Skip Navigation Links
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


Influence of Heat Generation/Absorption on the Nonlinear Convective Flow of a Casson Fluid over a Horizontal Plate

Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 523--538 | DOI:10.5890/DNC.2022.09.013

R. R. Kairi$^{1}$, Ch. Ramreddy$^{2}$, S. Roy$^{1}$

$^{1}$ Department of Mathematics, Cooch Behar Panchanan Barma University, Cooch Behar, West Bengal, India

$^{2}$ Department of Mathematics, National Institute of Technology, Warangal, Telangana, India

Download Full Text PDF



This work highlights the influence of nonlinear mixed convective flow of a non-Newtonian fluid over a horizontal plate in the presence of heat generation/absorption. The Casson fluid model is employed to express the non-Newtonian behavior of the fluid. Also, the density of the Casson fluid is assumed to be a nonlinear function of temperature. The boundary layer analysis is adopted by introducing a set of non-dimensional transformations for deriving the non-dimensional form of flow governing equations. The proposed problem does not permit a similarity solution. Thus, local similarity and local non-similarity methods are adopted to convert the set of nonlinear PDEs to the set of nonlinear ODEs. On account of local similarity and non-similarity method, the consequential ODEs are solved numerically by the Runge-Kutta method together with the shooting technique. The control of pertinent parameters on the velocity and temperature fields, and on the non-dimensional heat transfer rate as well as on the skin friction coefficient, are analyzed through graphical representation and explored in detail. Prior knowledge about the effect of these parameters on the heat transfer rate and skin friction coefficient can be very useful in the perspective of industrial applications.


Mr. Subrata Roy is thankful to the UGC, India, for funding to accomplish the research work under Junior Research Fellowship.


  1. [1]  Blasius, H. (1908), Grenzschichten in Flussigkeiten mitkleiner Reibung, Z. Math. Phys., 56(1), 1-37.
  2. [2]  Abussita, A.M.M. (1994), A note on a certain boundary layer equation, Appl. Math. Comput., 64, 73-77.
  3. [3]  Chamkha, A.J., Mujtaba, M., and Quadri, A. (2003), Thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge in the presence of a heat source or sink, Heat Mass Transfer, 39, 305-312.
  4. [4]  Cortell, R. (2005), Numerical solutions of the classical Blasius flat plate problem, Appl. Math. Comput., 170, 706-710.
  5. [5]  Fang, T., Fang, G., and Lee, C.F. (2006), A note on the extended Blasius equation, Appl. Math. Lett., 19, 613-617.
  6. [6]  Howarth, L. (1938), On the solution of the laminar boundary layer equations, Proc. R. Soc. Lond., 64, 547-579.
  7. [7]  Chamkha, A.J. (1997), Solar radiation assisted natural convection in uniform porous medium supported by a vertical flat plate, ASME Journal of Heat Transfer, 119(1), 89-96.
  8. [8]  Chamkha, A.J. (1997), MHD-free convection from a vertical plate embedded in a thermally stratified porous medium with Hall effects, Applied Mathematical Modelling, 21(10), 603-609.
  9. [9]  Chamkha, A.J. and Khaled, A.A. (2000), Similarity solutions for hydromagnetic mixed convection heat and mass transfer for Hiemenz flow through porous media, International Journal of Numerical Methods for Heat $\&$ Fluid Flow, 10(1), 94-115.
  10. [10]  Modather, M., Rashad, M., and Chamkha, A.J. (2009), An analytical study of MHD heat and mass transfer oscillatory flow of a micropolar fluid over a vertical permeable plate in a porous medium, Turkish Journal of Engineering and Environmental Sciences, 33, 245-257.
  11. [11]  Gorla, R.S.R. and Chamkha, R.S.R. (2011), Natural convective boundary layer flow over a non-isothermal vertical plate embedded in a porous medium saturated with a nanofluid, Nanoscale and Microscale Thermophysical Engineering, 15(2), 81-94.
  12. [12]  Chamkha, A.J., Mohamed, R.A., and Ahmed, S.E. (2011), Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects, Meccanica, 46(2), 399-411.
  13. [13]  Krishna, M.V. and Chamkha, A.J. (2019), Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid past an infinite vertical plate embedded in a porous medium, Result in Physics, 15, 102652
  14. [14]  Casson, N. (1959), A flow equation for the pigment oil suspensions of the printing ink type Ed., Rheology of Disperse Systems, Pergamon, NewYork.
  15. [15]  Mukhopadhyay, S. (2013), Casson fluid flow and heat transfer over a nonlinearly stretching surface, Chinese Physics B, 22(7), 074701-5.
  16. [16]  Pramanik, S. (2014), Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation, Ain Shams Engineering Journal, 5, 205-212.
  17. [17]  Shaw, S., Mahanta, G., and Sibanda, P. (2016), Non-linear thermal convection in a Casson fluid flow over a horizontal plate with convective boundary condition, Alexandria Engineering Journal, 55, 1295-130.
  18. [18]  Kataria, H.R. and Patel, H.R. (2018), Heat and mass transfer in magnetohydrodynamic (MHD) Casson fluid flow past over an oscillating vertical plate embedded in porous medium with ramped wall temperature, Propuls. Power Res., 7(3), 257-267.
  19. [19]  Kataria, H.R. and Patel, H.R. (2016), Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium, Alexandria Engineering Journal, 55, 583-595, (2016).
  20. [20]  Maboob, F. and Das, K. (2019), Outlining the impact of melting on MHD Casson fluid flow past a stretching sheet in a porous medium with radiation, Heliyon, 5, e01216.
  21. [21]  Takhar, H.S., Chamkha, A.J., and Nath, G. (2001), Unsteady three-dimensional MHD-boundary-layer flow due to the impulsive motion of a stretching surface, Acta Mechanica, 146, 59-71.
  22. [22]  Rashidi, M.M., Chamkha, A.J., and Keimanesh, M. (2011), Application of multi-step differential transform method on flow of a second-grade fluid over a stretching or shrinking sheet, American Journal of Computational Mathematics, 1(2), 119-128.
  23. [23]  Minkowycz, W.J. and Sparrow, E.M. (1974), Local non-similar solution for natural convection on a vertical cylinder, Journal of Heat Transfer, 96, 178-183.
  24. [24]  Patel, H.R. (2019), Effect of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation, Heliyon, 5, e01555, (2019).
  25. [25]  Qawasmeh, B.R., Mohammad, A., and Al-Dahidi, S. (2019), Forced convection heat transfer of Casson fluid in non-Darcy porous media, Advances in Mechanical Engineering, 11(1), 1-10.
  26. [26]  Partha, M.K. (2010), Nonlinear convection in a Non-Darcy porous medium, Applied Mathematics and Mechanics, 31, 565-574.
  27. [27]  Mandal, I.C. and Mukhopadhyay, S. (2019), Nonlinear convection in micropolar fluid flow past an exponentially stretching sheet in an exponentially moving stream with thermal radiation, Mechanics of Advanced Materials and Structures. DOI:10.1080/15376494.2018.1472325.
  28. [28]  Mehmood, K., Hussain, S., and Sagheer, M. (2016), Mixed convection flow with non-uniform heat source/sink in a doubly stratified magnetonanofluid, AIP Advances, 6, 065126.
  29. [29]  Khedr, M.E.M., Chamkha, A.J., and Bayomi, M. (2009), MHD flow of a micropolar fluid past a stretched permeable surface with heat generation or absorption, Nonlinear Analysis- Modelling and Control, 14(1), 27-40.
  30. [30]  Damseh, R.A., Al-Odat, M.Q., Chamkha, A.J., and Shannak, B.A. (2009), Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface, 48(8), 1658-1663.
  31. [31]  Chamkha, A.J. and Aly, A.M. (2010), MHD free convection flow of a nanofluid past a vertical plate in thepresence of heat generation or absorption effect, Chemical Engineering Communications, 198(3), 425-441.
  32. [32]  Chamkha, A.J., Aly, A.M., and Mansour, M.A. (2010), Similarity solution for unsteady heat and mass transfer from a stretching surface embedded in a porous medium with suction/injection and chemical reaction effects, Chemical Engineering Communications, 197(6), 846-858.
  33. [33]  Patel, H.R. (2019), Effect of cross diffusion and heat generation on mixed convective MHD flow of Casson fluid through porous medium with non-linear thermal radiation, Heliyon, 5, e01555 (2019).
  34. [34]  Srinivasacharya, D., Ramreddy, Ch., and Naveen, P. (2019), Effect of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition, Heat Transfer Asian Research, 48, 414-434.
  35. [35]  Ramreddy, Ch., Naveen, P., and Srinivasacharya, D. (2019), Influence of nonlinear Boussinesq approximation on natural convective flow of a power-law fluid along an inclined plate under convective thermal boundary condition, Nonlinear Engineering, 8, 94-106.
  36. [36]  Sparrow, E.M. and Yu, H.S. (1971), Local non‐similarity thermal boundary‐layer solutions, Journal of Heat Transfer, 93, 328‐334 (1971).
  37. [37]  Minkowycz, W.J. and Sparrow, E.M. (1974), Local non-similar solution for natural convection on a vertical cylinder, Journal of Heat Transfer, 96, 178-183.