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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


Unsteady Magnetohydrodynamic Boundary Layer Flow towards a Heated Porous Stretching Surface with Thermal Radiation and Heat Source/Sink Effects

Discontinuity, Nonlinearity, and Complexity 9(1) (2020) 141--151 | DOI:10.5890/DNC.2020.03.010

Santosh Chaudhary$^{1}$, Susheela Chaudhary$^{2}$, Sawai Singh$^{2}$

$^{1}$ Department of Mathematics, Malaviya National Institute of Technology, Jaipur - 302017, India

$^{2}$ Department of Mathematics, Government Science College, Sikar – 332001, India

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Mathematical model of unsteady boundary layer flow and heat transfer is explored for analyzing the study of influence of thermal radiation on incompressible viscous electrically conducting fluid over continuous stretching surface embedded in a porous medium in the presence of heat source/sink. The scope of influencing parameters that describing phenomenon are determined and governing time dependent boundary layer equations are transformed to ordinary differential equations by using appropriate similarity transformation. Numerical computation of the problem was carried out by shooting iteration technique together with Runge-Kutta fourth order integration scheme. Effects of unsteadiness parameter, permeability parameter, magnetic parameter, thermal radiation parameter, Prandtl number and heat source/sink parameter on velocity and temperature profiles are computed and illustrated graphically, whereas local skin friction coefficient and local Nusselt number are represented numerically through tables. In nonmagnetic flow condition the result is found in concordance with earlier investigations.


  1. [1]  Sakiadis, B.C. (1961), Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two dimensional and axisymmetric flow, AIChE J, 7, 26-28.
  2. [2]  Crane, L.J. (1970), Flow past a stretching plate, Z AngewMath Phys, 21, 645-647.
  3. [3]  Chen, C.K. and Char, M.I. (1988), Heat transfer of a continuous, stretching surface with suction or blowing, J Math Anal Appl, 135, 568-580.
  4. [4]  Andersson, H.I. (2002), Slip flow past a stretching surface, Acta Mech, 158, 121-125.
  5. [5]  Elbashbeshy, E.M.A. and Bazid, M.A.A. (2004), Heat transfer over an unsteady stretching surface, Heat Mass Tran, 41, 1-4.
  6. [6]  Jat, R.N. and Chaudhary, S. (2008),Magnetohydrodynamic boundary layer flow near the stagnation point of a stretching sheet, Il Nuovo Cimento, 123B, 555-566.
  7. [7]  Ishak, A., Nazar, R., and Pop, I. (2009), Heat transfer over an unsteady stretching permeable surface with prescribed wall temperature, Nonlinear Anal: Read World Appl, 10, 2909-2913.
  8. [8]  Aziz, R.C., Hashim, I., and Alomari, A.K. (2011), Thin film flow and heat transfer on an unsteady stretching sheet with internal heating, Meccanica, 46, 349-357.
  9. [9]  El-Aziz, M.A. (2014), Unsteady mixed convection heat transfer along a vertical stretching surface with variable viscosity and viscous dissipation, J. Egyp Math Soc, 22, 529-537.
  10. [10]  Chaudhary, S. and Choudhary,M.K. (2017), Viscous dissipation and Joule heating effects on an unsteady magnetohydrodynamic flow over a linearly stretching permeable surface with uniform wall temperature, Indian J Pure Appl Phys, 55, 864-872.
  11. [11]  Chaudhary, S. and Choudhary, M.K. (2018), Partial slip and thermal radiation effects on hydromagnetic flow over an exponentially stretching surface with suction or blowing, Therm Sci, 22, 797-808.
  12. [12]  Liu, L. and Liu, F. (2018), Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness, Appl Math Lett, 79, 92-99.
  13. [13]  Pop, I. and Ingham, D.B. (2001), Convective heat transfer: Mathematical and computational modelling of viscous fluids and porous media, Elsevier: UK.
  14. [14]  Vafai, K. (2005), Handbook of porous media (2nd edition), Taylor & Francis: US.
  15. [15]  Delgado, J.M.P.Q. (2013), Heat and mass transfer in porous media, Springer: New York.
  16. [16]  Nield, D.A. and Bejan, A. (2014), Convection in porous media (4th edition), Springer: New York.
  17. [17]  Vafai, K. and Tien, C.L. (1981), Boundary and inertia effects on flow and heat transfer in porous media, Int J Heat Mass Tran, 24, 195–203.
  18. [18]  Merrill, K., Beauchesne, M., Previte, J., Paullet, J., and Weidman, P. (2006), Final steady flow near a stagnation point on a vertical surface in a porous medium, Int J Heat Mass Tran, 49, 4681-4686.
  19. [19]  Pal, D. and Hiremath, P.S. (2010), Computational modeling of heat transfer over an unsteady stretching surface embedded in a porous medium, Meccanica, 45, 415-424.
  20. [20]  Chaudhary, S. and Kumar, P. (2014)MHD forced convection boundary layer flow with a flat plate and porous substrate, Meccanica, 49, 69-77.
  21. [21]  Hibi, Y. and Tomigashi, A. (2015), Evaluation of a coupled model for numerical simulation of a multiphase flow system in a porous medium and a surface fluid, J Contam Hydrol, 180, 34-55.
  22. [22]  Chaudhary, S. and Choudhary, M.K. (2016), Heat and mass transfer by MHD flow near the stagnation point over a stretching or shrinking sheet in a porous medium, Indian J Pure Appl Phys, 54, 209-217.
  23. [23]  Xu, H. and Cui, J. (2018),Mixed convection flow in a channel with slip in a porous medium saturated with a nanofluid containing both nanoparticles and microorganisms, Int J Heat Mass Tran, 125, 1043-1053.
  24. [24]  Cortell, R. (2005), Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/absorption and suction/blowing, Fluid Dyn Res, 37, 231-245.
  25. [25]  Layek, G.C., Mukhopadhyay, S., and Samad, Sk.A. (2007), Heat and mass transfer analysis for boundary layer stagnation-point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing, Int CommunHeat Mass Tran, 34, 347-356.
  26. [26]  Mukhopadhyay, S. and Layek, G.C. (2012), Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink, Meccanica, 47, 863-876.
  27. [27]  Jalilpour, B., Jafarmadar, S., Ganji, D.D., Shotorban, A.B., and Taghavifar, H. (2014), Heat generation/absorption on MHD stagnation flow of nanofluid towards a porous stretching sheet with prescribed surface heat flux, J Mol Liq, 195, 194-204.
  28. [28]  Harfash, A.J. (2016), Resonant penetrative convection in porous media with an internal heat source/sink effect, Appl Math Comput, 281, 323-342.
  29. [29]  Rashad, A.M., Armaghani, T., Chamkha, A.J., and Mansour, M.A. (2018), Entropy generation and MHD natural convection of a nanofluid in an inclined square porous cavity: Effects of a heat sink and source size and location, Chinese J Phys, 56, 193-211.
  30. [30]  Raptis, A. (1998), Radiation and free convection flow through a porous medium. Int Commun Heat Mass Tran, 25, 289-295.
  31. [31]  Raptis, A. and Perdikis, C. (2004), Unsteady flow through a highly porous medium in the presence of radiation, Trans Porous Media, 57, 171-179.
  32. [32]  Pal, D. and Mondal, H. (2009), Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity, Meccanica, 44, 133-144.
  33. [33]  Jat, R.N. and Chaudhary, S. (2010), Radiation effects on the MHD flow near the stagnation point of a stretching sheet, Z AngewMath Phys, 61, 1151-1154.
  34. [34]  Mahapatra, T.R. and Nandy, S.K. (2013), Stability of dual solutions in stagnation-point flow and heat transfer over a porous shrinking sheet with thermal radiation, Meccanica, 48, 23-32.
  35. [35]  Sinha, A. and Shit, G.C. (2015), Electromagnetohydrodynamic flow of blood and heat transfer in a capillary with thermal radiation, J Magn Magn Mater, 378, 143-151.
  36. [36]  Abbas, Z., Rahim, T., and Hasnain, J. (2017), Slip flow of magnetite-water nanomaterial in an inclined channel with thermal radiation, Int J Mech Sci, 122, 288-296.
  37. [37]  Mahanthesh, B. and Gireesha, B.J. (2018), Scrutinization of thermal radiation, viscous dissipation and Joule heating effects on Marangoni convective two-phase flow of Casson fluid with fluid-particle suspension, Results Phys, 8, 869- 878.
  38. [38]  Elbashbeshy, E.M.A. and Emam, T.G. (2011), Effects of thermal radiation and heat transfer over an unsteady stretching surface embedded in a porous medium in the presence of heat source or sink, Therm Sci, 15, 477-485.
  39. [39]  Rybicki, G.B. and Lightman, A.P. (2008), Radiative processes in astrophysics, Wiley-VCH: Germany.
  40. [40]  White, R.E. and Subramanian, V.R. (2010), Computational methods in chemical engineering with maple, Springer- Verlag Berlin Heidelberg: Chennai, India.