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Prof. Sanjay Kumar Pandey
Department of Mathematical Sciences, IIT(BHU), Varanasi, INDIA
Area of Interest: 
Bio mechanics, Atmospheric vortex dynamics (fluid mechanics), digital image processing, Graph Theory

Ph D in Biomechanics from Indian Institute of Technology, Kharagpur under the supervision of Professor J C Misra, 

  • M Sc in Mathematics with First Class from Patna University, Patna.
  • B Sc (Honours) in Mathematics with First Class from prestigious Patna Science College.

  • I Sc in First Division from prestigious Patna Science College.

  • Matriculation in First Division with distinction from SBH School, Mohania, Bihar School Examination Board, Patna.


  • Executive Editor, Journal of International Journal of Physical Sciences
  • Member, Editorial Board, ISST, Journal of Mathematics and Computing System
  • Adjunct Professor, International Institute of Information Technology, Naya Raipur (Aatal Nagar), Chhattisgarh.
  • Member, Board of Studies, National Institute of Technology, Patna
  • Member, Research Degree Committee, Dr APJ Abdul Kalam Technical University, Lucknow.


      • Senior Research Fellowship (UGC), awarded for the period 1991-93.
      • NET 1989.
      • Junior Research Fellowship (UGC) 1988, awarded for the period 1989-91.
      • State Merit Scholarship 1979, awarded for the period 1979-1981.
      • Topped in National Rural Scholarship 1974, awarded for the period 1974-1979.
      • Co-Principal Investigator:
      Project Title:: "Mathematical investigation of Tropical Cyclones: Structure and Analysis of their Stability"
             (TEQIP Collaborative Research Scheme) 
      Grant: Rs 1465000/-
      • ​Principal Investigator:
      Project Title:: "Mathematical modelling of peristaltic transport of physiological fluids",
                              (UGC minor research project, 2005-07).
      Grant: Rs 45000/-
      • Principal Investigator:
      Project Title: "Mathematical modelling of peristaltic flows" an Institute of Technology,
                              (BHU minor Project, 2006-08)
      Grant: Rs 45000/-
      • Principal Investigator
      DIH project: Mathematical modelling of swallowing in oesophagus suffering from hiatus hernia.
      • Principal Investigator
      ​​DIH project: Mathematical modelling of naturally occurring vortex type phenomena such as tornadoes, whirlwind etc.

      Executive Editor: Journal of International Academy of Physical sciences, Allahabad
      Editorial Boards

      • ISST Journal of Mathematics and Computing System

      Institute Level Committees

      • Member Advisory Committee, Training & Placement Cell, IIT-BHU.
      • ​Member, Institutee Rajbhasha Committee, IIT (BHU), Varanasi.

      Department Level Committees

      • Convener, Departmental; Undergraduate Committee (2013-14)

      • Convener Departmental Postgraduate Committee (2014-15, 2015-16)

      • Professor-in-charge, Training & Placement (2008-09, 2009-10, 2010-11, 2011-12, 2012-13, 2013,-14, 2015-16, 2016-17, 2017-18, 2018-19)

      • Convener, Departmental Space Committee (2016-17, 2017-18, 2018-19)

      • Member, Departmental Postgraduate Committee (2018-19)

      • Member, Departmental Users Committee (2016-17, 2017-18, 2018-19)

      • President: (2018-19. 2019-20)      
                                Mathematics & Computing Society,                 
                                Department of Mathematical Sciences,
        Indian Institute of Technology (BHU), Varanasi.

      • Participation:
                         Republic Day Parade 1982 at New Delhi as a member of Republic day Contingent NCC (Naval wing).                                                      Represented the State of Bihar as the coxswain of the Regatta Team at Republic Day Camp at New Delhi in 19

      • Languages known:  
        • ​​​Natural languages:       Hindi, English, Sanskrit, Bengali and German.
        • Computer Languages: C, C++, Java, Fortran
      • Fluid Dynamics
      • Numerical Analysis

      • Mathematical Methods.

      • Graph Theory and Applications.

      • Discrete Mathematics.

      • Mathematical Modelling and Simulation.

      • Computer Programming & Graphics in C.

      • Computer Programming with applications to Numerical Methods

      • Programming Languages.

      • Object Oriented Programming.

      • Computational Fluid Dynamics..

      • Digital Image Processing.

      Post doctoral Supervision

      • Dr Somnath Maiti (UGC Dr D S Kothari postdoctoral fellow)(2012-15) Research Area: Bio-fluid motion in uterus.

      Doctoral Supervision
      (Completed: 7)

      • Dharmendra Tripathi (2009)
              Title : "Mathematical modelling of peristaltic transport of non-Newtonian fluids: Application to physiological flows
      • Mithilesh Kumar Chaube (2010):

      Title : "Investigation of flow characteristics of peristalsis through mathematical models: Application to physiological flows"       

      • Manish Kumar Singh  (2014):
         (under co-supervison)
        "Study of spatially homogeneous and anisotropic cosmological models in modified theories of gravitation

      • Shailendra Kumar Tiwari (2017):
         Title :  
        "Mathematical modelling of peristaltic transport: Investigation of oesophageal swallowing in normal and pathological states"

      • Jagdish Prasad Maurya  (2018): 

              Title :  "Exploration of Characteristics governing dynamics of whirlwinds: Applications to  atmospheric vortices"  

      • Amirlal Singh  (2019): (Submitted)      
      ​          Title : "Exploration of flow dynamics od oesophageal swallowing in normal and pathological states"
      • ​​​​Raja Pathak (2020): (Submitted) (under co-supervision with Dr Shatrughna Tripathi, Department of Astrology, SVDV Sankay, BHU)


      (Ongoing: 4)

      • Subhash Chandra (Topic: Mathematical modelling of some bio- systems)

      • ​​Ajay Kumar Patel (Co-supervisor, Dr Lavanya S), (Area: Graph Theory)
      • ​​​Siddharth Singh (Biomechanics)

      • Anupam Kumar Pandey (Biomechanics)

      • Ankit Prajapati    (Biomechanics)
      • Prem Singh         (Vortex Dynamics)
      • Kriti Yadav          (Vortex Dynamics)
      • Deepanshu Kumar (Vortex Dynamics)
      • Shruti Madaan (Vortex Dunamics)

      Masters Level Supervision
      Completed (22), Continuing (2)
      M Tech Dissertation

        • Ms MItisha Pandey
        • Ms ShreerupaHarshiita


        • Ms. Praneetha
        • Ms Savita Meena


        • Md Basit
        • Khitij Gangwar
        • Debrup Roy Chowdhury
        • Sourabh Grag


        • Kanchan Meena (2018): Designing of routes for an Educational Campus by Kanchan Meena
        • Anuradha Meena (2018): A mathematical model for transport of a Newtonian fluid in a channel under the influence of peristaltic waves of dilating amplitude 


        • Hardik Wadhwa: Pricing put options using machine learning techniques 
        • Stock market simulation to study development of trading strategies &trend forcasting using machine learning techniques.


        • Suhani Garg: Exploration and Implementation of Inherent Algebraic Structures of Colour 
        • Yokila Arora: Design and Analysis of Image Compression Models 2014-15


        • Design and Analysis of Segmentation and Texture based featuire etraction methods for medical images by Pushkar


        • Moving Object Recognition by Akshay Nagpurkar 


        • Exploration of an inventory control model for a three echelon system with varying demand by Ankit Gupta 


        • Public Key Cryptography and Network Security by Johns Baby.

        • Advanced Management Controller (2012) by Ravindra Kumar.

        • Mathematical Modelling of Hiatus Hernia (MMST Dissertation) by Dr Gireesh Ranjan (IIT, Kharagpur)


        • New Stereo Matching Algorithm Based on Image Segmentation and Image Wrapping by Akshay Gupta.

        • Informatica Administrator Enhancement by Piyush Aggarwal.


        • Deepak Kumar Singh, Audio Watermarking
        • Mittal Gaurav Aerodynamics of Birds\92 Flight  2017-18

        MMST Dissertation

        • Dr Gireesh Ranjan, IIT, Kharagpu ​ ( Title:: Mathematical Modelling  of Hiatus Hernia)                                                                                                 

        Undergraduate Projects

        • Client side implementation of video conferencing solution over windows mobile” by Mr  Gaurav Mittal.

        • “Recognition of repetitive patterns from satellite images” by Gaurav Mittal.

        • “Design and Analysis of secure key exchange protocols” by Deepanshu Shukla.

        • “Study of Huffman Code in a C language” by Baljit Vikas.

        • “Development of Lan Based Multiplayer Game” by Ahmad Arsalan

        Summer Internship




        • Anuradha Meena (IDD, Maths & Computing Part-III)

        • Rahul Maurya (IDD, Maths & Computing Part-III)

        • Mihir Jitesh Vaidya, (IDD Biomedical Engg, Part-III)


        • Ms Shivani Kumari (B Tech Computer Engg Part III,Bhopal)


        • Computer Simulation of Mathematical Models on Genetics by Ms Sandhya Verma, (M Sc Bioinformatics, MMV BHU, Varanasi.

        H-index = 20
        Citations = 1411

        Research Papers in International Journals

        1. Sanjay Kumar Pandey, and Subhash Chandra,  Chandra, Transport of micro-polar fluids in an exponentially diverging tube by means of peristaltic waves of dilating amplitude, Zeitschrift für Angewandte Mathematik und Mechanik, Vol 102 issue 4, April 22, 2022 (Editor's Choice).
        2. Sanjay Kumar Pandey, Shailendra Kumar Tiwari and Kushagra Pandey, Fluid Transport in a Tube of Variable Cross-Srctional Area by Peristaltic Waves of Dilating Amplitude: A Mathematical Model for Investigating Impact of Hiatus Herniaon Swallowing, Vol 26 No. 1, 2022, pp 1-16.
        3. Ajay Kumar Patel, Lavanya S and Sanjay Kumar Pandey, "Energy and Inertia of the Eccentricity Matrix of Coalescence of Graphs"  Discrete Mathematics, 344(12), 112591 (Accepted on August 07, 2021).
        4. Sanjay Kumar Pandey and Subhash Chandra, Transportation of micro-polar fluid by dilating peristaltic waves, Journal of King Saud University-Sciencr, Vol 32(7), 2020 (accepted on July 21, 2020), 3939-2949. 
        5. Sanjay Kumar Pandey and Amirlal Singh,," Peristaltic transport in an elastic tube under the influence of dilating forcing amplitudes", International Journal of Biomathematics (Accepted on February 16, 2020, published 16 April, 2020), Vol 13 No. 4 2050027(1-13).
        6. Sanjay Kumar Pandey and Jagdish Prasad Maurya, "A general viscous model for some aspects of tropical cyclonic winds", Zeitschrift für Naturforschung A (accepted on January 14, 2020, published 6 March, 2020), Volume 75, Issue 4, Pages 301–315, 
        7. Sanjay Kumar Pandey and Shailendra Kumar Tiwari,"Fluid Transport with Suspended particles by means of Dilating Peristaltic Waves",SN Applied Sciences (accepted on November 05, 2019, published 8 April, 2020).
        8. Sanjay Kumar Pandey and Amirlal Singh, Peristaltic transport of Herschel–Bulkley fluids in tubes of variable cross section induced by dilating peristaltic waves: application to sliding hiatus hernia, International Journal of Dynamics and Control,  7, 407-418, 2019.
        9. S.K. Pandey, M.K. Chaube , D. Tripathi, Corrigendum to “Peristaltic transport of multilayered power-law fluids with distinct viscosities: A mathematical model for intestinal flows”[Journal of Theoretical Biology 278 (2011) 11–19], Journal of Theoretical Biology 470 (2019),  119.
        10. Subhash Chandra and Sanjay Kumar Pandey, A study on peristaltic flow of micro-polar fluids: an application to sliding hiatus hernia,  Journal of Physics: Conference Series, Volume 1141 (2018) 012092, IOP Publishing Ltd
        11. Sanjay Kumar Pandey, Amirlal Singh and Shailendra Kumar Tiwari, Flow of Herschel-Bulkley Fluids in circular cylindrical Tubes Caused by Dilating Peristaltic Waves, Austin Journal of Gastroenterology (Accepted: 07 August, 2018).
        12. Sanjay Kumar Pandey and Amirlal Singh, Unsteady Peristaltic Transport of a Particle–Fluid Suspension: Application to Oesophageal Swallowing, Zeitschrift für Naturforschung A., 73(12), pp 1143-1156 , 2018.                                      
        13. Sanjay Kumar Pandey and Jagdish Prasad Maurya, A Mathematical Model Governing Tornado Dynamics: An Exact Solution of a Generalized Model für Naturforschung A-2018-0206, 2018.
        14. Sanjay Kumar Pandey and Jagdish Prasad Maurya, Exact solutions for unsteady axi-symmetric vortex motions governing atmospheric vortices, Dynamics of Atmospheres and Oceans, 83, pp 111–12, 2018.                                                                                                  
        15. Sanjay Kumar Pandey, Jagdish Prasad Maurya, Exploration of characteristics Governing Dynamics of Whirlwinds: Application to dust devils, Zeitschrift fur Naturoshung A 72(8) a, 763-778, 2017.                                                                          
        16. Sanjay Kumar Pandey, Gireesh Ranjan, Shailendra Kumar Tiwari, Kushagra Pandey, Variation of pressure from cervical to distal end of oesophagus during swallowing: Study of a mathematical model, Mathematical Biosciences vol. 288, pp. 149–158, 2017.      
        17. S K Pandey and Shailendra Kumar Tiwari, Swallowing of Casson fluid in oesophagus under the influence of peristaltic waves of varying amplitude, International Journal of Bio-Mathematics, Vol. 10, No. 2,  1750017, 2017.                                                          
        18. S K Pandey and Maiti Somnath,  Rheological fluid motion in tube by metachronal waves of cilia, Applied  Mathematics and  Mechanics. -Engl. Ed., 38(3), pp 393–410, 2017.
        19. S. K. Pandey, M. K. Chaube, and Dharmendra Tripathi, Flow Characteristics of Distinctly Viscous Multilayered Intestinal Fluid Motion, Applied Bionics and Biomechanics,   2015, Article ID 515241, 5, pages,, 2015.
        20. S.K Pandey, M. K. Chaube, and D. Tripathi, Flow characteristics of distinctly viscous multilayered intestinal fluid motion, Applied Bionics and Biomechanics, 2014.
        21. Dharmendra Tripathi, S K Pandey, Abdul Siddiqui and O Anwar B\E9g, Non-steady peristaltic propulsion with exponential variable viscosity: A study of transport through the digestive system, Computer Methods in Biomechanics and Biomedical Engineering Vol.17, No. 6, pp 591-603, 2013.                                                                                                 
        22. S K Pandey and D. Tripathi, Unsteady peristaltic transport of a Maxwell fluid through finite length tube: application to oesophageal swallowing, Applied Mathematics and Mechanics (English Edition) 33(1), pp 15-24, 2012..
        23. S K Pandey and M K Chaube, Peristaltic transport of a Maxwell fluid in a channel of varying cross section induced by asymmetric waves: application to embryo transport within uterine cavity, Journal of Mechanics in Medicine and Biology 11(3), pp. 675, June 2011.
        24. S K Pandey and M K Chaube, Study of Wall Properties on Peristaltic Transport of a Couple-stress Fluid, Meccanica 46, pp. 1319-1330, 2011 
        25. S K Pandey and M K Chaube, Effect of magnetic field on peristaltic transport of couple-stress fluid through porous medium, Journal of Biological Systems 19(2) , pp. 1-12, 2011 
        26. S K Pandey, M K Chaube, Peristaltic flow of a microploar fluid through a porous medium in the presence of an external magnetic field, Communications in non-linear sciences and numerical simulation 16, pp. 3591-3601, 2011.
        27. S K Pandey and M K Chaube and D. Tripathi, Peristaltic transport of multilayered power-law fluids with distinct viscosities: A mathematical model for intestinal flows, Journal of Theoretical Biology. Vol. 278, Issue 1, 7, , pages 11-19,  June 2011.
        28. S K Pandey and D. Tripathi, A mathematical model for swallowing of concentrated fluids in oesophagus, Applied Bionics and Biomechanics, 8, pp. 309-6321, 2011.               
        29. S K Pandey and Dharmendra Tripathi, A Mathematical Model for Peristaltic Transport of Micropolor fluids, Applied Bionics and Biomechanics 8, pp. 1\9615, 2011
        30. S K Pandey and D. Tripathi, Unsteady peristaltic flow of micro-polar fluid in a finite channel, Zeitschrift fuer Naturforsch. A, 66a,181-192, 2011.  .
        31. D. Tripathi, S K Pandey and S. Das, Peristaltic Flow of Viscoelastic Fluids of Fractional Generalized Burgers\92 Model through Channels, Acta Astronautica , 69, Issues 1\962, , pp. 30-38, July\96 August 2011.
        32. S K Pandey and D. Tripathi, Effects of non-integral number of peristaltic waves transporting couple stress fluids in finite length channels, Zeitschrift fuer Naturforsch.A, 66A, pp. 172-180, 2011.
        33. D. Tripathi, T. Hayat, N. Ali, S. K. Pandey, Effects of transverse magnetic field on the peristaltic transport of viscoelastic fluid with Jeffrey model in a finite length channel, International Journal of Modern Physics B, Vol. 25(26), pp. 3455-3471, 20 October 2011.
        34. S K Pandey and M K Chaube, Peristaltic Transport of a Viscoelastic Fluid in a tube of varying Cross-section. Mathematical and Computer Modelling, vol. 52, issues3-4, pp 501-514, 2010.
        35. S K Pandey and D. Tripathi, Peristaltic Flow Characteristics of Maxwell and Magneto-hydrodynamic Fluids in Finite Channels: Models for Oesophageal Swallowing, Journal of Biological Systems 18, number 3, September 2010.
        36. D. Tripathi, S K Pandey and S Das, Peristaltic Flow of Viscoelastic Fluid with Fractional Maxwell Model through a Channel, Applied Mathematics and Computation, 215, 3645\963654, 2010.
        37. S K Pandey and D. Tripathi, Unsteady model of transportation of Jeffrey-fluid by peristalsis, International Journal of Biomathematics, Vol. 3(4), pp. 473-491,  2010..
        38. S K Pandey and D. Tripathi, Influence of Magnetic Field on Peristaltic Flow of Viscous Fluid through a Finite Length Cylindrical Tube, Applied Bionics and Biomechanics, Vol. 7, No. 3, pp.169\96176, September 2010.
        39. M.K. Chaube, S K Pandey and D. Tripathi, Slip Effect on Peristaltic Transport of Micropolar Fluid, Applied Mathematical Sciences Vol. 4, no. 43, pp. 2105-2117, 2010               
        40. S K Pandey and D. Tripathi, Peristaltic Transport of a Casson Fluid in a Finite Channel: Application to Flows of Concentrated Fluids in Oesophagus, International Journal of Biomathematics, Vol. 3, N0. 4 pp. 453-472, 2010 .
        41. D Tripathi, S K Pandey and M K Chaube, Mechanical Efficiency and Reflux of Peristaltic Pumping through a Finite Length Vessel, Int. J. Appl. Math. Comput., 2, pp. 63-72, 2010.
        42. D Tripathi, S K Pandey and M K Chaube, Peristaltic Transport of Power law fluid in Finite Length Vessels, International Journal of Mathematical Science and Engineering Applications ISSN 0973-9424, Vol.3 No. 111, pp.279-289, 2009.
        43. J C Misra and S K Pandey, Peristaltic transport of blood in small vessels: Study of a Mathematical Model, Computer and Mathematics with Applications, vol. 43, no. 8-9, pp. 1183-1193, 2002.
        44. J C Misra and S K Pandey, A mathematical model for oesophageal swallowing of a food bolus, Mathematical and Computer Modelling, vol. 33, no 8-9, pp-997-10009, 2001.
        45. J C Misra and S K Pandey, Peristaltic flow of a multi-layered power-law fluid through a cylindrical tube, International Journal of Engineering Science, vol. 39, pp. 387-402, 2001.
        46. J C Misra and S K Pandey, Peristaltic transport of a non-Newtonian fluid with a peripheral layer, International journal of Engineering Science, vol. 37, pp. 1841-1858, 1999.
        47. J C Misra and S K Pandey, Peristaltic transport in a tapered tube, Mathematical and Computer Modelling, vol. 22, no. 8, pp. 137-151, 1995.
        48. J C Misra and S K Pandey, Peristaltic transport of particle-fluid suspension in a cylindrical tube, Computer and Mathematics with Applications, vol. 28, no. 4, pp. 131-145, 1994.

        Chapters in books

        1. J C Misra, S K Pandey, Peristaltic transport of physiological fluids, Biomathematics: Modelling and Simulation (Editor: J C Misra), Chapter 7, pp.167-193, 2006 World Scientific, London, USA, Singapore.


        Hot topics
        Theoretical Biology
        Reports from S.K. Pandey and Co-Researchers Add New Data to Research in Theoretical Biology
        Published in Science Letter, June 21st, 2011
        2011 JUN 21 -- "This paper is concerned with the theoretical study of two-dimensional peristaltic flow of power-law fluids in three layers with different viscosities. The analysis is carried out under low Reynolds number and long wavelength approximations," investigators in Uttar Pradesh, India report.
        "The shapes of the interfaces are described by a system of nonlinear algebraic equations which are solved numerically as streamlines. It is found that the non-uniformity in the intermediate and peripheral layers diminishes when the viscosity of the intermediate layer is increased and that of the outermost layer is kept unaltered for both the pseudo-plastic...
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