexander, S., Mudi, K.Y., Olaniyan, O. & Samuel, F. (2023). Evaluating the effectiveness of proportional nodes method in curve fitting for surfaces: Application to data of dynamic viscosity of ammonia-water solution. International Journal of Science, Technology, Engineering and Mathematics, 3 (4), 1-29. https://doi.org/10.53378/353024
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