knrai.apm's picture
Dr. K. N. Rai
Retired
Mathematical Sciences
knrai.apm@iitbhu.ac.in
9935346251
Area of Interest: 
Differential Equation, Mathematical Methods, Nonlinear Mathematics, Mathematical Modelling, Heat and Mass Transfer, Bio-transport Process, Moving Boundary Problems.

M.Sc. (Mathematics), Faculty of Science, BHU, 1970
Ph.D. (Mathematics), Faculty of Science, BHU, 1974
 

Scientist pool:                                01.08.75 to 02.12.76
Lecturer:                                        03.12.76 to 30.04.77
Scientist pool:                                01.05.77 to 08.05.77
Lectureship (T):                             09.05.77 to 23.01.80
Permanent Lecturer:                      24.01.80 to 24.10.86
Reader:                                          25.10.86 to 24.10.94
Professor:                                      25.10.1994 to 31.07.2012
HAG Scale                                    01.08.2012 to 31.07.2014  
Institute Professor                         02.01.2015 to 30.06.2019
Emeritus Professor                        01.07.2019 to 31.12. 2019

i. Head, Department of Applied Mathematics (from 01.08.2006 to 31.07.2009).
ii. Chairman SPGC, IIT (BHU).
iii. Convener DPGC, Department of Applied Mathematics, IIT (BHU).
iv. Member FAC, Department of Applied Mathematics, IIT (BHU).
v. Member of Space Committee, Department of Applied Mathematics, IIT (BHU).
vi. Member of Finance Committee, Department of Applied Mathematics, IIT (BHU).
 

i. Member of Selection Committee of a number of Central Universities, NIT and other Organizations.
ii. Reviewer of National and International Journals.
iii. Member of DRC of NIT Patna.
iv. Examiner of Ph. D. and D.Sc. Thesis in Mathematics of various Universities.

i. Number of Ph.D. Awarded:  18
 
Sl. No. Name of Student
Year
 Title of Thesis
  1.  
 Dr. Subramanyam Upadhyay
  1.  
 Modelling and Wavelet Based Simulations of                       Heat Mass Transfer in Food Drying
  1.  
 Dr. Pappu Kumar 2017 Modelling and Simulation of Phase-Lag Phenomenon in Biological Tissue During Thermal Therapy
  1.  
 Dr. Dinesh Kumar
  1.  
 Mathematical Modeling and  Simulation of Heat Transfer in Biological Tissue                                                             
  1.  
 Dr. Sarita Yadav
  1.  
 Mathematical Modelling and Simulation of Moving Boundary Problems
 
  1.  
 Dr. Tadkeshwar Nath Mishra
  1.  
 A Study on Single-Phase and Dual-Phase-Lagging Heat conduction
  1.  
 Dr. Surjan Singh
  1.  
 Mathematical Modelling and Simulation of Heat Transfer in Fin
  1.  
 Dr. Jitendra Singh
  1.  
 Study on Mathematical Modelling of Moving Boundary Problems Arising in Engineering Sciences
  1.  
 Dr. Praveen Kumar Gupta
  1.  
 Some Studies on Mathematical Modelling of Heat Transfer in Biological Tissue
  1.  
 Dr. Vineet Srivastava
  1.  
 Mathematical Modelling in Numerical Studies of Some Biomedical Transport Process
  1.  
 Dr. Rajeev
  1.  
 Study of a Class of Moving Boundary Problems
  1.  
 Dr. Dinesh Chandra Rai
  1.  
 Free Boundary Problems in Heat and Mass Transfer
  1.  
 Dr. Sanjay Kumar Rai
  1.  
 Analysis of Heat Transfer in Biological Tissue and Application
  1.  
 Dr. Sawal Kisore Singh
  1.  
 Numerical Methods in Heat and Mass Transfer
  1.  
 Dr. Lakshamn Takur
  1.  
 Some Problems in Heat and Mass Transfer
  1.  
 Dr. Kapil Dev Rai
  1.  
 Numerical Methods in Heat and Fluids Flow
  1.  
 Dr. Surendra Rai
  1.  
 Moving Boundary Problems in Heat and Mass Transfer
  1.  
 Dr. Surendra Nath Dubey
  1.  
 Integrals Transforms and Their Applications
  1.  
 Dr. Rajesh Pandey
  1.  
 A Study of the Generalized Polynomial {Se n*(x, y)}
                  
ii. Ongoing: 04
  1. Mr. Piyush Kumar Singh (DST-CIMS, BHU)
  2. Mr. Vineet Kumar Singh (DST-CIMS, BHU)
  3. Mr. Mukesh Kumar (DST-CIMS, BHU)
  4. Mr. Mahesh Kumar (Department of Mathematical Sciences, IIT (BHU) 

iii. Number of M. Tech. Guided

  1.              Completed: M. Tech. Student: 04 and M. Sc.: 01

iv. Research works undertaken:

  • Mathematical modelling of moving boundary problem in engineering sciences including bio-medical engineering.
  • Mathematical modelling of heat transfer in biological systems such as tissues, tumors (thermal therapy, cryosurgery, hyperthermia, cryopreservation, thermoregulation). 
  • Mathematical modelling of first to third degree burn injury.
  • Mathematical modelling and simulation of heat transfer at micro-scale.
  • Developed mathematical models for biological systems such as parabolic and hyperbolic bio heat equations.
  • Developed mathematical methods for solving non-classical heat conduction such as dual-phase-lagging heat conduction model, fractional single-phase-lagging heat conduction and single-phase-lagging heat conduction.
  • Principal Investigator of Mathematical Modelling and Computational aspects Group of DST-Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, from the date of its establishment i.e. since 20th November, 2007.
(i) Published Papers
  1. A single-phase-lag model of heat mass transfer for different geometries of food during drying, Heat Transfer Research (2018), with S. Upadhyay (in press).
  2. Legendre wavelet modified Petrov-Gelerkin method in two dimensional moving boundary problem, Zeitschrift fur Naturforschung Section A-A Journal of  Physical Sciences73(1) (2018), 23-34, with S. Yadav and S. Upadhyay
  3. Analytical solution of Fourier and non Fourier heat transfer in longitudinal fin with internal generation and periodic boundary condition, International Journal of Thermal Sciences 125 (2018) 166-175, with Surjan Singh and Dinesh Kumar.
  4. Modelling and simulation of moving boundary problem arising during immersion frying of foods, National Academic of Science (2017), with S. Upadhyay and S. Yadav (in press).
  5. Numerical solution of non-linear dual phase lag bio heat transfer equation within skin tissue, Mathematical Biosciences 293 (2017) 56-63, with Dinesh Kumar and P. Kumar.
  6. Legendre wavelet collocation solution for system of linear and nonlinear delay differential equations, Int. J. Applied and Computational Mathematics (2017) 1-16, with S. Upadhyay, Dinesh Kumar and Surjan Singh.
  7. Gelerkin and Collocation methods for solution of initial value problem of generalized van der pol equation, Int. J. Engineering System Modelling and Simulation 9(2) (2017) 103-112, with S. Upadhyay
  8. Numerical simulation of time fractional dual-phase-lag model of heat transfer with skin tissue during thermal therapy, Journal of Thermal Biology (2017), with Dinesh Kumar.
  9. A parallel algorithm for wavelet transform based color image compression, Journal of Intelligent System (2017), with P.K. Singh and R.S. Singh.
  10. Finite element Legendre wavelet Gelerkin approach in investigation of non-Fourier and non Fic’s effects on heat mass transfer during drying of foods, Computational Thermal Sciences: An Int. Journal (2018), with S. Upadhyay.
  11. Unsteady free convection oscillatory coquette flow through a variable porous medium with concentration profile, Int. J. of Nonlinear Analysis and Application 8(1) (2017) 177-186, with Surjan Singh, N.S. Tomer and P. Kumar.
  12. Numerical simulation of dual-phase-lag bio heat transfer model during thermal therapy, Mathematical Bioscience 281 (2016) 82-91, with P. Kumar and Dinesh Singh.
  13. Non-linear dual-phase-lag model for analyzing heat transfer phenomenon in living tissues during thermal ablation, Journal of Thermal Biology 60 (2016) 204-212, with P. Kumar and Dinesh Kumar.
  14. Fractional modelling of hyperbolic bioheat transfer during thermal therapy, Journal of Mechanics in Medicine and Biology 17(3) (2016) 1750058, with P. Kumar
  15. A study on thermal damage during hyperthermia treatment based on DPL model for multilayer approach, Journal of Thermal Biology 62 (2016) 170-180, with Dinesh Kumar.
  16. A mathematical model for solidification of binary eutectic system including relaxation time, Computational thermal sciences: An Int. Journal 8(1) (2016) 11-30, with S. Yadav and S. Upadhyay.
  17. Numerical solution of FSPL heat conduction equation for analysis of thermal propagation, Applied Mathematics and Computation 273 (2016), 1006-1017, with T. N. Mishra
  18. Fractional single-phase-lagging heat conduction model for describing anomalous diffusion, Journal of Propulsion and Power Research 5(1) (2016), 45-54, with T. N. Mishra.
  19. Highly accurate compact difference scheme for SPL heat conduction model of general body, Zeitschrift fur Naturforschung Section A-A Journal of  Physical Sciences 71(11) (2016), 985-994, with T. N. Mishra
  20. A study on DPL model of heat transfer in bi-layer tissues during MFH treatment, Computer in Biology and Medicine 75 (2016) 160-172, with Dinesh kumar and P. kumar.
  21. Analysis of classical Fourier, SPL and DPL heat transfer model in biological tissues in presence of metabolic and external heat source 52(6) (2016) 1089-1107, Journal of Heat Mass Transfer, with Dinesh Kumar, Surjan Singh.
  22. Numerical solution of 2D SPL heat conduction model for analyzing thermal wave oscillations, Journal of Multidisciplinary Engineering Science and Technology 2(10) (2015), 2759-2764, with T. N. Mishra
  23. Numerical analysis for the dual-phase-lag model of bioheat transfer in living biological tissues in the 23rd National and 1st International Heat Mass Transfer Conference, during December 17-20, 2015, Thiruvananthapuram, Kerla, with P. Kumar.
  24. High order finite difference scheme for analyzing thermal wave propagation in SPL model in the 23rd National and 1st International Heat Mass Transfer Conference, during December 17-20, 2015, Thiruvananthapuram, Kerla, with T. N. Mishra.
  25. Numerical study on non-Fourier bioheat transfer during thermal ablation in Procedia Engineering 127 (2015) 1300-107, with Dinesh Kumar and P. Kumar.
  26. Coupled heat and mass transfer with one sublimation moving interface and freezing zone in Computational Thermal Sciences: An Int. Journal 7(4) (2015) 327-337, with S.K. Singh and T. N. Mishra.
  27. A mathematical model for hyperbolic space-fractional bioheat transfer during thermal therapy in Procedia Engineering 127 (2015) 56-62, with P. Kumar and Dinesh Kumar.
  28. Numerical solution of two point boundary value problems by wavelet Galerkin method, Int. J. Applied Mathematical Research 4(4) (2015), 496-512, with S. Upadhyay, S. Singh, S. Yadav.
  29. Comparative Study between DCT and Wavelet Transform Based Image Compression Algorithm, IOSR Journal of Computer Engineering 17(1) (2015), 53-57, with P.K. Singh and Neha Singh.
  30. Wavelet collocation solution of non-linear Fin problem with temperature dependent thermal conductivity and heat transfer coefficient, Int.  J. Nonlinear Analysis and Application 6 (1), (2015), 105-118, with Surjan Singh, Dinesh Kumar
  31. A numerical study on dual-phase-lag model of bio-heat transfer during hyperthermia treatment, Journal of Thermal Biology, 49-50, (2015), 98-105, with P. Kumar, Dinesh Kumar
  32. Thermal effect in FSPL heat conduction model irradiated by laser heat source, Proceeding of ICHMT- Int. Symposium on Advances on Computational Heat Transfer, May 25-29, 2015, with T. N. Mishra.
  33. Analytical approximation for one-phase-space-time fractional moving boundary problem with time varying temperature on surface, Proceeding of ICHMT- Int. Symposium on Advances on Computational Heat Transfer, May 25-29, 2015, with Jitendra Singh. 
  34. Implicit finite difference approximation for time fractional heat conduction under boundary condition of second kind, Int. J. Applied Mathematical Research, 4(1) (2015), 135-149, with T. N. Mishra
  35. Finite element Legendre wavelet Gelerkin approach to inward solidification in simple body under most generalized boundary conditions, Zeitschrift fur Naturforschung A 69 (2014) 501-510, with S. Yadav and Dinesh Kumar.
  36. Convective-radiative fin with temperature dependent thermal conductivity, heat transfer coefficient and wavelength dependent surface emissivity, J. Propulsion and Power Research 3(4) (2014), 207–221, with S. Singh, Dinesh Kumar
  37. Comparative analysis of power-law type fin problem using wavelet collocation and Gelerkin methods, Int. J. Applied Mathematical Research, 3 (4) (2014) 534-546, with S. Singh , S. Upadhyay
  38. Exact and wavelet collocation solution of Fin problem with temperature dependent internal heat generation, Proceeding of ICHMT-International Symposium on Convective Heat and Mass Transfer, June 08-14, 2014, with S. Singh and Dinesh Kumar.
  39. Wavelet Gelerkin and wavelet collocation method in moving boundary problem with temperature dependent thermal physical properties, Proceeding of ICHMT-International Symposium on Convective Heat and Mass Transfer, June 08-14, 2014, Sarita Yadav and S. Upadhayaya.
  40. Steady state temperature distribution in biological tissue using wavelet collocation method, Proceeding of Int. Conference on Emerging Trends in Computational and Applied Mathematics, June 02-04, 2014, with S. Singh and Dinesh Kumar.
  41. Effect of geometrical configuration on temperature distribution in Fin, Proceeding of Int. Conference on Emerging Trends in Computational and Applied Mathematics, June 02-04, 2014, with S. Singh and Dinesh Kumar.
  42. Comparative study of image compression techniques based on wavelet transform and wavelet packet transform, Proceeding of International Conference on Recent Trends in Computer Science and Engineering, February 08-09, 2014, 203-210,with P. K. Singh, R. S. Singh, S. Jaiswal.
  43. Collocation method applied to unsteady flow gas through a porous media, Int. J. Appl. Mathematical Research 3(3) (2014), 251-259, with S. Upadhayay.
  44. Numerical solution of dual-phase-lagging heat conduction model for analyzing overshooting phenomena, Applied Mathematics and Computation 236 (2014), 693-708, with T.N. Mishra, S. Sarkar.
  45. Compact difference scheme for solving 1 D dual-phase-lagging heat transport equation, Proceeding of 11th International and 22nd National ASME-ISHMT Heat Mass Transfer Conference, December 28-31, 2013, with T.N. Mishra.
  46. Wavelet collocation solution for convective-radiative continuously moving Fin with temperature dependent thermal conductivity, Int. J. Eng. Advanced Tech. 2(4) (2013), 10-16, with Surjan Singh.
  47. A Numerical Study on heat transfer in tissues during hyperthermia, Journal of Mathematical and Computer Modeling 57 (2013), 1018-1037, with Praveen Kumar Gupta, Jitendra Singh. 
  48. Solution of heat transfer problem in tissue during hyperthermia by finite difference –decomposition method, Journal of Applied Mathematics and Computation 219 (2013), 6882-6892, with Praveen Kumar Gupta, Jitendra Singh, S. K. Rai.
  49. Application of He’s Homotopy perturbation method for multi-dimensional fractional Helmholtz equation, International Journal of Numerical Methods of Heat and Fluid Flow 22(4)  (2012), 424-435, with Praveen Kumar Gupta, A. Yildrin.
  50. Homotopy perturbation method to space–time fractional solidification in a finite slab, Applied Mathematical Modeling 35 (2011), 1937-45, with Jitendra Singh and Praveen Kumar Gupta.
  51. Variational iteration method to solve moving boundary problem with temperature dependent physical properties, Thermal Science 15 (2011), S229-S239, with Jitendra Singh and Praveen Kumar Gupta.  
  52. Solution of fractional bioheat equations by finite difference method and HPM, Mathematical and Computer Modeling 54 (2011), 2316-25, with Jitendra Singh and Praveen Kumar Gupta.
  53. Numerical simulation for heat transfer in tissues during thermal therapy, Journal of Thermal Biology 35 (2010), 295-301, with Praveen Kumar Gupta, Jitendra Singh. 
  54. A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissue, Journal of Mathematical and Computer Modeling 51 (2010), 616-624, with V. Srivastava.
  55. Application of He’s Homotopy  Perturbation Method to Fractional Diffusion Equations, Zeitschrift fur Naturforschung 65a  (2010), 53-58, with P. K. Gupta, V.S. Pondey, S. Das.
  56. Numerical solution of a moving-boundary problem with variable latent heat, International Journal of Heat and  Mass Transfer 52 (2009), 1913-1917, with Rajeev, S. Das.
  57. Solution of one dimensional moving boundary problem with periodic boundary condition by variational iteration method, Thermal Science 13 (2009), 199-204, Rajeev, S. Das.
  58. Analytic approach to micro scale bio- film heat transport using Homotopy perturbation method, Int. J. of Appl. Math. and Computation 1(3) (2009), 148-158, with V. Srivastava.
  59. Mathematical modeling of first to third degree burn injury by sinusoidal heating source, International Journal of Applied Mechanics and Engineering 14(2) (2009), with V. Srivastava.
  60. Approximate Analytical Solution of 3D Fractional Micro-scale Heat Equation Using Modified Homotopy Perturbation Method, Journal of Applied Mathematical Sciences 3(32) (2009), 1557-1565, with V. Srivastava.
  61. A finite element method for solution of free boundary problem, Proceeding of ASME Heat Transfer/Fluid Engineering Summer Conference (2004), 1237-1245, with D.C. Rai.
  62. Finite element method for two dimensional Stefan Problem, National Conferences on Separation in Process Industries  (2003), 245-253, with D.C. Rai.
  63. Planer melting/freezing of a semi-infinite medium with time dependent surface temperature and temperature dependent thermal diffusivity, Fourth National Conference on Thermal System 326 332 (2003), 404-409, with S.K. Singh and S.N. Gupta.
  64. Heat transfer in tissues during hyperthermia, Fourth National Conference on Thermal System (2003), 290-297, with S.K. Rai.
  65. Boundary fixation approach to one dimensional inverse Stefan problem in non-ideal biological tissues, Fourth National Conferences on Thermal System (2003), 278-289, with S.K. Rai.
  66. A numerical technique for the solution of transport problems, Forth National Conferences on Thermal System (2003), 268-277, with K.D. Rai.
  67. Numerical solution for inward solidification of slabs, cylinders and sphere, Fourth National Conferences on Thermal Systems (2003), 259 267, with D.C. Rai.
  68. Heat and Mass Transfer analysis of solidification over a cylindrical heat sink, Thermal System and Heat Transfer (2001), 23-29.
  69. Determination of melt and vaporization zone width and initial concentration of frozen bounded substance, Thermal System and Heat Transfer (2001), 17-22, with K.D. Rai.
  70. An analytical study of melting and vaporization in a porous half-space, Thermal System and Heat Transfer (2001), 11-16, with S. Rai.
  71. Heat transfer inside the tissues with a supplying vessel for the case when metabolic heat generation and blood perfusion are temperature dependent, Heat and Mass Transfer 35 (1999), 345-350, with S. K. Rai.
  72. Effect of metabolic heat generation and blood perfusion on the heat transfer in the tissues with a blood vessel, Heat and Mass Transfer 35 (1999),  74-79, with S. K. Rai
  73. Numerical solution of moving boundary problem in a finite domain, Heat and Mass Transfer 34 (1998),  295-298, with S. K. Singh.
  74. Solidification of a binary eutectic system by a line heat sink with temperature dependent thermal conductivity; Conference on Thermal Systems, VII 8.1-7 .12 (1995), with L. Thakur and S.K. Singh.
  75. Solidification of a binary eutectic system due to a line heat sink, Conference on Thermal Systems, VII 7.1-7.12(1995), with L. Thakur and S.K. Singh.
  76. Approximate closed form analytical solution of the desublimation problem in a porous medium, Int. J. Energy Research 19 (1995), 279-288, with S. Rai.
  77. An analytical study of the solidification in a semi-infinite porous medium, Int. J. Engg. Sci. 30(2) (1992), 247-256, with S. Rai.
  78. A mathematical interpretation of diffusion processes with concentration dependent diffusion coefficient, Astrophysics and Space Science (1991), with L. Thakur.
  79. Approximate closed form analytical solution of molar molecular heat and mass transfer in a porous body of simple configuration, Proc. Indian National Sc. Academy 57A (1) (1990), 45-59, with S. Rai.
  80. An analytical study of the desublimation problem in a porous medium in presence of thermal diffusion, The Eurotherm Seminar, Thermal Non-Equilibrium in Two Phase Flow, Rome Palazzo Baleni ( 1989), 409-429, with S. Rai.
  81. Application of the Galerkin method to a problem of molar molecular heat and mass transfer in an infinite cylindrical porous body, Indian Journal of Technology 26 (1988), 359-364, with S. Rai.
  82. Approximate closed form analytical solution of diffusion equation, Transfer Processes in Multiphase Systems (1987), 434-438, with S. Rai.
  83. Limited diffusion processes in an infinite cylinder of glass or crystal; Transfer Process in Multiphase Systems (1987), 422-433, with B.N. Trivedi.
  84. Integral balance approach to heat and mass transfer in an infinite porous plate with parabolic initial conditions, Proceeding of Transfer Processes in Multiphase System (1987), 411-421, with R.N. Pandey.
  85. Molar molecular heat and mass transfer in a capillary porous body of spherical geometry, Commun. Fac. Sci. Univ. Ank. Series A2-A3 (36) (1987), 21-34.
  86. Limited diffusion processes in a body of simple geometry, Indian Journal of Technology 25 (1987), 164-170, with S.N. Dubey.
  87. Approximate closed form analytical solution of heat conduction in bodies of simple configuration, Indian Journal of Technology 25 (1987), 160-163, with S.N. Sinha.
  88. Approximate closed form analytical solution of heat and mass transfer problem, Conference on thermal System (1986), 323-328.
  89. Molecular and molar transfer of heat and mass in a capillary porous body, The Journal of Sci. Research 34(2) (1984), 91-129, with R.N. Pandey.
  90. Heat and Mass Transfer in an infinite cylinderical porous body under the generalized boundary conditions, The Journal of Scientific Research 33(2) (1983), 193-207, with R.N. Pandey.
  91. Heat and Mass Transfer in porous bodies of simple geometry, Indian Journal of Pure and Appl. Math. 13(1) (1982), 96-109, with R.N. Pandey.
  92. Boundary Layer approach to Non-linear Heat and Mass Transfer in a infinite cylindrical, porous body under boundary conditions of the second kind, The Journal of Scientific Research XXXXII (2) (1981-82), with R.N. Pandey.
  93. Heat and Mass Transfer in a capillary porous body of spherical geometry under boundary conditions of the first kind, Indian Journal of Technology 18 (1980), 488-493, with L.P. Rai.
  94. Boundary layer approach to heat and mass transfer in porous bodies of cylindrical geometry, Int. J. Engng. Sci. 14 (1976), 975-990, with K. N. Pandey.
  95. Heat and Mass Transfer in an infinite porous plate, Indian J. Pure and Appl. Math. 6(10) (1975), 1113-1126, with R.N. Pandey.
  96. Temperature fields in a system consisting of a finite rod and a semi-infinite rod, Istanbul Teknik Universitesi Bulteni, 28(2) (1975), 80-92, with R.N. Pandey.
  97. Temperature distribution in a parallelepiped under the influence of heat source with boundary conditions of second kind, The Proceedings of the Indian Academy of Sciences. LXXIX, Sec. A, (3) (1974), 111-138, with R.N. Pandey.
  98. Temperature distribution in an infinite plate under the boundary conditions of the fourth kind, The Journal of Scientific Research XXIV (1-2) (1973-74), 288-303, with R.N. Pandey, K.N. Shukla, S. Kumar.
  99. Temperature fields in a hollow cylinder in presence of heat source under the boundary conditions of the second kind, The Proceedings of the Indian Academy of Sciences LXXVII Sec A, (2) ( 1973), 62-82, with S. Kumar and Lalmani.
  100.  Temperature fields in a system consisting of two semi-infinite rods (Part II), Indian J. Phys. 47 (1973), 267-276, with R.N. Pandey.
  101. General solutions to a class of unsteady heat conduction problems in a circular disc, The Journal of Scientific Research XXII (2) (1971-72), 95-102, with R.N. Pandey.
  102. Temperature fields in a system consisting of two semi-infinite rods (PartI), The Journal of Scientific Research XXII (1) (1971-72), 161-177, with A.K Bahal and R.N. Pandey.
  103. Temperature distribution in a sphere of finite radius in presence of arbitrary volume heat source with boundary conditions of third kind, The Journal of Scientific Research XXII(1) (1971-72), 153-159, with R.N. Pandey.

(ii) Published Book (01)

  • K.N. Rai, S.K. Singh, S.K. Singh, “Next generation e-Content on Numerical Methods and its Application” (Investigator in a pilot of Rs.5,00,000/-(Rupees five Lakhs only)  sanctioned vide no. F. 16-146/2009-DL, Government of India, MHRD).

(iii) Book Chapter Published/Chapter Published in Conference Proceeding (03)

  1. Comparative study of image compression techniques based on wavelet transform and wavelet packet transform, Computer Science and Engineering: Recent Trends, Narosa Publishing House (ISBN: 978-81-8487-391-7), with P.K. Singh, R.S. Singh and S. Jaiswal.
  2. Wavelets and its application in image compression, Emerging Technologies in Intelligent Applications for Image and Video Processing, IGI Global, USA (ISBN: 9781466696860), with P.K. Singh and R.S. Singh.
  3. An image encryption algorithm based on XOR operation with approximation component in wavelet transform, Fifth National Conference on Computer Vision, Pattern Recognition, Image Processing and Graphics (ISBN: 978-1-4673-8564-0), with P.K. Singh, R.S. Singh.
S.N. Conference/Symposium Place / Year Special contribution (if any )
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(Ganit evam uske Anuprayog)		 Neharu Gram Bharti, Deemed Vishwavidyalaya, Allahabad, February 16-17, 2018 **vkO;wg fo?kVu O;kidhd`r O;qRdze ,oa mlds vuqiz;ksx**
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2 33rd Annual National Conference of The Mathematical-BHU on Recent Advances in Mathematical Modelling and Analysis Department of Mathematics, Institute of sciences, BHU, February 16-18, 2018 Delivered an invited  talk on A study of wavelet based numerical methods
3 Biology and Medicine Through Mathematics conference Richmond, Virginia Commonwealth University, USA, May 18-20, 2017 Paper entitled “Numerical investigation of phase-lag phenomena within living biological tissue during thermal therapy application
4 Workshop on  Advances in stability analysis on dynamical system Department of Mathematics, NIT Silchar,  March 08-12, 2017 Delivered an invited  talk on Advances in stability analysis on dynamical system
5 ICHMT- Int. Symposium on Advances on Computational Heat Transfer Rutgers University, USA, May 25-29, 2015 Paper entitled “Thermal effect in FSPL heat conduction model irradiated by laser heat source”, with T. N. Mishra
6 ICHMT- Int. Symposium on Advances on Computational Heat Transfer Rutgers University, USA, May 25-29, 2015 Paper entitled “Analytical approximation for one-phase-space-time fractional moving boundary problem with time varying temperature on surface”, with Jitendra Singh
7 International Conference on Advances in Scientific Computing Department of Mathematics and Statistics, IIT Madras, November 28-30, 2016 Delivered an invited  talk on Wavelets and its Applications
8 ICHMT-International Symposium on Convective Heat and Mass Transfer Pine Bay Holiday Resort, Kusadasi, Turkey, June 08-14, 2014 Paper entitled “Exact and wavelet collocation solution of Fin problem with temperature dependent internal heat generation” with S. Singh et al., published in proceeding.
9 ICHMT-International Symposium on Convective Heat and Mass Transfer Pine Bay Holiday Resort, Kusadasi, Turkey, June 08-14, 2014 Paper entitled “Wavelet Galerkin and Wavelet collocation method in moving boundary problem with temperature dependent thermal physical properties” with S. Yadav et al., published in proceeding and presented by K. N. Rai.
10 International Conference on Emerging Trends in Computational and Applied Mathematics ITM, Gurgaon, June 02-04, 2014 Paper entitled “Steady state temperature distribution in biological tissue using wavelet collocation method” with Dinesh Kumar et. al., published in proceeding and presented by Dinesh Kumar.
11 International Conference on Emerging Trends in Computational and Applied Mathematics ITM, Gurgaon, June 02-04, 2014 Paper entitled “Effect of geometrical configuration on temperature distribution in Fin” with Surjan Singh et. al., published in proceeding and presented by Surjan Singh.
12 International Conference on Recent Trends in Computer Science and Engineering, Department of Computer Science, Central University of Bihar, February 08-09, 2014 Paper entitled “Comparative study of image compression techniques based on wavelet transform and wavelet packet transform” with P. K. Singh et. al., published in proceeding and presented by P. K. Singh.
13 29th Annual Conference of Mathematical Society of Banaras Hindu University Department of Mathematics, Banaras Hindu University, February 03-04, 2014 Paper entitled  “Compact difference scheme for solving fractional single-phase-lagging heat conduction model” with T. N. Mishra, presented by T. N. Mishra
14 11th International and 22nd National ASME-ISHMT Heat Mass Transfer Conference Department of Mechanical Engineering, IIT Kharagpur, December 28-31, 2013 Paper entitled “Compact difference scheme for solving 1 D dual-phase-lagging heat transport equation” with T. N. Mishra,  published in proceeding and presented by T.N. Mishra
15 National Conference on Emerging Trends in Physics of Fluids and Solids Department of Mathematics, Jadavpur University, Calcutta, February 27-28, 2013 Paper entitled  “Implicit finite difference approximation for  time fractional heat conduction equation under most generalized boundary condition” with T. N. Mishra, presented by T. N. Mishra
16 Lecture series on Matrix Decomposition Method DST-CIMS, BHU, 2013
 		 Delivered a number of talks in the Lecture Series
17 National Seminar and Training on Mathematical Modeling Department of Mathematics, Mahatma Gandhi Chitrakoot Gramoday  Gramodaya Vishwavidhyalaya, 2013 Delivered an invited  talk on Mathematical Modelling
 
 
18 Advanced Training Programme on Integral Transform, Wavelets, Distribution Theory and Applications DST-CIMS, BHU, 2012 Delivered two invited  talks on Integral Transform
19 Lecture Series on Integral Equations Department of Mathematics, DDU,  Gorakhpur 2011 Delivered two invited  talks in the Lecture Series
20 Lecture series on Matrix Decomposition Method DST-CIMS, BHU, 2011 Delivered lectures on Fridays
21 National Workshop on   Linear and Non linear systems Department of Mathematics, Banasthali University, Rajasthan, 2011 Delivered an invited  talk on Non Linear System
22 ASME Heat Transfer/Fluid Engineering Conference Charlotte North Carolina, USA, 2004 Paper entitled  “Finite element method for the solution of free boundary problem” presented by Prof. Rai
23 International Conference on Industrial Mathematics Department of Mathematics I.I.T. Bombay, 2002 Paper presented by Prof. Rai
24 National Conference in Mathematics Department of Mathematics, University of Allahabad, 2002 Prof. Rai delivered an invited  talk
25 International Conference on Special Function Institute of Mathematical Sciences Chennai, 2002 Paper presented by Prof. Rai
26 Seventeenth Annual Conference of Ramanujan Mathematical Society Department of Applied Mathematics, I.T., B.H.U., 2002 Prof. Rai delivered an invited  talk on Moving Boundary Problem
27 Conference on Thermal Systems and Heat Transfer Department of Mechanical Engineering, I.T., B.H.U., 2001 Paper presented by Prof. Rai
28 National Symposium on Recent Trends in Membrane Transport School of Biomedical Engineering I.T., B.H.U., 1998 Paper presented by Prof. Rai
29 National Symposium on Advances in Chemical Reaction Engineering Department of Chemical Engineering I.T., B.H.U., 1997 Paper presented by Prof. Rai
30 Conference on Mathematics and its Applications in Engineering and Industry Department of Mathematics, University of Roorkee, 1996 Paper presented by Prof. Rai
31 International Symposium on Recent Advances in Rings Modules and Groups with Homological Techniques and their Applications Department of Applied Mathematics, I.T., B.H.U., 1995 Prof. Rai was a Member of Academic Programme Committee
32 A symposium on Operators and Dynamical systems Department of Mathematics, University  of Jammu, 1995 Prof. Rai delivered an invited  talk
33 Conference on Thermal System Department of Mechanical Engineering I.T., B.H.U., 1995 Paper presented by Prof. Rai

i. Member of Indian Mathematical Society.
ii. Member of Jammu Mathematical Society.
iii. EX-Member of American Mathematical Society.

  1. International Journal of Heat and Mass Transfer, Elsevier, Amsterdam, Netherlands awarded a "Certificate of Outstanding Contribution in Reviewing" in recognition of the contribution made to the quality of the Journal in January 2018.
  2. International Journal of Thermal Sciences, Elsevier, Amsterdam, Netherlands awarded a "Certificate of Reviewing" in recognition of the review made for the Journal in December 2017.
  3. International Journal of Heat and Mass Transfer, Elsevier, Amsterdam, Netherlands awarded a "Certificate of Reviewing" in recognition of the review made for the Journal in October 2016.