Article ID: MTJPAM-D-20-00022

Title: MHD Free Convective Flow over an Impulsively Started Vertical Plate With Second Order Chemical Reaction and Heat Source

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-20-00022; Volume 3 / Issue 2 / Year 2021, Pages 38-46

Document Type: Research Paper

Author(s): Bharat Keshari Swain a

aDepartment of Mathematics, IGIT, Sarang, Dhenkanal, Odisha, India

Received: 28 July 2020, Accepted: 6 March 2021, Published: 15 May 2021.

Corresponding Author: Bharat Keshari Swain (Email address:

Full Text: PDF


Present study has been carried out to elucidate a laminar free convective flow of an incompressible chemically reactive fluid over an impulsively started vertical plate embedded in a porous medium. The influence of both second order chemical reaction and heat source make the study interesting. The governing coupled partial differential equations are solved by using Crank-Nicolson method. The impacts of pertinent parameters on the velocity, temperature and concentration have been explored through graphs. The results of the present study agree well with the previous solutions. Some important findings are: velocity and concentration profiles decrease with increase in chemical reaction parameter, there is a reduction in temperature with increase in the Prandtl number, temperature improves with higher values of Q. Applications of the present study are shown in material processing systems and chemical industries etc.

Keywords: MHD, Porous medium, Second order chemical reaction, Radiation, Heat source

  1. S. Ahmed, Numerical analysis for magneto hydrodynamic chemically reacting and radiating fluid past a non-isothermal impulsively started vertical surface adjacent to a porous regime, Ain Shams Engineering Journal (Elsevier) 5, 923–933, 2014.
  2. S. Ahmed and A. Batin, Convective laminar radiating flow over an accelerated vertical plate embedded in a porous medium with an external magnetic field, IJET 3, 66–72, 2013.
  3. S. Ahmed and K. Kalita, Unsteady MHD chemically reacting fluid through a porous medium bounded by a non-isothermal impulsively-started vertical plate: A numerical technique, J. of Naval Architecture and Marine Engineering 11, 39–54, 2014.
  4. I. M. Alarifi, A. G. Abokhalil, M. Osman, L. A. Lund, M. B. Ayed, H. Belmabrouk and I. Tlili MHD Flow and Heat Transfer over Vertical Stretching Sheet with Heat Sink or Source Effect, Symmetry 11, 297, 2019.
  5. B. Carnahan, H. A. Luther and J. O. Wilkes, Applied Numerical Methods, John Wily and Sons, New York, 1969.
  6. M. Ferdows, Q. M. Al-Mdallal, Effects of order of chemical reaction on a boundary layer flow with heat and mass transfer over a linearly stretching sheet, American Journal Of Fluid Dynamics 2, 89–74, 2012.
  7. R. Kandasamy, T. Hayat and S. Obaidat, Group theory transformation for Soret and Dufour effects on free convective heat and mass transfer with thermophoresis and chemical reaction over a porous stretching surface in the presence of heats source/sink, Nuclear Engineering and Design 241, 2155–2161, 2011.
  8. R. Kandasamy, K. Periasamy, K. K.P. Sivagnana, Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects, International Journal Heat Mass Transfer. 48, 4557–4561, 2005.
  9. D. Khan, A. Khan, I. Khan, F. Ali, F. Karim and I. Tili, Efects of relative magnetic field, chemical reaction, heat generation and newtonian heating on convection flow of casson fluid over a moving vertical plate embedded in a porous medium, Scientific Reports 9, 1–18, 2019.
  10. N. N. W. Khalili, A. A. Samson, A. S. A. Aziz and Z. M. Ali, Chemical reaction and radiation effects on MHD flow past an exponentially stretching sheet with heat sink, J. Phys.: Conf. Ser. 890, 012025, 2017.
  11. N. Kishan, P. Amrutha, Effects of viscous dissipation on MHD flow with heat and mass transfer over a stretching surface with heat source, thermal stratification and chemical reaction, Journal of Naval Architecture Marine Engineering 7, 11–18, 2011.
  12. M. Li, Y. Wu, Y. Tian and Y. Zhai, Non-thermal equilibrium model of the coupled heat and mass transfer in strong endothermic chemical reaction system of porous media, International Journal Heat Mass Transfer 50, 2936–2943, 2007.
  13. O. D. Makinde and P. Sibanda, Effects of chemical reaction on boundary layer flow past a vertical stretching surface in the presence of internal heat generation, International Journal of Numerical Fluid Flows In press. 2, 89–94, 2012.
  14. S. Mohammed Ibrahim, Unsteady MHD convective heat and mass transfer past an infinite vertical plate embedded in a porous medium with radiation and chemical reaction under the influence of Dufour and Soret effects, Chemical and Process Engineering 19, 25–38, 2014.
  15. F. Mohammed Nasser El-Fayez, Effects of chemical reaction on the unsteady free convection flow past an infinite vertical permeable moving plate with variable temperature, Journal of Surface Engineered Materials and Advanced Technology 2, 100–109, 2012.
  16. S. Ostrach, Laminar natural convection flow and heat transfer of fluid with and without heat source in channel with wall temperature, NACA TN 2863, 1952.
  17. H. R. Patel, Effects of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation, Heliyon 5, 1–26, 2019.
  18. K. Pravin Kashyap, O. Ojjela and S. K. Das, MHD slip flow of chemically reacting UCM fluid through a dilating channel with heat source/sink, Nonlinear Engineering 8, 523–533, 2019.
  19. A. A. Raptis, Free convection and mass transfer effects on the flow past an infinite moving vertical porous plate with constant suction and heat source, Astrophy Space Sci. 86, 43–53, 1982.
  20. B. K. Sharma, A. K. Jha and R.C. Chaudhary, Hall effect on MHD mixed convective flow of a viscous incompressible fluid past a vertical porous plate immersed in a porous medium with heat source/sink, Rom. Journ. Phys. 52, 487–503, 2007.
  21. R. Siegel and J. R. Howell, Thermal radiation heat transfer, 4th edition, Taylor & Francis, Newyork, 2002.
  22. A. K. Singh, MHD free convection and mass transfer flow with heat source and thermal diffusion, J. of Energy, Heat and Mass Transfer 23, 227–249, 2001.
  23. P. Sreenivasulu, T. Poornima and N. R. Bhaskar, Internal heat generation effect on radiation heat transfer mhd dissipating flow of a micropolar fluid with variable wall heat flux, Journal of Naval Architecture and Marine Engineering 15, 53–64, 2018.
  24. B. K. Swain and N. Senapati, The effect of mass transfer on MHD free convective radiating flow over an impulsively started vertical plate embedded in a porous medium, Journal of Applied Analysis and Computation 5, 18–27, 2015.
  25. B. K. Swain, N. Senapati and M. Dash, The effect of chemical reaction and thermal radiation on the hydro magnetic free convective rotating flow past an accelerated vertical plate in the presence variable heat and mass diffusion, Der Chemica Sinica 5, 56–66, 2014.
  26. B. K. Swain, N. Senapati and M. Dash, Chemical reaction effect on mhd convective flow with heat and mass transfer past a semi-infinite Vertical Porous Plate, Journal of Advanced Mathematics and Applications 6, 1–8, 2017.
  27. R. S. Tripathy, G. C. Dash, S. R. Mishra and S. Baag, Chemical reaction effect on MHDfree convective surface over a moving vertical plate through porous medium, Alexandria Engineering Journal 54, 673–679, 2015.
  28. Z. Uddin and M. Kumar, Radiation effect on unsteady MHD heat and mass transfer flow on a moving inclined porous heated plate in presence of chemical reaction, International Journal of Mathematical Modeling, Simulation and Applications 3 (2), 155–163, 2010.