Abstract
In this paper, we have considered the classical problem effects of radiation, temperature dependent plastic dynamic viscosity and thermal conductivity with steady incompressible laminar free convective MHD Falkner–Skan flow of Casson fluid past a moving permeable wedge. By using suitable transformation, the governing PDEs corresponding to the momentum and energy equations are converted into non-linear coupled ODEs and solved by bvp4c method. The influence of various physical parameters like Casson fluid parameters radiation parameter, variable plastic dynamic viscosity parameter, variable thermal conductivity parameter, magnetic field parameter, local porosity parameter, thermal buoyancy parameter, Prandtl number, local Eckert number, moving wedge parameter on velocity and temperature profiles are discussed and display graphically. Local Nusselt number and skin friction coefficient are tabulated.
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Ullah, I., Khan, I., Shafie, S.: Hydromagnetic Falkner–Skan flow of Casson fluid past a moving wedge with heat transfer. Alex. Eng. J. 55, 2139–2148 (2016)
Yih, K.A.: MHD forced convection flow adjacent to a non-isothermal wedge. Int. Commun. Heat Mass Transf. 26(6), 819–827 (1999)
Kandasamy, R., Muhaimin, I., Khamis, A.B.: Thermophoresis and variable viscosity effects on MHD mixed convective heat and mass transfer past a porous wedge in the presence of chemical reaction. Heat Mass Transf. 45, 703–712 (2009)
Pal, D., Mondal, H.: Influence of temperature-dependent viscosity and thermal radiation on MHD forced convection over a non-isothermal wedge. Appl. Math. Comput. 212(1), 194–208 (2009)
Roy, N.C., Akther, P., Halder, A.K.: MHD mixed convection flow of a micropolar fluid past a wedge fixed in a fluctuating free stream and surface temperature. Dhaka Univ. J. Sci. 64(1), 65–70 (2016)
Ishak, A., Nazar, R., Pop, I.: Falkner–Skan equation for flow past a moving wedge with suction or injection. J. Appl. Math. Comput. 25(1), 67–83 (2007)
Ishak, A., Nazar, R., Pop, I.: Moving wedge and flat plate in a micropolar fluid. Int. J. Eng. Sci. 44(18–19), 1225–1236 (2006)
Hsiao, K.L.: MHD mixed convection for viscoelastic fluid past a porous wedge. Int. J. Non-Linear Mech. 46(1), 1–8 (2011)
Mukhopadhyay, S., Mondal, I.C., Chamkha, A.J.: Casson fluid flow and heat transfer past a symmetric wedge. Heat Transf. Asian Res. 42, 665–675 (2013). doi:10.1002/htj.21065
Animasaun, I.L., Adebile, E.A., Fagbade, A.I.: Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. J. Niger. Math. Soc. 35, 1–17 (2016)
Shaw, S., Mahanta, G., Sibanda, P.: Non-linear thermal convection in a Casson fluid flow over a horizontal plate with convective boundary condition. Alex. Eng. J. 55, 1295–1304 (2016)
Animasaun, I.L.: Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction. J. Niger. Math. Soc. 34, 11–31 (2015)
Sulochana, C., Ashwinkumar, G.P., Sandeep, N.: Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions”. J. Niger. Math. Soc. 35, 128–141 (2016)
Megaheda, A.M.: MHD viscous Casson fluid flow and heat transfer with second-order slip velocity and thermal slip over a permeable stretching sheet in the presence of internal heat generation/absorption and thermal radiation. Eur. Phys. J. Plus 130, 81 (2015)
Malik, M.Y., Khan, M., Salahuddin, T., Khan, I.: Variable viscosity and MHD flow in Casson fluid with Cattaneo–Christov heat flux model: using Keller box method. Eng. Sci. Technol. Int. J. 19, 1985–1992 (2016)
Bhattacharyya, K., Uddin, M.S., Layek, G.C.: Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation. Alex. Eng. J. 55, 1703–1712 (2016)
Raju, C.S.K., Sandeepa, N., Saleem, S.: Effects of induced magnetic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid. Eng. Sci. Technol. Int. J. 19, 875–887 (2016)
Bala, P., Reddy, A.: Magnetohydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction. Ain Shams Eng. J. 7, 593–602 (2016)
Jain, S., Parmar, A., Comparative study of flow and heat transfer behavior of Newtonian and non-Newtonian fluids over a permeable stretching surface. Glob stochast Anal. SI, 41–50 (2017)
Bhattacharya, K.: Boundary layer stagnation point flow of Casson fluid and heat transfer towards a shrinking/stretching sheet. Front Heat Mass Transf. 4, 1–9 (2013). doi:10.5098/hmt.v4.2.3003
Hari, R., Kataria, A., Patel, H.R.: Soret and heat generation effects on MHD Casson fluid flow past an oscillating vertical plate embedded through porous medium. Alex. Eng. J. 55, 2125–2137 (2016)
Nadeem, S., Haq, R.U., Lee, C.: MHD flow of a Casson fluid over an exponentially shrinking sheet. Sci. Iran. 19, 1550–1553 (2012)
Nadeem, S., Haq, R.U., Akbar, N.S., Khan, Z.H.: MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. Alex. Eng. J. 52, 577–582 (2013)
Nadeem, S., Raju, C.S.K., Sugunamma, V., Babu, M.J., Reddy, J.V.R.: Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Sci. Technol. Int. J. Eng. (2015). doi:10.1016/j.jestch.2015.05.010
Mukhopadhyay, S., De, P.R., Bhattacharyya, K., Layek, G.C.: Casson fluid flow over an unsteady stretching surface. Ain Shams Eng. J. 4, 933–938 (2013)
Mukhopadhyay, S., Moindala, I.C., Hayat, T.: MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation. Chin. Phys. 23, 104701 (2014)
Mahanta, G., Shaw, S.: 3D Casson fluid flow past a porous linearly stretching sheet with convective boundary condition. Alex. Eng. J. (2015). doi:10.1016/.aej.2015.04.014
Mustafa, M., Khan, J.A.: Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects. AIP Adv. 5, 077148 (2015)
Das, M., Mahato, R., Nandkeolyar, R.: Newtonian heating effect on unsteady hydro-magnetic Casson fluid flow past a flat plate with heat and mass transfer. Alex. Eng. J. (2015). doi:10.1016/j.aej.2015.07.007
Ramesh, K., Devakar, M.: Some analytical solutions for flows of Casson fluid with slip boundary conditions. Ain Shams Eng. J. 6, 967–975 (2015)
Khalid, A., Khan, I., Khan, A., Shafie, S.: Unsteady MHD free convection flow of Casson fluid past over an oscillating vertical plate embedded in a porous medium. Eng. Sci. Technol. Int. J. (2014). doi:10.1016/j.jestch.2014.12.006
Hayat, T., Shehzad, S.A., Alsaedi, A.: Three-dimensional MHD flow of Casson fluid in porous medium with heat generation. J. Appl. Fluid Mech. 9, 215–223 (2016)
Hayat, T., Ashraf, M.B., Shehzad, S.A., Alsaedi, A.: Mixed convection flow of Casson nanofluid over a stretching sheet with convectively heated chemical reaction and heat source/sink. J. Appl. Fluid Mech. 8, 803–813 (2015)
Makinde, O.D.: Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation. Meccanica 47, 1173–84 (2012)
Dasa, K., Sharma, R.P., Sarkar, A.: Heat and mass transfer of a second-grade magneto-hydrodynamic fluid over a convectively heated stretching sheet. J. Comput. Des. Eng. 3, 330–336 (2016)
Chauhan, D.S., Agrawal, R.: MHD flow through a porous medium adjacent to a stretching sheet: numerical and an approximate solution. Eur. Phys. J. Plus 126(47), 1–14 (2011)
Chauhan, D.S., Rastogi, P.: Heat transfer and entropy generation in MHD flow through a porous medium past a stretching sheet. Int. J. Energy Technol. 3(15), 1–13 (2011)
Chauhan, D.S., Agrawal, R.: MHD flow and heat transfer in a channel bounded by a shrinking sheet and a porous medium bed: homotopy analysis method. ISRN Thermodyn. 2013, 1–10 (2013)
Layek, G.C., Mukhopadhyay, S., Samad, S.K.A.: Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. Int. J. Heat Mass Transf. 48, 4460–4466 (2005)
Animasaun, I.L., Aluko, O.B.: Analysis on variable fluid viscosity of non-Darcian flow over a moving vertical plate in a porous medium with suction and viscous Dissipation. Int. Organ. Sci. Res. J. Eng. 04, 18–32 (2014)
Animasaun, I.L., Oyem, A.O.: Effect of variable viscosity, Dufour, Soret and thermal conductivity on free convective heat and mass transfer of non-Darcian flow past porous flat surface. Am. J. Comput. Math. 4, 357–365 (2014)
Animasaun, I.L., Aluko, O.B.: Semi-analytic solution of non-linear coupled differential equation using Adomian decomposition. World J. Young Res. 3, 23–30 (2013)
Mukhopadhyay, S.: Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chin. Phys. 2013, 22–27 (2013)
Shahzad, A., Ali, R., Khan, M.: On the exact solution for axisymmetric flow and heat transfer over a nonlinear radially stretching sheet. Chin. Phys. Lett. 29(8), 084705 (2012)
Shahzad, A., Ali, R., Khan, M., Ayub, M.: Analytic and numerical solutions for axisymmetric flow with partial slip. Eng. Comput. 32(1), 149–154 (2016)
Shahzad, A., Ali, R.: Approximate analytic solution for magneto-hydrodynamic flow of a non-Newtonian fluid over a vertical stretching sheet. Can. J. Appl. Sci. 2, 202–215 (2012)
Masood, K., Ramzan, A., Shahzad, A.: MHD Falkner–Skan flow with mixed convection and convective boundary conditions. Walailak J. Sci. Technol. 10(5), 517–529 (2013)
Shahzad, A., Ramzan, A.: MHD flow of a non-Newtonian Power law fluid over a vertical stretching sheet with the convective boundary condition. Walailak J. Sci. Technol. 10(1), 43–56 (2012)
Ahmed, J., Shahzad, A., Khan, M., Ali, R.: A note on convective heat transfer of an MHD Jeffrey fluid over a stretching sheet. AIP Adv. 5(11), 117117 (2015)
Aziz, T., Mahomed, F.M., Shahzad, A.: Travelling wave solutions for the unsteady flow of a third-grade fluid induced due to impulsive motion of flat porous plate embedded in a porous medium. J. Mech. 30(05), 527–535 (2014)
Shampine, L.F., Thompson, S.: Solving Delay Differential Equations with dde23. Appl Numer Math. 37, 441–458 (2001)
Kumari, M., Takhar, H.S., Nath, G.: Mixed convection flow over a vertical wedge embedded in a highly porous medium. Heat Mass Transf. 37, 139–146 (2001)
Ganapathirao, M., Ravindran, R., Momoniat, E.: Effects of chemical reaction, heat and mass transfer on an unsteady mixed convection boundary layer flow over a wedge with heat generation/absorption in the presence of suction or injection. Int. J. Heat Mass Transf. 51, 289–300 (2015)
Watanabe, T.: Thermal boundary layer over wedge with uniform suction or injection in force flow. Acta Mech. 83, 119–126 (1990)
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Parmar, A. MHD Falkner–Skan Flow of Casson Fluid Flow and Heat Transfer with Variable Property Past a Moving Wedge. Int. J. Appl. Comput. Math 3 (Suppl 1), 611–629 (2017). https://doi.org/10.1007/s40819-017-0373-x
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DOI: https://doi.org/10.1007/s40819-017-0373-x