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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Effects of Thermal Radiation on Fully Developed MHD Nanofluid Flow in a Vertical Square Duct

Discontinuity, Nonlinearity, and Complexity 12(1) (2023) 87--97 | DOI:10.5890/DNC.2023.03.007

Chandra Shekar Balla$^1$, Ramesh Alluguvelli$^{2}$, Kishan Naikoti$^3$

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This paper addresses the effects of thermal radiation on fully developed flow in the containing nanoparticles in the presence of external magnetic field. A square vertical duct of side L is considered. At four sides of the duct Dirchlet boundary conditions are assumed. The governing nonlinear partial differential equations(PDE) are transformed into dimensionless PDE using suitable nondimensional parameters. Finite element method is employed to solve the highly nonlinear and coupled dimensionless PDE. The results are analyzed in terms of velocity contours and temperature distributions. It is observed that the fully developed nanofluid flow is significantly controlled by radiation and magnetic field.


  1. [1]  Choi, S.U.S. (1995), Enhancing thermal conductivity of fluids with nanoparticles, In: Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA. ASME, FED 231/MD; 66, 99-105.
  2. [2]  Daungthongsuk, W. and Wongwises, S. (2007), A critical review of convective heat transfer nanofluids, Renewable and Sustainable Energy Reviews, 11, 797-817.
  3. [3]  Wang, X. and Mujumdar, A.S. (2007), Heat transfer characteristics of nanofluids: a review, International Journal of Thermal Sciences, 46, 1-19.
  4. [4]  Hartnett, J.P. and Kostic, M. (1989), Heat transfer to newtonian and non-Newtonian fluids in rectangular ducts, Advances in Heat Transfer, 19, 247-356.
  5. [5]  Cheng, C.H., Weng, C.J., and Aung, W. (2000), Buoyancy-assisted flow-reversal and convective heat transfer in entrance region of a vertical rectangular duct, International Journal of Heat and Fluid Flow, 21, 403-411.
  6. [6]  Lee, K.T. (1999), Laminar natural convection heat and mass transfer in vertical rectangular ducts, Int. J. Heat Mass Transfer, 42, 4523-4534.
  7. [7]  Hwang, G.J., Tzeng, S.C., and Soong, C.Y. (2001), A computer-aided parametric analysis of mixed convection in ducts, International Journal of Heat And Mass Transfer, 44, 1857-1867.
  8. [8]  Sparrow, E.M. and Cess, R.D. (1978), Radiation Heat Transfer, Brooks/Cole, Belmont, Calif., Hemisphere Publishing Corp., Washington, D.C.
  9. [9]  Siegel, R. and Howell, J.R. (1981), Thermal Radiation Heat Transfer, McGraw-Hill Book Co., New York.
  10. [10]  Krishnamurthy, M.R., Prasannakumara, B.C., Gorla, R.S.R., and Gireesha, B.J. (2016), Non-linear thermal radiation and slip effect on boundary layer flow and heat transfer of suspended nanoparticles over a stretching sheet embedded in porous medium with convective boundary conditions, Journal of Nanofluids, 5(4), 522-530.
  11. [11]  Gireesha, B.J., Umeshaiah, M., Prasannakumara, B.C., Shashikumar, N.S., and Archana, M. (2020), Impact of nonlinear thermal radiation on magnetohydrodynamic three dimensional boundary layer flow of Jeffrey nanofluid over a nonlinearly permeable stretching sheet, Physica A: Statistical Mechanics and its Applications, 549, 124051.
  12. [12]  Lick, W. (1965), Transient energy transfer by radiation and conduction, International Journal of Heat and Mass Tramfer, 8, 119-127.
  13. [13]  Larson, D.W. and Vikanta, R. (1976), Transient combined laminar free convection and radiation in a rectangular enclosure, Journal of Fluid Mechanics, 78(1), 65-85.
  14. [14]  Tiwari, S.N. (1985), Radiative interactions in transient energy transfer in Gaseous systems, NASA-CR-176644 NAS, 1(26), 176644.
  15. [15]  Tiwari, S.N., Singh, D.J., and Kumar, A. (1987), Transient radiative energy transfer in nongray gases, AIAA, 87, 0323.
  16. [16]  Ozisik, M.N. (1987), Interaction of radiation with convection, In: Handbook of Single-Phase Convective Heat Transfer, Wiley, New York, pp. 19.1-19.34.
  17. [17]  Modest, M.F. (2003), Radiative Heat Transfer, 2nd edition, Academic Press, New York.
  18. [18]  Ali, K., Ahmad, S., Ahmad, S., Ashraf, M., and Asif, M. (2015), On the interaction between the external magnetic field and nanofluid inside a vertical square duct, AIP Advances, 5(10), 107120.
  19. [19]  Kays, W.M., Crawford, M.F., and Weigand, B. (2005), Convective Heat and Mass Transfer, 4th ed, McGraw-Hill, NewYork.
  20. [20]  Incropera, F.P. and Dewitt, D.P. (2011), Fundamentals of Heat and Mass Transfer, John Wiley and Sons Ltd.
  21. [21]  Dong, Z.F. and Ebadian, M.A. (1995), Analysis of combined natural and forced convection in vertical semicircular ducts with radial internal fins, Numerical Heat Transfer, Part A: Applications, 27(3), 359-372.
  22. [22]  Brewester, M.Q. (1992), Thermal Radiative Transfer and Properties, John Wiley and Sons, New York.
  23. [23]  Reddy, J.N. (2019), Introduction to the Finite Element Method, McGraw-Hill Education.
  24. [24]  Balla, C.S. and Naikoti, K. (2016), Finite element analysis of magnetohydrodynamic transient free convection flow of nanofluid over a vertical cone with thermal radiation, Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 230(3), 161-173.
  25. [25]  Kishan, N. and Shekar, B.C. (2015), Finite element analysis of fully developed unsteady MHD convection flow in a vertical rectangular duct with viscous dissipation and heat source/sink, Journal of Applied Science and Engineering, 18(2), 143-152.
  26. [26]  Alluguvelli, R., Balla, C.S., Bandari, L., and Naikoti, K. (2020), Investigation on natural convective flow of ethylene glycol nanofluid containing nanoparticles Fe3O4 in a porous cavity with radiation, In AIP Conference Proceedings, 2269(1), 060004.
  27. [27]  Macha, M. and Kishan, N. (2016), Finite element analysis of heat and mass transfer by MHD mixed convection stagnation-point flow of a non-Newtonian power-law nanofluid towards a stretching surface with radiation, Journal of the Egyptian Mathematical Society, 24(3), 458-470.