DOI: https://doi.org/10.14710/jfma.v7i1.22480

MIXTURE PURIFICATION MODEL WITH CASCADING TANK CONFIGURATION

*Yanuar Bhakti Wira Tama  -  Departement of Mathematics, Institut Teknologi Kalimantan, Balikpapan, Indonesia
Robby Robby  -  Department of Mathematics, Parahyangan Catholic University, Bandung, Indonesia

Citation Format:
Abstract
Consider mixing problems which are often found in Calculus or Differential Equation courses. Under some assumptions, this problem can be used to model the purification process in a polluted mixture. In this case, the cascading configuration will be investigated for modelling the spread of pollution from one mixture to another. There are two main problems: finding time needed so the amount of pollutant in mixture inside the certain tank does not exceed certain threshold and finding the number of tanks needed so that the amount of mixture in the last tank does not exceed certain threshold. The solution for the second problem will be simplified by using Stirling approximation, which approximates factorial into exponential term. For the first problem, the time needed depends on the number of tanks, initial value of the pollutant, the rate of flow, and the volume of solution inside the tanks. For the second problem, the number of tanks only depends on the initial value of the pollutant.
Fulltext
Keywords: mixing problem; system of differential equations; Stirling approximation

Article Metrics:

Article Info
Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
Recent articles
OPTIMAL CONTROL OF MATHEMATICAL MODELS IN BIOENERGY SYSTEMS AS EMPOWERMENT OF SUSTAINABLE ENERGY SOURCES THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER. PRIME LABELING OF SOME WEB GRAPHS WITHOUT CENTER More recent articles
  1. C. H. Edwards, D. E. Penney, Elementary Differential Equations, sixth edition, Pearson, Upper Saddle River, NJ, 2008
  2. Varberg, Edwin Joseph Purcell, Steven E. Rigdon, Calculus, ninth edition, Prentice Hall, 2007
  3. W. E. Boyce, R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, ninth edition, Wiley, New York, 2009
  4. Alnoor, Fatima Omer, and Thwiba Abdulslam Khalid. "A short note on a technique for solving mixing problems by using the Laplace transform", TechHub Journal, 1.2 pp. 1-5, 2021
  5. Slavík, Antonín, "Mixing Problems with Many Tanks", The Mathematical Association of America, vol. 120 pp. 806–821, 2013
  6. Efendi, Rustam and Sagita, Diang, "Penerapan Sistem Persamaan Diferensial Linier pada Simulasi Debit Air pada Pipa", JMPM (Jurnal Material dan Proses Manufaktur), vol. 5 pp. 10-17, 2021
  7. Hadi, Ahmad Nurul and Djauhari, Eddy and Supriatna, Asep K and Johansyah, Muhamad Deni, "Teknik Penentuan Solusi Sistem Persamaan Diferensial Linear Non-Homogen Orde Satu", Matematika: Jurnal Teori dan Terapan Matematika, vol. 18, 2019
  8. Maswar, Maswar and Mujib, Mujib, "Analisis Metode Mutua dan Aplikasinya Terhadap Diferensial Linear Orde $n$", Kadikma vol. 13 pp. 174-190, 2022
  9. Nugraha, Alpi Mahisha and Nurullaeli, Nurullaeli, "Penyelesaian Numerik Persamaan Differensial Biasa Orde Satu dan Orde Dua Berbasis Graphical Unit Interface MATLAB", Diskusi Panel Nasional Pendidikan Matematika vol. 9, 2023
  10. Pratama, Herlangga Jaka and Ramdani, Yani, "Membangun Fungsi Green untuk Persamaan Diferensial Linear Non Homogen Orde-2 Koefesien Konstan", Jurnal Riset Matematika pp. 55-64, 2022
  11. Sitompul, Hery Andi and Siahaan, Enzo WB, "Solusi Numerik Persamaan Diferensial Biasa Orde Tinggi Melalui Pendekatan Metode Beda Pusat Newton", Jurnal Ilmiah Teknik Sipil, vol. 11 pp. 168-173, 2023
  12. Berg, Christian and Massa, Eugenio and Peron, Ana P, "A Family of Entire Functions Connecting the Bessel Function J1 and the Lambert W Function", Constructive Approximation, vol. 53 pp. 121-154, 2021
  13. Bharatbhai, Narola Harsh and Deshmukh, PC and Scott, Robert B and Roberts, Ken and Valluri, Sree Ram, "Lambert W function methods in double square well and waveguide problems", Journal of Physics Communications, vol. 4 pp. 065001, 2020
  14. Calasan, Martin and Aleem, Shady HE Abdel and Hasanien, Hany M and Alaas, Zuhair M and Ali, Ziad M, "An Innovative Approach for Mathematical Modeling and Parameter Estimation of PEM Fuel Cells Based on Iterative Lambert W function", Energy vol. 264 pp. 126165, 2023
  15. Gerov, Radmila and Jovanovc, Zoran, "Parameter Estimation of the IPDT Model Using the Lambert W Function", 2019 14th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS), pp. 400-403, 2019
  16. Jamilla, Cristeta and Mendoza, Renier and Mező, István, "Solutions of Neutral Delay Differential Equations using a Generalized Lambert W function", Applied Mathematics and Computation, vol. 382 pp. 125334, 2020
  17. Mainardi, Francesco and Masina, Enrico and Gonzalez-Santander, Juan Luis, "A Note on the Lambert W Function: Bernstein and Stieltjes Properties for a Creep Model in Linear Viscoelasticity", Symmetry vol. 15 pp. 1654, 2023
  18. Mendonca, J Ricardo G, "Electromagnetic Surface Wave Propagation in a Metallic Wire and the Lambert W Function", American Journal of Physics vol. 87 pp. 476-484, 2019
  19. Wang, J and Moniz, NJ, "Analysis of thermodynamic problems with the Lambert W function", American Journal of Physics, vol. 87 pp. 752-757, 2019

Last update:

No citation recorded.

Last update:

No citation recorded.