Hydromagnetic Blasius-Sakiadis flows with variable features and nonlinear chemical reaction

Document Type : Research Note


1 Department of Mathematics, Sri Venkateswara University, Tirupati-517502, India

2 Department of Mathematics, Abu Dhabi Polytechnic, Abu Dhabi, United Arab Emirates

3 Department of Mathematics, GITAM School of Science, Bangalore-561203, Karnataka, India

4 Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan

5 Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan


Time-dependent, two-dimensional Sakiadis flow of quiescent fluid is considered. The flow is induced by stationary flat plate via uniform free-stream (Blasius flow). The variable conductivity and viscosity ratio parameters and non-linear chemical reaction are employed in the mathematical equations. Similarity variables are employed in the governing transport expressions to convert into the ordinary differential system. The transformed system is computed numerically by employing Runge-Kutta scheme via shooting criteria. Results of concentration, velocity and temperature distributions are studied through plots. Moreover, mass and heat transfer rates and friction factor have been discussed in detail. The constraint of chemical reaction slow down the friction-factors and heat transportation rates for the Sakiadis-Blasius flow situations and enhances the mass transportation rate in both cases. Rate of mass transportation is smaller in Sakiadis flow as comparative to Blasius flow. The present results of the heat transfer rate are matched with the literature and excellent agreement is noticed.


1. Blasius, H. "Grenzschichten in ussigkeiten mit kleiner Reibung", Z. Angew. Math. Physik, 56, pp. 1-37 (1908).
2. Sakiadis, B.C. "Boundary layer behavior on continuous solid surfaces: the boundary layer on a continuous  at surface", AIChE J., 7, pp. 221-225 (1961).
3. Pop, H. and Watanabe, W. "The effects of suction or injection in boundary layer  flow and heat transfer on a continuous moving surface", Technis. Mech., 13, pp.49-54 (1992).
4. Ishak, A., Yacob, N.A., and Bachok, N. "Radiation effects on the thermal boundary layer  flow over a moving plate with convective boundary condition", Meccanica, 46, pp. 795-801 (2011).
5. Yao, S., Fang, T., and Zhong, Y. "Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions", Commun. Nonlinear Sci. Numer. Simulat., 16, pp. 752-760 (2011).
6. Cortell, R. "Fluid  flow and radiative nonlinear heat transfer over a stretching sheet", J. King Saud Uni.-Sci., 26, pp. 161-167 (2014).
7. Khan, S.I., Khan, U., Ahmed, N., et al. "Effects of viscous dissipation and convective boundary conditions on Blasius and Sakiadis problems for Casson  fluid", Natl. Acad. Sci. Lett., 38, pp. 247-250 (2015).
8. Olanrewaju, P.O., Gbadeyan, J.A., Agboola, O.O., et al. "Radiation and viscous dissipation effects for the Blasius and Sakiadis  flows with a convective surface boundary condition", Int. J. Adv. Sci. Tech., 2, pp. 102-115 (2011).
9. Sheikholeslami, M. "New computational approach for exergy and entropy analysis of nano fluid under the impact of Lorentz force through a porous media", Comput. Methods Appl. Mech. Eng., 344, pp. 319-333 (2019).
10. Sheikholeslami, M. "Numerical approach for MHD Al2O3-water nano fluid transportation inside a permeable medium using innovative computer method", Comput. Methods Appl. Mech. Eng., 344, pp. 306-318 (2019).
11. Hsiao, K. "Stagnation electrical MHD nano fluid mixed convection with slip boundary on a stretching sheet", Appl. Thermal Eng., 98, pp. 850-861 (2016).
12. Hsiao, K. "Combined electrical MHD heat transfer thermal extrusion system using Maxwell  fluid with radiative and viscous dissipation effects", Appl. Thermal Eng., 112, pp. 1281-1288 (2017).
13. Li, B., Zhang, W., Zhu, L., et al. "On mixed convection of two immiscible layers with a layer of non-Newtonian nano fluid in a vertical channel", Powder Tech., 310, pp. 351-358 (2017).
14. Si, X., Li, H., Zheng, L., et al. "A mixed convection flow and heat transfer of pseudo-plastic power law nano fluids past a stretching vertical plate", Int. J. Heat Mass Transf., 105, pp. 350-358 (2017).
15. Sheikholeslami, M. "Influence of magnetic field on nano fluid free convection in an open porous cavity by means of Lattice Boltzmann method", J. Mol. Liq., 234, pp. 364-374 (2017).
16. Zhu, J., Wang, S., Zheng, L., et al. "Heat transfer of nano fluids considering nanoparticle migration and second-order slip velocity", Appl. Math. Mech., 38, pp. 125-136 (2017).
17. Abbasi, F.M., Hayat, T., Shehzad, S.A., et al. "Impact of Cattaneo-Christov heat  flux on flow of two-types viscoelastic fluid in Darcy-Forchheimer porous medium", Int. J. Numer. Methods Heat Fluid Flow, 27, pp. 1955- 1966 (2017).
18. Kumari, M. and Nath, G. "MHD boundary-layer  flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream", Acta Mech., 146, pp. 139-150 (2001).
19. Akbar, N.S., Nadeem, S., Haq, R.U., et al. "Radiation effects on MHD stagnation point  flow of nano fluid towards a stretching surface with convective boundary condition", Chin. J. Aeronaut., 26, pp. 1389-1397 (2013).
20. Devi, S.P.A. and Suriyakumar, P. "Effect of magnetic field on Blasius and Sakiadis  flow of nano fluids past an inclined plate", J. Taibah Uni. Sci., 11, pp. 1275-1288 (2017).
21. Isa, S.S.P.M., Arifin, N.M., Nazar, R., et al. "The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet", J. Phys.: Conf. Series, 949, pp. 1-14 (2017).
22. Hamad, M.A.A., Uddin, M.J., AND Ismail, A.I.M. "Radiation effects on heat and mass transfer in MHD stagnation-point flow over a permeable at plate with thermal convective surface boundary condition, temperature dependent viscosity and thermal conductivity", Nuclear Eng. Design, 242, pp. 194-200 (2012).
23. Ferdows, M., Uddin, M.J., and Afify, A.A. "Scaling group transformation for MHD boundary layer free convective heat and mass transfer flow past a convectively heated nonlinear radiating stretching sheet", Int. J. Heat Mass Transf., 56, pp. 181-187 (2013).
24. Ullah, H., Islam, S., Khan, I., et al. "MHD boundary layer flow of an incompressible upper convected Maxwell fluid by optimal homotopy asymptotic method", Sci. Iran., 24, pp. 202-210 (2017).
25. Khan, M.I., Waqas, M., Hayat, T., et al. "A comparative study of Casson  fluid with homogeneousheterogeneous reactions", J. Coll. Inter. Sci., 498, pp. 85-90 (2017).
26. Ramli, N., Ahmad, S., and Pop, I. "MHD forced convection flow and heat transfer of ferro fluids over a moving at plate with uniform heat  flux and secondorder slip effects", Sci. Iran., 25, pp. 2186-2197 (2018).
27. Kumar, S.G., Varma, S.V.K., Kumar, R.V.M.S.S.K., et al. "Three-dimensional hydromagnetic convective flow of chemically reactive Williamson  fluid with nonuniform heat absorption and generation", Int. J. Chem. Reac. Eng., 17, Article ID 20180118 (2019).
28. Hussain, S.M., Jain, J., Seth, G.S., et al. "Effect of thermal radiation on magneto-nano fluids free convective flow over an accelerated moving ramped temperature plate", Sci. Iran., 25, pp. 1243-1257 (2018).
29. Abbasi, F.M., Shanakhat, I., and Shehzad, S.A. "Entropy generation analysis in peristalsis of nano fluid with Ohmic heating and Hall effects", Phys. Scrip., 94, Article ID 025001 (2019).
30. Wang, J., Muhammad, R., Khan, M.I., et al. "Entropy optimized MHD nanomaterial flow subject to variable thicked surface", Comput. Methods Programs Biomed., 189, Article ID 105311 (2020). 
31. Khan, M.I., Alzahrani, F., and Hobiny, A. "Heat transport and nonlinear mixed convective nanomaterial slip flow of Walter-B  fluid containing gyrotactic microorganisms", Alex. Eng. J., 59, pp. 1761-1769 (2020).
32. Abbas, S.Z., Khan, M.I., Kadry, S., et al. "Fully developed entropy optimized second order velocity slip MHD nano fluid flow with activation energy", Comput. Methods Programs Biomed., 190, Article ID 105362 (2020).
33. Grubka, L.J. and Bobba, K.M. "Heat transfer characteristics of a continuous, stretching surface with variable temperature", J. Heat Transf., 107, pp. 248- 250 (1985).
34. Ali, M.E. "Heat transfer characteristics of a continuous stretching surface", Warme and Stoffubertragung, 29, pp. 227-234 (1994).
35. Ishak, A., Nazar, R., and Pop, I. "Boundary layer  flow and heat transfer over an unsteady stretching vertical surface", Meccanica, 44, pp. 369-375 (2009).