Research and Publications

Research Background:

My research is mainly in applied mathematics and fluid mechanics, focusing on solute-dispersion phenomena in fluid flows. I study the fundamental mechanisms of solute transport using analytical and computational techniques, particularly examining dispersion in different directions and flow configurations. This work has practical relevance in biological flows, particularly in the transport of nutrients, drugs, and other solutes in blood flow through arteries. It also has applications in microfluidic transport processes, environmental fluid mechanics, including pollutant transport in rivers and groundwater, and mixing processes in engineering systems. In addition to these studies, I have worked on the mathematical modelling of tumour–immune interactions and on many-body problems in quantum mechanics. Currently, I am interested in exploring solute dispersion in various flow geometries and the stability of fluid flows.

Publications (Journal):

1. Jyotirmoy Rana, Ashis Kumar Roy, Sudip Debnath, and Ramkarn Patne (2026): Solute dispersion in pulsatile Casson fluid flow with exchange between phases using the extended Gill’s approach, Journal of Fluid Mechanics, 1028, A35. Cambridge University Press.

2. Kartick Mahata, Dipika Robi Das, Ramkarn Patne, and Jyotirmoy Rana (2025): Shear-enhanced dispersion in Kolmogorov flow, Physics of Fluids 37(4), AIP Publishing.

3. Kartick Mahata, Jyotirmoy Rana, and Ramkarn Patne (2025): Solute dispersion in Phan-Thien–Tanner (PTT) fluid flows, Physics of Fluids 37(2), AIP Publishing. 

4. Tarekegn Dinku, Boka Kumsa, Jyotirmoy Rana (2025): A mathematical approach to cancer growth: The role of smoking through fractional order models with Mittag-Leffler kernels, Alexandria Engineering Journal 124, 46-65.

5. Tarekegn Dinku, Boka Kumsa, Jyotirmoy Rana, and Aiyappan Srinivasan (2025): Fractional-order models of tumor and oncolytic virus interaction incorporating the Beddington–DeAngelis functional response: Sensitivity and cost-effectiveness analysis, Results in Physics 108516.

6. Tarekegn Dinku, Boka Kumsa, Jyotirmoy Rana, and Aiyappan Srinivasan (2025): Stability analysis and optimal control of tumour-immune interaction problem using fractional order derivative, Mathematics and Computers in Simulation 233, 187-207.

7. Tarekegn Dinku, Boka Kumsa, Jyotirmoy Rana, and Aiyappan Srinivasan (2024): A Mathematical Model of Tumor-Immune and Host Cells Interactions with Chemotherapy and Optimal Control, Journal of Mathematics 3395825.

8. Santanu Das, Kartick Mahata, Ramkarn Patne, Sanjeev Kumar, and Jyotirmoy Rana (2024): Unsteady solute dispersion in large arteries under periodic body acceleration, Physics of Fluids 36(10), AIP Publishing. 

9. Jyotirmoy Rana, Prosanjit Das, Sarifuddin, Prashanta Kumar Mandal, and Ramkarn Patne (2024): Dispersion of a non-uniform solute slug in pulsatile viscoelastic fluid flow, Physics of Fluids 36(9), AIP Publishing. 

10. Prosanjit Das, Sarifuddin, Jyotirmoy Rana and Prashanta Kumar Mandal (2022): Unsteady solute dispersion in the presence of reversible and irreversible reactions, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 478, 20220127, The Royal Society. 

11. Prosanjit Das, Sarifuddin, Jyotirmoy Rana and Prashanta Kumar Mandal (2021): Solute dispersion in transient Casson fluid flow through stenotic tube with exchange between phases, Physics of Fluids 103, 023206, AIP Publishing. 

12. Ling Liu, Jyotirmoy Rana and Shijun Liao (2021): Analytical solutions for the hydrogen atom in plasmas with electric, magnetic, and Aharonov-Bohm flux fields, Physical Review E 103, 023206, American Physical Society. 

13. Jyotirmoy Rana and Shijun Liao (2019): On time-independent Schrödinger equations in quantum mechanics by the homotopy analysis method, Theoretical and Applied Mechanics Letters 9, 376-381, Elsevier. 

14. Jyotirmoy Rana and Shijun Liao (2019): A general analytical approach to study solute dispersion in non-Newtonian fluid flow, European Journal of Mechanics B Fluids 77, 183-200, Elsevier. 

15. Jyotirmoy Rana, P.V.S.N. Murthy and Rama Subba Reddy Gorla (2017): Oxygen Transport in and around the Systemic Capillary in Hyperbaric Environment, Chemical Engineering Communications 204, 111–121, Taylor & Francis.

16. Jyotirmoy Rana and P.V.S.N. Murthy (2017): Unsteady Solute Dispersion in Small Blood Vessels using a Two-Phase Casson Model, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 473, 20170427, The Royal Society. 

17. Jyotirmoy Rana and P.V.S.N. Murthy (2016): Unsteady Solute Dispersion in Herschel-Bulkley Fluid in a Tube with Wall Absorption, Physics of Fluids 28, 111903, AIP Publishing. 

18. Jyotirmoy Rana and P.V.S.N. Murthy (2016): Unsteady Solute Dispersion in Non-Newtonian Fluid Flow in a Tube with Wall Absorption, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 472, 20160294, The Royal Society. 

19. Jyotirmoy Rana and P.V.S.N. Murthy (2016): Solute dispersion in pulsatile Casson fluid flow in a tube with wall absorption, Journal of Fluid Mechanics 793, 877–914, Cambridge University Press. 

Publications (Conference):

1. Sohel Ahmed, Nanda Poddar, Jyotirmoy Rana, and Kajal Kumar Mondal (2024): Mixing of a Solute in a Micropolar Blood Flow Model Through a Capillary Tube with an Absorptive Wall, International Conference on Nonlinear Dynamics and Applications 436-451. Cham: Springer Nature Switzerland, 2024.