Mathematical Aspects of Green Energy

Authors

  • Shivesh Mani Tripathee Department of Applied Sciences and Humanities, FOET. Dr Shakuntala Misra National Rehabilitation University, Lucknow, Uttar Pradesh, India Author
  • Pawan Kumar Department of Applied Sciences and Humanities, FOET. Dr Shakuntala Misra National Rehabilitation University, Lucknow, Uttar Pradesh, India Author
  • Sumit Tripathi Department of Applied Sciences and Humanities, FOET. Dr Shakuntala Misra National Rehabilitation University, Lucknow, Uttar Pradesh, India Author

DOI:

https://doi.org/10.59436/ijpsr.v2i2.5.3139-342X

Keywords:

Green energy, mathematical modelling, mathematical aspects, sustainable future

Abstract

Mathematics is fundamental in various aspects of green energy: energy generation, energy storage, energy distribution, and energy consumption. The most common branches of mathematics are calculus, linear algebra, differential equations, statistics, and optimization. Mathematics provide a diverse avenue for the establishment of green energy technologies. This includes in such areas as predictive modelling, optimization, and data analysis, which are enabling the efficiency and sustainability of green energy systems. Understanding the mathematical aspects should be the focus of any researcher, engineer, and policymaker striving for a cleaner and more sustainable future.

References

[1] http://www.nrel.gov/learning/student_resources.html .

[2] Spath, Pamela L. and Mann, Margaret K., Life Cycle Assessment of Hydrogen Production Via Natural Gas Wind/Electrolysis, National Renewable Energy Labo ratory, Colorado,( 2004).

[3] Duffie, J. A., & Beckman, W. A. Solar engineering of thermal processes. John Wiley & Sons. (2013).

[4] Spath, Pamela L. and Mann, Margaret K., Life Cycle Assessment of Hydrogen Pro duction Via Natural Gas Steam Reforming, National Renewable Energy Laboratory, Colorado, (2001)

[5] Manwell, J. F., McGowan, J. G., & Rogers, A. L. (2009). Wind energy explained: theory, design and application. John Wiley & Sons.

[6] Halliday, D., Resnick, R., & Walker, J. (2014). Fundamentals of physics. John Wiley & Sons.

[7] Gueymard, C. (2004). The sun's angle and its components. Solar Energy, 76(1), 423-457.

[8] Jonkman, J. M., & Butterfield, S. (2009). Dynamics of offshore wind turbines. Springer Science & Business Media.

[9] Kirschen, D. S., & Strbac, G. (2010). Fundamentals of power system economics. John Wiley & Sons.

[10] Reference: Lund, H., Østergaard, J., & Mathiesen, B. V. (2017). Energy storage systems. Elsevier.

[11] ISO 14040:2006, Environmental management—Life cycle assessment—Principles and framework.

[12] Boardman, A. E., Greenberg, D. H., Vining, A. R., & Weimer, D. L. (2011). Cost-benefit analysis: concepts and practice. Pearson Education.

[13] P..T. Anastas et al.Catalysis as a foundational pillar of green chemistry Appl. Catal. Gen. (2001)

[14] N.D. Austin et al. Computer-aided molecular design: an introduction and review of tools, applications, and solution techniques Chem. Eng. Res. Des. (2016)

[15] P.T. Benavides et al. Optimal design of adsorbents for NORM removal from produced water in natural gas fracking. Part 2: CAMD for adsorption of radium and barium Chem. Eng. Sci. (2015)

[16] S. Chavali et al. Environmentally-benign transition metal catalyst design using optimization techniques Comput. Chem. Eng. (2004)

[17] H.C. Cheng et al. Optimal biocompatible solvent design for a two-stage extractive fermentation process with cell recycling Comput. Chem. Eng. (2008)

[18] H.C. Cheng et al. Computer-aided biocompatible solvent design for an integrated extractive fermentation–separation process Chem. Eng. J. (2010)

[19] R. Gani Chemical product design: challenges and opportunities Comput. Chem. Eng. (2004)

[20] R. Gani et al. Product design – molecules, devices, functional products, and formulated products Comput. Chem. Eng.(2015)

[21] M. Hostrup et al. Design of environmentally benign processes: integration of solvent design and separation process synthesis Comput. Chem. Eng. (1999)

[22] A.T. Karunanithi et al. A computer-aided molecular design framework for crystallization solvent design Chem. Eng. Sci. (2006).

[23] Accolla, C., Vaugeois, M., Grimm, V., Moore, A. P., Rueda‐Cediel, P., Schmolke, A., & Forbes, V. E. (2021). A review of key features and their implementation in unstructured, structured, and agent‐based population models for ecological risk assessment. Integrated environmental assessment and management, 17(3), 521-540. https://doi.org/10.1002/ieam.4362

[24] Barwell, R. (2018). Some Thoughts on a Mathematics Education for Environmental Sustainability. In: Ernest, P. (eds) The Philosophy of Mathematics Education Today. ICME-13 Monographs. Springer, Cham. 145-160. https://doi.org/10.1007/978-3-319-77760-3_9

[25] Billionnet, A. (2013). Mathematical optimization ideas for biodiversity conservation. European Journal of Operational Research, 231(3), 514-534. https://doi.org/10.1016/j.ejor.2013.03.025

[26] Emlen, J. M., Duda, J. J., Kirchhoff, M. D., & Freeman, D. C. (2006). Interaction assessment: a modelling tool for predicting population dynamics from field data. Ecological modelling, 192(3-4), 557-570. https://doi.org/10.1016/j.ecolmodel.2005.07.012

[27] Estes, R. D. (2014). The Gnu’s world: Serengeti wildebeest ecology and life history. University of California Press.

[28] Filipsson, M. (2011). Uncertainty, variability and environmental risk analysis (Doctoral dissertation, Linnaeus University Press). https://www.diva-portal.org/smash/get/diva2:405602/FULLTEXT01.pdf

[29] Friedman R., Ansell C., Diamond S., & Haimes Y. Y. (1984). Use of models for water resources management, planning, and policy. Water Resource Research. 20 (7). 793-803. https://doi.org/10.1029/WR020i007p007 93

[30] Gharye Mirzaei, M., Gholami, S., & Rahmani, D. (2023). A mathematical model for the optimization of agricultural supply chain under uncertain environmental and financial conditions: the case study of fresh date fruit. Environment, Development and Sustainability, 1-34. https://doi.org/10.1007/s10668-023-03503-7

[31] Gómez Sánchez, M., Macia, Y. M., Fernández Gil, A., Castro, C., Nuñez González, S. M., & Pedrera Yanes, J. (2021). A mathematical model for the optimization of renewable energy systems. Mathematics, 9(1), 39. https://doi.org/10.3390/math9010039

[32] Grundy, E., & Murphy, M. J. (2015). Demography and public health. ‘Demography and public health’, in Roger Detels et al., (Eds), Oxford Textbook of Global Public Health, 6 edn, https://doi.org/10.1093/med/ 9780199661756.003.0126

[33] He, S., Tang, S., Zhang, Q., Rong, L., & Cheke, R. A. (2023). Modelling optimal control of air pollution to reduce respiratory diseases. Applied Mathematics and Computation, 458, 128223. https://doi.org/10.1016/ j.amc.2023.128223

[34] IBM (2024).What is optimization modelling?IBM. Retrieved from https://www.ibm.com/topics/optimization-model Accessed May 2, 2024

[35] Johnston, A. S., Boyd, R. J., Watson, J. W., Paul, A., Evans, L. C., Gardner, E. L., & Boult, V. L. (2019). Predicting population responses to environmental change from individual-level mechanisms: towards a standardized mechanistic approach. Proceedings of the Royal Society B, 286(1913), 20191916

[36] Kern, F. (2013). Implementing the green economy. Ökologisches Wirtschaften-Fachzeitschrift, 28(3), 20-22.

[37] Klijn, F., de Bruijn, K. M., Knoop, J., & Kwadijk, J. (2012). Assessment of the Netherlands’ flood risk management policy under global change. Ambio, 41, 180-192. https://doi.org/10.1007%2Fs13280-011-0193-x

[38] Kundu, S. (2018). Mathematical modelling as a tool for sustainable development. J. Artic. Math. Educ, 5, 348-350. http://ijrar.com/upload _issue/ijrar_issue_1052.pdf

[39] Law, R., Murrell, D. J., & Dieckmann, U. (2003). Population growth in space and time: spatial logistic equations. Ecology, 84(1), 252-262. https://doi.org/10.1890/0012-9658(2003)084[0252:PGISAT]2.0.CO;2

[40] Li, X., Song, J., Lin, T., Dixon, J., Zhang, G., & Ye, H. (2016). Urbanization and health in China, thinking at the national, local and individual levels. Environmental Health, 15, 113-123. https://doi.org/10.1186/s 12940-016-0104-5

[41] Li, Y. P., Huang, G. H., Nie, S. L., Chen, B., & Qin, X. S. (2013). Mathematical modelling for resources and environmental systems. Mathematical Problems in Engineering, 2013.

[42] Tripathee,Mani.Shivesh. (2017), Assessment of mucus transport rate in the human lung airways using mathematical model, J. Biol. Sci. Med. (2017) 3 (4): 17-25.

[43] Tripathee S M, Verma VS (2016) Mucus flow in human lung airways: Effects of Air velocity cilia tip velocity and porosity parameter. International J Sci nad Res 632-636 Verma VS (2007) A mathematical study on mucus transport in the lung. J Nat Acad Math 21:107-117.

[44] Tripathee, S.M. and Mishra Lokesh (2023), Biomathematics: An Introduction, international Journal of Innovative Research in Engineering Volume 4, Issue 1 (January-February 2023), PP: 170-172.

[45] Verma V S (2008) A planar two layer unsteady state for mucociliary transport. JTS India 2:115-127.

[46] Verma VS (2009) Mucus transport: A fluid mechanical Steady state model. J Rajasthan Acad Phy Sci 8(3):371-384.

[47] Verma VS (2010) A planar model for mucus transport in human respiratory tract: Effect of air-flow, porosity and and mucus viscoelasticity. J Nat Acad Math 24:53-60.

[48] Verma VS, Tripathee S M (2011) A study on mucus flow in human lung airways. JPS 2(1):113-120.

[49] Verma VS (2012) Mucus flow in lung airways: A planar two layer steady state mathematical model. JTS India 6(1):69-77.

[50] Verma VS, Tripathee SM (2013) A planar model for mucociliary transport in the human lung: Effects of mucus viscoelasticity, cilia beating and porosity. IJMRS’s International J Mathemat Model Phy Sci 1(1):19-25.

[51] Tripathee Mani Shivesh, Dwivedi Amit, Kumar Pawan (2024), Journal of Science Innovations and Nature of Earth Vol. 4, Issue 1, Page 04-06. www.doi.org/10.59436/https://jsiane.com/archives4/1/115 .

[52] Harendra Verma, Vishnu Narayan Mishra, Pankaj Mathur (2022), Effectiveness of lock down to curtail the spread of corona virus: A mathematical model, ISA Transactions, Volume 124, , Pages 124-134,ISSN 0019-0578,https://doi.org/10.1016/j.isatra.2021.01.033.

[53] Tripathee Mani Shivesh, Singh Aakash, Yadav Singh Ajay, Verma Harendra (2024), Mucus flow in human lung airways by using mathematical methods, Futuristic Trends in Chemical, Material Sciences &Nano Technology e-ISBN: 978-93-5747-750-5 IIP Series, Volume 3, Book 14, Part 2, Chapter 1.

[54] Harendra Verma, Nidhi Pandya, Vishnu Narayan Mishra, Pankaj Mathur, Modeling and analysis of media’s role in popularizing the blue whale game, International Journal of Mathematics for Industry Volume 12 (1), 2020 Article no 2050008.

[55] Verma, H., Mishra, V.N. & Mathur, P. Modeling of the chaotic situation in the recruitment processes. Adv. in Comp. Int. 3, 17 (2023). https://doi.org/10.1007/s43674-023-00064-0.

[56] Pathak, Rachana, Bhadauria, Archana Singh, Chaudhary, Manisha, Verma, Harendra, Mathur, Pankaj, Agrawal, Manju and Singh, Ram. "Role of ecotourism in conserving forest biomass: A mathematical model" Computational and Mathematical Biophysics, vol. 11, no. 1, 2023, pp. 20220153. https://doi.org/10.1515/cmb-2022-0153

[57] Verma, H., Antwi-Fordjour, K., Hossain, M. et al. A “Double” fear effect in a tri-trophic food chain model. Eur. Phys. J. Plus 136, 905 (2021). https://doi.org/10.1140/epjp/s13360-021-01900-3.

Published

2026-06-16

How to Cite

Shivesh Mani Tripathee, Pawan Kumar, & Sumit Tripathi. (2026). Mathematical Aspects of Green Energy. International Journal of Primary and Secondary Research (IJPSR), 2(2), 24-28. https://doi.org/10.59436/ijpsr.v2i2.5.3139-342X