In the present work, mixed convection boundary layer flow of MHD Casson fluid flow over an upward stretching sheet encapsulated in a porous media with slip conditions is considered. The guiding nonlinear partial differential equations are converted into a set of nonlinear ordinary differential equations by utilizing some suitable similarity transformations. The resulting nonlinear ordinary differential equations are solved using an implicit finite difference method named Keller-Box method. The effects of Casson parameter, magnetic parameter, mixed convection parameter, slip parameter, suction parameter, and Prandtl number are investigated by plotting the corresponding velocity and temperature profiles using MATLAB software. To validate the numerical method, skin friction values are calculated for greater values of Casson parameter. It is found that the results are in good agreement with the existing literature.

MHD, Casson fluid, porous medium, mixed convection, slip effects, skin friction.

Received: September 10, 2020; Revised: October 12, 2020; Accepted: November 28, 2020; Published: April 12, 2021

How to cite this article: W. Sridhar, G. R. Ganesh, B. V. Appa Rao and E. Haile Gorfie, Mixed convection boundary layer flow of MHD Casson fluid on an upward stretching sheet encapsulated in a porous medium with slip effects, JP Journal of Heat and Mass Transfer 22(2) (2021), 133-149. DOI: 10.17654/HM022020133

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

[1] H. Alfven, Existence of electromagnetic-hydrodynamic waves, Nature 150 (1942), 405-406. https://doi.org/10.1038/150405d0.
[2] J. M. Burgers, The transportation of magnetic lines of force by a highly conducting fluid, Journal of the Society for Industrial and Applied Mathematics 13(1) (1965), 184-205. https://doi.org/10.1137/0113012.
[3] J. H. Merkin, Mixed convection boundary layer flow on a vertical surface in a saturated porous medium, J. Engrg. Math. 14 (1980), 301-313. https://doi.org/10.1007/bf00052913.
[4] J. D. Jackson, M. A. Cotton and B. P. Axcell, Studies of mixed convection in vertical tubes, International Journal of Heat and Fluid Flow 10(1) (1989), 2-15. https://doi.org/10.1016/0142-727x(89)90049-0.
[5] M. Ali and F. Al. Yousef, Laminar mixed convection from a continuously moving vertical surface with suction/injection, Heat and Mass Transfer 33(4) (1998), 301-306. https://doi.org/10.1007/s00231005019.
[6] H. I. Anderson, Slip flow past a stretching surface, Acta Mechanica 158 (2002), 121-125. https://doi.org/10.1007/bf01463174.
[7] Y. Y. Lok, N. Amin, D. Campean and I. Pop, Steady mixed convection flow of a micro polar fluid near the stagnation point on a vertical surface, International Journal of Numerical Methods for Heat and Fluid Flow 15(7) (2005), 654-670. https://doi.org/10.1108/09615530510613861.
[8] R. Damseh, Magnetohydrodynamics-mixed convection from radiate vertical isothermal surface embedded in a saturated porous media, Journal of Applied Mechanics 73(1) (2006), 54-59. https://doi.org/10.1115/1.1991863.
[9] Syakila Ahmad and Ioan Pop, Mixed convection boundary layer flow from a vertical flat plate embedded in a porous medium filled with nanofluids, International Communications in Heat and Mass Transfer 27(8) (2010), 987-991. https://doi.org/10.1016/j.icheatmasstransfer.2010.06.004.
[10] F. M. Ali, R. Nazar, N. M. Arifin and I. Pop, MHD mixed convection boundary layer flow toward a stagnation point on a vertical surface with induced magnetic field, Journal of Heat Transfer 133(2) (2011), 022502, 6 pp.
https://doi.org/10.1115/1.4002602.
[11] Krishnendu Bhattacharyya, Md. Sharif Uddin and G. C. Layek, Effect of partial slip on boundary layer mixed convective flow adjacent to a vertical permeable stretching sheet in porous medium, Acta Technica 58 (2013), 27-39. https://doi.org/10.1016/j.asej.2012.09.003.
[12] Krishnendu Bhattacharyya, Kuppanapalle Vajravelu and Tasawar Hayat, Slip effects on the parametric space and the solution for boundary layer flow of Casson fluid over a porous stretching/shrinking sheet, International Journal of Fluid Mechanics Research 40(6) (2013), 482-493.
https://doi.org/10.1615/interjfluidmechres.v40.i6.20
[13] Gilbert Makanda, Sachin Shaw and Precious Sibanda, Effects of radiation on MHD free convection of a Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation, Boundary Value Problems 2015, Article number 75.
https://doi.org/10.1186/s13661-015-0333-5.
[14] F. Mabood, W. A. Khan and A. I. M. Ismail, Multiple slips effects on MHD Casson fluid flow in porous media with radiation and chemical reaction, Canadian Journal of Physics 94(1) (2016), 26-34. https://doi.org/10.1139/cjp-2014-0667.
[15] S. M. Ibrahim, F. Mabood, K. Suneetha and G. Lorenzini, Effects of chemical reaction on combined heat and mass transfer by laminar mixed convection flow from vertical surface with induced magnetic field and radiation, Journal of Engineering Thermophysics 26(2) (2017), 234-255.
https://doi.org/10.1134/s1810232817020084.
[16] M. Dhanalakshmi, K. J. Reddy and K. Ramakrishna, Chemical reaction and Soret effects on radiating MHD boundary layer flow over a moving vertical porous plate with heat source, Journal of Advanced Research in Dynamical and Control Systems 9 (2017), 2155-2166.
[17] T. Hymavathi and W. Sridhar, Numerical study of flow and heat transfer of Casson fluid over an exponentially porous stretching surface in presence of thermal radiation, International Journal of Mechanical and Production Engineering Research and Development 8(4) (2018), 1145-1154.
https://doi.org/10.24247/ijmperdaug2018118.
[18] V. Manjula and K. V. Chandra Sekhar, Unsteady MHD Casson fluid flow past an oscillating permeable vertical surface with Newtonian heating and thermal radiation, International Journal of Mechanical Engineering and Technology 9(7) (2018), 1068-1079. https://doi.org/10.1016/j.ijthermalsci.2014.08.009.
[19] P. R. Kumari and D. Sree Devi, Effect of radiation and radiation absorption on convective heat and mass transfer flow of a viscous electrically conducting fluid in a non-uniformly heated vertical channel, Int. J. Mech. and Prod. Engg. Res. and Dev. (IJMPERD) 8(7S) (2018), 1382-1390.
[20] K. Vijaya and G. V. R. Reddy, Magnetohydrodynamic Casson fluid flow over a vertical porous plate in the presence of radiation, Soret and chemical reaction effects, Journal of Nanofluids 8(6) (2019), 1240-1248.
https://doi.org/10.1166/jon.2019.1684.
[21] J. R. Konda, N. P. Madhusudhana and R. Konijeti, MHD mixed convection flow of radiating and chemically reactive Casson nanofluid over a nonlinear permeable stretching sheet with viscous dissipation and heat source, Multidiscipline Modeling in Materials and Structures 14(3) (2018), 609-630.
https://doi.org/10.1108/mmms-10-2017-0127.
[22] M. Dhanalakshmi, V. Jyothi and K. Jayarami Reddy, Soret and Dufour effects on MHD convective flow past a vertical plate through porous medium, Journal of Physics: Conference Series 1344(1) (2019), 012008.
https://doi.org/10.1088/1742-6596/1344/1/012008.
[23] G. Dharmaiah, N. Vedavathi, C. B. Rani and K. S. Balamurugan, MHD boundary layer flow and heat transfer of a nanofluid past a radiative and impulsive vertical plate, Frontiers in Heat and Mass Transfer 11 (2018).
https://doi.org/10.5098/hmt.11.14.
[24] K. V. C. Sekhar and V. Manjula, MHD slip flow of Casson fluid over an exponentially stretching inclined permeable sheet with Soret-Dufour effects, International Journal of Civil Engineering and Technology 9(3) (2018), 400-417.
[25] Y. H. Krishna, G. V. R. Reddy and O. D. Makinde, Chemical reaction effect on MHD flow of Casson fluid with porous stretching sheet, Defect and Diffusion Forum 389 (2018), 100-109.
https://doi.org/10.4028/www.scientific.net/ddf.389.100.
[26] A. K. Jhankal, R. N. Jat and D. Kumar, MHD mixed convection boundary layer flow on a vertical permeable stretching sheet embedded in a porous medium with slip effects, Indian Journal of Pure and Applied Physics 57 (2019), 400-405.
[27] G. R. Ganesh, W. Sridhar, T. Hymavathi and D. S. Kumar, Forced convection heat transfer of MHD Casson fluid in non-Darcy porous media, International Journal of Advanced Science and Technology 29(6) (2020), 1313-1326.
[28] Kuppalapalle Vajravelu and Swathi Mukhopadhay, Fluid flow, Heat and Mass Transfer at Bodies of Different Shapes, Academic Press, 2015.
[29] T. Cebeci and P. Bradshaw, Physical and Computational Aspects of Convective Heat Transfer, Springer-Verlag, New York, 1988.
[30] Kuppalapalle Vajravelu and Kerehalli V. Prasad, Keller-Box Method and its Application, De Gruyter, 2014.