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Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment
Research Article | Published: 28 December 2025
International Journal of Thermo-Fluid Systems and Sustainable Energy Volume 1, Issue 2, 2025: 96-107
Volume 1, Issue 2, International Journal of Thermo-Fluid Systems and Sustainable Energy
Volume 1, Issue 2, 2025
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International Journal of Thermo-Fluid Systems and Sustainable Energy, Volume 1, Issue 2, 2025: 96-107

Open Access | Research Article | 28 December 2025
Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment
by
D. Gowthaman D. Gowthaman 1
A. Shamadhani Begum A. Shamadhani Begum 2
S. Thamizh Suganya S. Thamizh Suganya 1
Muhammad Rafiq Muhammad Rafiq 3
Muhammad Ijaz Khan Muhammad Ijaz Khan 4 *
1 Department of Mathematics, AMET Deemed to be University, Chennai 603112, India
2 Department of Science and Humanities, Sri Krishna College of Engineering and Technology, Coimbatore 641008, India
3 College of Business Administration, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
4 Department of Mechanical Engineering, Prince Mohammad Bin Fahd University, Al Khobar 31952, Saudi Arabia
* Corresponding Author: Muhammad Ijaz Khan, [email protected]
DOI: 10.62762/IJTSSE.2025.805399
ARK: ark:/57805/ijtsse.2025.805399
Received: 24 November 2025, Accepted: 18 December 2025, Published: 28 December 2025  
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Abstract
This study presents an analytical mathematical model for an integrated microbial fuel cell--oxic--anoxic bioreactor (MFC--OB--ANB) system designed for simultaneous slaughterhouse wastewater treatment and energy recovery. The model incorporates bioelectrochemical oxidation, nitrification, and denitrification processes using acetate as a representative substrate. Closed-form analytical solutions are derived for substrate degradation, nitrogen transformation, current density, and system voltage. The effects of biofilm thickness, membrane conductivity, and influent substrate concentration on treatment efficiency and power generation are systematically investigated. Results reveal that enhanced biofilm conductivity and reduced membrane resistance significantly improve energy recovery, while optimized substrate loading enhances nitrogen removal performance. The proposed framework provides valuable insights for the design and optimization of integrated bioelectrochemical wastewater treatment systems.
Graphical Abstract
Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment
Keywords
microbial fuel cell
mathematical model
Nernst-Monod model
slaughterhouse wastewater
new homotopy perturbation method
nonlinear equations
nitrification and de-nitrification model
Data Availability Statement
Data will be made available on request.
Funding
This work was supported without any funding.
Conflicts of Interest
The authors declare no conflicts of interest.
Ethical Approval and Consent to Participate
Not applicable.
References
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Cite This Article
APA Style
Gowthaman, D., Begum, A. S., Suganya, S. T., Rafiq, M., & Khan, M. I. (2025). Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment. International Journal of Thermo-Fluid Systems and Sustainable Energy, 1(2), 96–107. https://doi.org/10.62762/IJTSSE.2025.805399
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TY  - JOUR
AU  - Gowthaman, D.
AU  - Begum, A. Shamadhani
AU  - Suganya, S. Thamizh
AU  - Rafiq, Muhammad
AU  - Khan, Muhammad Ijaz
PY  - 2025
DA  - 2025/12/28
TI  - Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment
JO  - International Journal of Thermo-Fluid Systems and Sustainable Energy
T2  - International Journal of Thermo-Fluid Systems and Sustainable Energy
JF  - International Journal of Thermo-Fluid Systems and Sustainable Energy
VL  - 1
IS  - 2
SP  - 96
EP  - 107
DO  - 10.62762/IJTSSE.2025.805399
UR  - https://www.icck.org/article/abs/IJTSSE.2025.805399
KW  - microbial fuel cell
KW  - mathematical model
KW  - Nernst-Monod model
KW  - slaughterhouse wastewater
KW  - new homotopy perturbation method
KW  - nonlinear equations
KW  - nitrification and de-nitrification model
AB  - This study presents an analytical mathematical model for an integrated microbial fuel cell--oxic--anoxic bioreactor (MFC--OB--ANB) system designed for simultaneous slaughterhouse wastewater treatment and energy recovery. The model incorporates bioelectrochemical oxidation, nitrification, and denitrification processes using acetate as a representative substrate. Closed-form analytical solutions are derived for substrate degradation, nitrogen transformation, current density, and system voltage. The effects of biofilm thickness, membrane conductivity, and influent substrate concentration on treatment efficiency and power generation are systematically investigated. Results reveal that enhanced biofilm conductivity and reduced membrane resistance significantly improve energy recovery, while optimized substrate loading enhances nitrogen removal performance. The proposed framework provides valuable insights for the design and optimization of integrated bioelectrochemical wastewater treatment systems.
SN  - 3069-1877
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  -
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@article{Gowthaman2025Mathematic,
  author = {D. Gowthaman and A. Shamadhani Begum and S. Thamizh Suganya and Muhammad Rafiq and Muhammad Ijaz Khan},
  title = {Mathematical Modeling of an Integrated Microbial Fuel Cell-Bioreactor System for Slaughterhouse Wastewater Treatment},
  journal = {International Journal of Thermo-Fluid Systems and Sustainable Energy},
  year = {2025},
  volume = {1},
  number = {2},
  pages = {96-107},
  doi = {10.62762/IJTSSE.2025.805399},
  url = {https://www.icck.org/article/abs/IJTSSE.2025.805399},
  abstract = {This study presents an analytical mathematical model for an integrated microbial fuel cell--oxic--anoxic bioreactor (MFC--OB--ANB) system designed for simultaneous slaughterhouse wastewater treatment and energy recovery. The model incorporates bioelectrochemical oxidation, nitrification, and denitrification processes using acetate as a representative substrate. Closed-form analytical solutions are derived for substrate degradation, nitrogen transformation, current density, and system voltage. The effects of biofilm thickness, membrane conductivity, and influent substrate concentration on treatment efficiency and power generation are systematically investigated. Results reveal that enhanced biofilm conductivity and reduced membrane resistance significantly improve energy recovery, while optimized substrate loading enhances nitrogen removal performance. The proposed framework provides valuable insights for the design and optimization of integrated bioelectrochemical wastewater treatment systems.},
  keywords = {microbial fuel cell, mathematical model, Nernst-Monod model, slaughterhouse wastewater, new homotopy perturbation method, nonlinear equations, nitrification and de-nitrification model},
  issn = {3069-1877},
  publisher = {Institute of Central Computation and Knowledge}
}
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CC BY Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
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