Finite element solutions of non-Newtonian dissipative Casson fluid flow past a vertically inclined surface surrounded by porous medium including constant heat flux, thermal diffusion, and diffusion thermo

References

• K. B. Pavlov, “Magnetohydrodynamic flow of an incompressible viscous fluid caused by deformation of a plane surface,” Magnitnaya Gidrodinamika, vol. 4, pp. 146–147, 1974.
   Google Scholar
• A. Ishak, R. Nazar, and I. Pop, “Magnetohydrodynamic (MHD) flow and heat transfer due to a stretching cylinder,” Energy Convers. Manage., vol. 49, no. 11, pp. 3265–3269, 2008. DOI: https://doi.org/10.1016/j.enconman.2007.11.013.
   Web of Science ®Google Scholar
• S. Mukhopadhyay, M. G. Arif, M. Wazed, and P. K. Ali, “MHD boundary layer flow along a stretching cylinder,” Acta Tech., vol. 58, pp. 239–251, 2013.
   Google Scholar
• K. U. Rehman, M. Y. Malik, T. Salahuddin, and M. Naseer, “Dual stratified mixed convection flow of Eyring-Powell fluid over an inclined stretching cylinder with heat generation/absorption effect,” AIP Adv., vol. 6, no. 7, pp. 075112, 2016. DOI: https://doi.org/10.1063/1.4959587.
   Web of Science ®Google Scholar
• A. Shahzad and R. Ali, “MHD flow of a non-Newtonian power law fluid over a vertical stretching sheet with the convective boundary condition,” Walailak J. Sci. Technol., vol. 10, no. 1, pp. 43–56, 2013.
   Google Scholar
• M. Khan, R. Ali, and A. Shahzad, “MHD Falkner-Skan flow with mixed convection and convective boundary conditions,” Walailak J. Sci. Technol., vol. 10, no. 5, pp. 517–529, 2013.
   Google Scholar
• R. Ali, A. Shahzad, M. Khan, and M. Ayub, “Analytic and numerical solutions for axisymmetric flow with partial slip,” Eng. Comput., vol. 32, no. 1, pp. 149–154, 2016. DOI: https://doi.org/10.1007/s00366-015-0405-2.
   Web of Science ®Google Scholar
• M. Y. Malik and K. U. Rehman, “Effects of second order chemical reaction on MHD free convection dissipative fluid flow past an inclined porous surface by way of heat generation: A Lie group analysis,” Inf. Sci. Lett., vol. 5, no. 2, pp. 35–45, 2016. DOI: https://doi.org/10.18576/isl/050201.
   Google Scholar
• P. S. Rao, B. Kumbhakar, and B. V. R. Kumar, “Effect of thermal radiation on MHD flow with variable viscosity and thermal conductivity over a stretching sheet in porous media,” J. Adv. Math. Appl., vol. 5, no. 1, pp. 44–52, 2016. DOI: https://doi.org/10.1166/jama.2016.1090
   Google Scholar
• Y. H. Gangadharaiah, “Penetrative Marangoni convection in fluid layer with Soret effect,” J. Adv. Math. Appl., vol. 4, no. 1, pp. 11–16, 2015. DOI: https://doi.org/10.1166/jama.2015.1068
   Google Scholar
• Y. H. Gangadharaiah, “Effects of internal heat generation and variable viscosity on Marangoni convection in superposed fluid and porous layers,” J. Adv. Math. Appl., vol. 3, no. 2, pp. 158–164, 2014. DOI: https://doi.org/10.1166/jama.2014.1062
   Google Scholar
• R. M. Darji and M. G. Timol, “Similarity analysis for unsteady free convective boundary layer flow of power law fluids via group theory,” J. Adv. Math. Appl., vol. 3, no. 1, pp. 9–19, 2014. DOI: https://doi.org/10.1166/jama.2014.1046
   Google Scholar
• V. S. Patil and M. G. Timol, “On the class of three dimensional unsteady incompressible magneto-hydrodynamic boundary layer equations of non-Newtonian power law fluids,” J. Adv. Math. Appl., vol. 1, no. 2, pp. 264–268, 2012. DOI: https://doi.org/10.1166/jama.2012.1020
   Google Scholar
• N. Casson, “A flow equation for pigment oil suspensions of the printing ink type,” in Rheology of Disperse Systems, C. C. Mill, Ed. Oxford: Pergamon Press, 1959, pp. 84–102.
   Google Scholar
• R. Srinivasa Raju, B. Mahesh Reddy, and G. Jithender Reddy, “Finite element solutions of free convective Casson fluid flow past a vertically inclined plate submitted in magnetic field in presence of heat and mass transfer,” Int. J. Comput. Methods Eng. Sci. Mech., vol. 18, no. 4–5, pp. 250–265, 2017. DOI: https://doi.org/10.1080/15502287.2017.1339139.
   Web of Science ®Google Scholar
• R. Srinivasa Raju, B. Mahesh Reddy, and G. Jithender Reddy, “Influence of angle of inclination on unsteady MHD Casson fluid flow past a vertical surface filled by porous medium in presence of constant heat flux, chemical reaction and viscous dissipation,” J Nanofluids, vol. 6, no. 4, pp. 668–679, 2017. DOI: https://doi.org/10.1166/jon.2017.1368
   Web of Science ®Google Scholar
• R. Srinivasa Raju, G. Jithender Reddy, and G. Anitha, “MHD Casson viscous dissipative fluid flow past a vertically inclined plate in presence of heat and mass transfer: A finite element technique,” Front. Heat Mass Transf., vol. 8, pp. 27, 2017.
   Web of Science ®Google Scholar
• S. V. Sailaja, B. Shanker, and R. Srinivasa Raju, “Double diffusive effects on MHD mixed convection Casson fluid flow towards a vertically inclined plate filled in porous medium in presence of Biot number: A finite element technique,” J. Nanofluids, vol. 6, no. 3, pp. 420–435, 2017. DOI: https://doi.org/10.1166/jon.2017.1337
   Web of Science ®Google Scholar
• S. V. Sailaja, B. Shanker, and R. Srinivasa Raju, “Behaviour of non-Newtonian Casson fluid on MHD free convective flow past a vertically inclined surface surrounded by porous medium including thermal diffusion: A finite element technique,” J. Nanofluids, vol. 6, no. 5, pp. 946–955, 2017. DOI: https://doi.org/10.1166/jon.2017.1389
   Web of Science ®Google Scholar
• R. Srinivasa Raju, “Numerical treatment of Casson fluid free convection flow past an infinite vertical plate filled in magnetic field in presence of angle of inclination and thermal radiation: A finite element technique,” Int. J. Eng. Appl. Sci., vol. 8, no. 4, pp. 119, 2016.
   Google Scholar
• C. S. K. Raju, N. Sandeep, and S. Saleem, “Effects of induced magnetic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid,” Eng. Sci. Technol. Int. J., vol. 19, no. 2, pp. 875–887, 2016. DOI: https://doi.org/10.1016/j.jestch.2015.12.004. [Database]
   Google Scholar
• G. Makanda, S. Shaw, and P. 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,” Bound. Value Prob., vol. 1, pp. 1–14, 2015.
   Google Scholar
• R. Dash, K. Mehta, and G. Jayaraman, “Casson fluid flow in a pipe filled with a homogeneous porous medium,” Int. J. Eng. Sci., vol. 34, no. 10, pp. 1145–1156, 1996. DOI: https://doi.org/10.1016/0020-7225(96)00012-2.
   Web of Science ®Google Scholar
• C. Y. Cheng, “Soret and Dufour effects on free convection heat and mass transfer from an arbitrarily inclined plate in a porous medium with constant wall temperature and concentration,” Int. Commun. Heat Mass Transf., vol. 39, no. 1, pp. 72–77, 2012. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2011.09.003.
   Web of Science ®Google Scholar
• M. Turkyilmazoglu and I. Pop, “Soret and heat source effects on the unsteady radiative MHD free convection flow from an impulsively started infinite vertical plate,” Int. J. Heat Mass Transf., vol. 55, no. 25–26, pp. 7635–7644, 2012. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2012.07.079.
   Web of Science ®Google Scholar
• F. M. Abbasi, T. Hayat, A. Alsaedi, and B. Ahmed, “Soret and Dufour effects on peristaltic transport of MHD fluid with variable viscosity,” Appl. Math. Inf. Sci., vol. 8, no. 1, pp. 211–219, 2014. DOI: https://doi.org/10.12785/amis/080126
   Google Scholar
• M. Ramzan, M. Farooq, T. Hayat, A. Alsaedi, and J. Cao, “MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects,” J. Cent. South Univ., vol. 22, no. 2, pp. 707–716, 2015. DOI: https://doi.org/10.1007/s11771-015-2574-y.
   Web of Science ®Google Scholar
• T. Hayat, S. A. Shehzad, and A. Alsaedi, “Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid,” Appl. Math. Mech.-Engl. Ed., vol. 33, no. 10, pp. 1301–1312, 2012. DOI: https://doi.org/10.1007/s10483-012-1623-6.
   Google Scholar
• J. A. Rao and R. Srinivasa Raju, “The effects of Hall currents, Soret and Dufour on MHD flow and heat transfer along a porous flat plate with mass transfer,” J. Ener. Heat Mass Transf., vol. 33, pp. 351–372, 2011.
   Google Scholar
• S. R. Sheri and R. Srinivasa Raju, “Soret effect on unsteady MHD free convective flow past a semi–infinite vertical plate in the presence of viscous dissipation,” Int. J. Comput. Methods Eng. Sci. Mech., vol. 16, no. 2, pp. 132–141, 2015. DOI: https://doi.org/10.1080/15502287.2015.1009583
   Google Scholar
• R. S. Raju, K. Sudhakar, and M. Rangamma, “The effects of thermal radiation and heat source on an unsteady MHD free convection flow past an infinite vertical plate with thermal diffusion and diffusion thermo,” J. Inst. Eng. India Ser. C, vol. 94, no. 2, pp. 175–186, 2013. DOI: https://doi.org/10.1007/s40032-013-0063-3
   Google Scholar
• R. Srinivasa Raju, “Combined influence of thermal diffusion and diffusion thermo on unsteady MHD free convective fluid flow past an infinite vertical porous plate in presence of chemical reaction,” J. Inst. Eng. India Ser. C, vol. 97, no. 4, pp. 505–515, 2016. DOI: https://doi.org/10.1007/s40032-016-0258-5
   Google Scholar
• R. Srinivasa Raju, G. Jithender Reddy, J. Anand Rao, M. M. Rashidi, and R. Subba Reddy Gorla, “RETRACTED: Analytical and numerical study of unsteady MHD free convection flow over an exponentially moving vertical plate with Heat Absorption,” Int. J. Therm. Sci., vol. 107, pp. 303–315, 2016. DOI: https://doi.org/10.1016/j.ijthermalsci.2016.04.005.
   Web of Science ®Google Scholar
• P. K. Sahu and U. S. Rajput, “Thermal diffusion and chemical reaction effects on free convection MHD flow through a porous medium bounded by a vertical surface with constant heat flux,” Int. J. Math. Sci. Comput., vol. 3, pp. 44, 2013.
   Google Scholar
• R. Srinivasa Raju, B. M. Reddy, M. M. Rashidi, and R. S. R. Gorla, “Application of finite element method to unsteady magnetohydrodynamic free-convection flow past a vertically inclined porous plate including thermal diffusion and diffusion thermo effects,” J. Por. Media, vol. 19, no. 8, pp. 701–722, 2016. DOI: https://doi.org/10.1615/JPorMedia.v19.i8.40
   Web of Science ®Google Scholar
• K. Bhattacharyya, T. Hayat, and A. Alsaedi, “Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet,” Z. Angew. Math. Mech., vol. 94, no. 6, pp. 522–528, 2014. DOI: https://doi.org/10.1002/zamm.201200031
   Web of Science ®Google Scholar
• I. Ullah, K. Bhattacharyya, S. Shafie, and I. Khan, “Unsteady MHD mixed convection slip flow of Casson fluid over nonlinearly stretching sheet embedded in a porous medium with chemical reaction, thermal radiation, heat generation/absorption and convective boundary conditions,” PLoS One, vol. 11, no. 10, pp. e0165348, 2016. [PMC][ [27776174]
   PubMed Web of Science ®Google Scholar
• K. Bhattacharyya, “Boundary layer stagnation-point flow of Casson fluid and heat transfer towards a shrinking/stretching sheet,” Front. Heat Mass Transf., vol. 4, pp. 023003, 2013.
   Google Scholar
• S. Mukhopadhyay, K. Bhattacharyya, and T. Hayat, “Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects,” Chin. Phys. B, vol. 22, no. 11, pp. 114701, 2013. DOI: https://doi.org/10.1088/1674-1056/22/11/114701
   Web of Science ®Google Scholar
• K. Bhattacharyya, M. S. Uddin, and G. C. Layek, “Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation,” Alex. Eng. J., vol. 55, no. 2, pp. 1703–1712, 2016. DOI: https://doi.org/10.1016/j.aej.2016.03.010
   Web of Science ®Google Scholar
• A. Zaib, K. Bhattacharyya, M. Sharif Uddin, and S. Shafie, “Dual solutions of non-Newtonian Casson fluid flow and heat transfer over an exponentially permeable shrinking sheet with viscous dissipation,” Model. Simul. Eng., vol. 2016, Article ID, pp. 6968371, 2016.
   Web of Science ®Google Scholar
• A. Zaib, M. M. Rashidi, A. J. Chamkha, and K. Bhattacharyya, “Numerical solution of second law analysis for MHD Casson nanofluid past a wedge with activation energy and binary chemical reaction,” Int. J. Numer. Methods Heat Fluid Flow, vol. 27, no. 12, pp. 2816–2834, 2017.
   Web of Science ®Google Scholar
• K. R. Cramer and and S. I. Pai, Magnetofluid Dynamics for Engineers and Applied Physicists. New York, NY: McGraw Hill Book Company, 1973.
   Google Scholar
• M. Q. Brewster, Thermal Radiative Transfer and Properties. New York, NY: Wiley, 1992.
   Google Scholar
• K. J. Bathe, Finite Element Procedures. New Jersey, NJ: Prentice – Hall, 1996.
   Google Scholar