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Applied Math Research

K.N. Rai

Designation: Professor & Ex-Head

Phone: +91-9935346251, 0542-2307034 (O)

E-mail: knrai.apm@itbhu.ac.in

Research Areas: Heat & Mass Transfer, Bio-transport Processes, Free Boundary Problems, Mathematical Methods

 

 

Biography:

Dr. K.N. Rai did his M.Sc., Ph.D. in Mathematics from Banaras Hindu University. He is the currently Co-coordinator of DST-CIMS Project (Mathematical modeling and computational aspects).

He is a life member of following bodies:

  1. Indian Mathematics Society
  2. Jammu Mathematical Society

Teaching Experience : UG: 34 yrs., PG: 34 yrs.

Research Experience : 37 yrs

Ph.D. Supervision : Eight produced, One Co-Supervised, One Submitted, One in progress.

Publications:

List of Papers Published:

  1. K.N. Rai and R.N. Pandey; 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, Vol. XXII(1) pp. 153-159 (1971-72).
  2. K.N. Rai, A.K Bahal and R.N. Pandey; Temperature fields in a system consisting of two semi-infinite rods (Part I), The Journal of Scientific Research, Vol. XXII(1) pp. 161-177 (1971-72).
  3. K.N. Rai and R.N. Pandey; General solutions to a class of unsteady heat conduction problems in a circular disc, The Journal of Scientific Research, Vol. XXII(2) pp. 95-102 (1971-72).
  4. K.N. Rai and R.N. Pandey; Temperature fields in a system consisting of two semi-infinite rods (Part II), Indian J.Phys, Vol. 47, pp. 267-276 (1973).
  5. R.N. Pandey, K.N. Shukla, S. Kumar and K.N. Rai; Temperature distribution in an infinite plate under the boundary conditions of the fourth kind, The Journal of Scientific Research, Vol. XXIV(1-2), pp. 288-303 (1973-74).
  6. K.N. Rai, S. Kumar and Lalmani; 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, Vol. LXXVIIm Sec A, No.2, pp. 62-82( 1973),
  7. K.N. Rai and R.N. Pandey; 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, Vol. LXXIX, Sec.A, No.3, pp. 111-138(1974).
  8. K.N. Rai and R.N. Pandey; Temperature fields in a system consisting of a finite rod and a semi-infinite rod, Istanbul Teknik Universitesi Bulteni, Vo. 28 No.2 pp. 80-92 (1975).
  9. K.N. Rai and R.N. Pandey; Heat and Mass Transfer in an infinite porous plate, Indian J. Pure and Appl. Math., Vol. 6 No(10) pp 1113-1126 (1975).
  10. K.N. Rai and KN. Pandey; Boundary layer approach to heat and mass transfer in porous bodies of cylindrical geometry, Int. J. Engng. Sci., Vol. 14, pp. 975-990 (1976).
  11. KN. Rai and L.P. Rai; Heat and Mass Transfer in a capillary porous body of spherical geometry under boundary conditions of the first kind, Indian Journal of Technology, Vol. 18, pp. 488-493 December (1980).
  12. K.N. Rai and R.N. Pandey; 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. Vol. XXXXII(2) (1981-82).
  13. K.N. Rai and R.N. Pandey; Heat and Mass Transfer in porous bodies of simple geometry, Indian Journal of Pure and Appl. Math, Vol. 13(1) pp. 96-109 January (1982).
  14. K.N. Rai and R.N. Pandey; Heat and Mass Transfer in an infinite cylinderical porous body under the generalized boundary conditions, The Journal of Scientific Research, Vol. 33(2) pp. 193-207 June(1983).
  15. K.N. Rai and R.N. Pandey; Molecular and molar transfer of heat and mass in a capillary porous body, The Journal of Sci. Research, Vol. 34(2), pp. 91-129 (1984).
  16. K.N. Rai and S.N. Sinha; Approximate closed form analytical solution of heat conduction in bodies of simple configuration, Indian Journal of Technology, Vol. 25 pp. 160-163 April (1987).
  17. K.N. Rai and S.N. Dubey; Limited diffusion processes in a body of simple geometry, Indian Journal of Technology, Vol. 25 pp. 164-170 April (1987).
  18. K.N. Rai; Molar molecular heat and mass transfer in a capillary porous body of spherical geometry, Commun. Fac. Sci. Univ. Ank. Series A2, A3 Vol 36, pp.21­ 34 (1987).
  19. K.N. Rai, S. Rai; 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, Vol. 26, pp. 359-364 August (1988).
  20. K.N. Rai and L. Thakur; Approximate closed form analytical solution of molar molecular heat and mass transfer in a porous body of simple configuration, Proc. Indian National Sc. Academy, Vol. 57A No.1 pp. 45-59(1990).
  21. K.N. Rai and S. Rai; An analytical study of the solidification in a semi-infinite porous medium, Int. J. Engg. Sci. Vol. 30 No.2 pp. 247-256 (1992).
  22. K.N. Rai and L. Thakur; A mathematical interpretation of diffusion processes with concentration dependent diffusion coefficient, Astrophysics and Space Science (1991).
  23. K.N. Rai and S. Rai; Approximate closed form analytical solution of the desublimation problem in a porous medium, Int. J. Energy Research, Vol. 19 pp. 279-288(1995).
  24. K.N. Rai; Approximate closed form analytical solution of heat and mass transfer problem, Conference on thermal System, pp. 323-328 (1986).
  25. K.N. Rai, S. Rai and R.N. Pandey; Integral balance approach to heat and mass transfer in an infinite porous plate with parabolic initial conditions, Transfer Processes in Multiphase System, pp. 411-421 (1987).
  26. K.N. Rai, S.Rai and B.N. Trivedi; Limited diffusion processes in an infinite cylinder of glass or crystal; Transfer Process in Multiphase Systems, pp. 422-433 (1987).
  27. K.N. Rai and S. Rai; Approximate ~closed form analytical solution of diffusion equation, Transfer Processes in Multiphase Systems, pp. 434-438(1987).
  28. K.N. Rai and S. Rai; 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, pp 409­429( 1989).
  29. K.N. Rai, L. Thakur and S.K. Singh; Solidification of a binary eutectic system due to a line heat sink, Conference on Thermal Systems, VII 7.1-7.12(1995).
  30. K.N. Rai, L. Thakur and S.K. Singh; 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).
  31. K.N. Rai and S.K. Singh; Numerical solution of moving boundary problem in a finite domain, Heat and Mass Transfer, 34 pp 295-298 (1998).
  32. K.N. Rai and S.K. Rai; Effect of metabolic heat generation and blood perfusion on the heat transfer in the tissues with a blood vessel, Heat and Mass Transfer 35 pp.75-79 (1999).
  33. K.N. Rai and S.K. Rai; 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 pp.345-350 (1999).
  34. K.N. Rai and S. Rai; An analytical study of melting and vaporization in a porous half-space, Thermal System and Heat Transfer, pp. 11-16 (2001).
  35. K.N. Rai, S. Rai and K.D. Rai, Determination of melt and vaporization zone width and initial concentration of frozen bounded substance, Thermal System and Heat Transfer, pp. 17-22 (2001).
  36. K.N. Rai and S. Rai; Heat and Mass Transfer analysis of solidification over a cylindrical heat sink, Thermal System and Heat Transfer, pp. 23-29 (2001).
  37. K.N. Rai and D.C. Rai; Numerical solution for inward solidification of slabs, cylinders and sphere, Fourth National Conferences on Thermal Systems, pp. 259­ 267 (2003).
  38. K.N. Rai and K.D. Rai; A numerical technique for the solution of transport problems, Forth National Conferences on Thermal System, pp. 268-277 (2003).
  39. K.N. Rai and S.K. Rai; Boundary fixation approach to one dimensional inverse Stefan problem in non-ideal biological tissues, Fourth National Conferences on Thermal System, pp. 278-289 (2003).
  40. K.N. Rai and S.K. Rai; Heat transfer in tissues during hyperthermia, Fourth National Conference on Thermal System, pp. 290-297 (2003).
  41. S.K. Singh, K.N. Rai and S.N. Gupta; Planer melting/freezing of a semi-infinite medium with time dependent surface temperature and temperature dependent thermal diffusivity, Fourth National Conference on Thermal System, pp. 326­332,404-409 (2003).
  42. K.N. Rai and D.C. Rai; Finite element method for two dimensional Stefan Problem, National Conferences on Separation in Process Industries, pp. 245-253 (2003).
  43. K.N. Rai and S.K. Singh; Coupled heat and mass transfer with one sublimation moving interface and one freezing zone, Communicated for publication.
  44. K.N. Rai and D.C. Rai; A Finite element method for the solution of free boundary problem, accepted for presentation in 2004 ASME Heat Transfer/Fluid Engineering Summer Conference, Carolina (U.S.A.) 2004
  45. P. K. Gupta, Jitendra Singh and K. N. Rai, Numerical Simulation for Heat Transfer in tissues during Thermal therapy, Journal of Thermal Biology, V. 35(6), pp. 295-301, 2010. 
  46. J. Singh, P. K. Gupta and K. N. Rai, Homotopy perturbation Method to space-time fractional solidification in a finite slab, Applied Mathematical Modelling, V. 35(4), pp. 1937-1945, 2011.
  47. J. Singh, P. K. Gupta and K. N. Rai, Variational iteration method to solve moving Boundary problem with temperature dependent Physical properties, Thermal Sciences, Accepted (2010).. 

Conferences/Seminars Attended:

Name

Place/Year

Special contribution (if any)

1. Conference on thermal system

Dept. of Mechanical Engg. I.T., B.H.U., 1986

Papers presented

2. Thermal Processes in multiphase system

Dept. of Chemical Engg. I.T., B.H.U., 1987

-do-

3. 33rd congress of the Indian Society of Theoretical and Applied Mechanics

Dept. of Mechanical Engg. I.T., B.H.U., 1988

-do-

4. Conference on thermal system

Dept. of Mechanical Engg. I.T., B.H.U., 1995

-do-

5. A symposium on operators and Dynamical systems

Dept. of Mathematics, Univ. of Jammu, 1995

A talk

6. International Symposium on Recent advances in Rings Modules and Groups with homological techniques and their applications

Dept. of Applied Mathematics, I.T., B.H.U., 1995

Member Academic Programme Committee

7. Conference on mathematics and its applications in Engineering and Industry

Dept. of Mathematics, Univ. of Roorkee, 1996

Papers presented

8. National  Symposium on Advances in Chemical Reaction Engineering

Dept. of Chemical Engg. I.T., B.H.U., 1997

Papers presented

9. National  Symposium on Recent trends in membrane transport

School of Biomedical Engg. I.T., B.H.U., 1998

Papers presented

10. Thermal Systems and Heat Transfer

Dept. of Mechanical Engg., 2001

Papers presented

11. Seventeenth Annual Conference of Ramanujan Mathematical Society

Dept. of Applied Mathematics, I.T., B.H.U., 2002

A talk

12. International Conference on special function

Institute of Mathematical Sciences Chennai, 2002

Paper presented

13. National Conference in Mathematics

University of Allahabad, 2002

A talk

14. International Conference on Industrial Mathematics

I.I.T., Bombay, 2002

Paper presented

15. 2004 ASME Heat Transfer/Fluid Engg. Conference

North Carolina, USA, 2004

Paper presented

 
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