Engineering Transactions, 68, 2, pp. 177–198, 2020

Navier Slip Condition on Time-Dependent Radiating Nanofluid with the Soret Effect

Sangapatnam SUNEETHA
Yogi Vemana University

Yogi Vemana University

Yogi Vemana University

Bala Anki Reddy POLU
VIT University

This work concentrates on the study of the two-dimensional hydromagnetic flow of nanofluids over an suddenly started nonlinear stretching sheet in the presence of radiation and dissipation. The Soret effect and heat generation are also taken into consideration. The transformed ordinary differential equations (ODEs) are solved numerically via the MATLAB RK4S approach bvp4c solver with the assistance of similarity variables. The effects of various parameters are explored and shown in graphs and tables. It is noted that the concentration increases as the Soret number increases within the boundary layer. An increase in velocity slip decreases the velocity and a reverse effect is observed for temperature. This model has significance in different areas such as polymer chemical and metallurgical industries, and other fields that use the latest technology and thermo-processed materials such as metallic and glass sheets.
Keywords: nanofluids; MHD; thermal radiation; viscous dissipation; heat generation; Soret effect
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Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).


Choi S.U.S., Eastman J.A., Enhancing thermal conductivity of fluids with nanoparticles, Unites States, 1995.

Das Sk., Choi S.U.S., Wenhua Yu, Pradeep T., Nanofluids: Science and Technology, John Wiley & Sons, Inc., 2008.

Afridi M.I., Qasim M., Khan N.A., Hamdani M., Heat transfer analysis of Cu-Al2O3-water and Cu-Al2O3-kerosene oil hybrid nanofluids in the presence of frictional heating: using 3-stage Lobatto IIIA formula, Journal of Nanofluids, 8(4): 885–891, 2019, doi: 10.1166/jon.2019.1626.

Afridi M.I., Tlili I., Goodarzi M., Osman M., Khan N.A., Irreversibility analysis of hybrid nanofluid flow over a thin needle with effects of energy dissipation, Symmetry, 11(5): 663, 2019, doi: 10.3390/sym11050663.

Crane LJ., Flow past a stretching plate, Journal of Applied Mathematics and Physics, 21(4): 645–647, 1970.

Mustafa M., Khan J.A., Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects, AIP Advances, 5(7): 1–11, 2015, doi: 10.1063/1.4927449.

Das K., Nanofluid flow over a non-linear permeable stretching sheet with partial slip, Journal of the Egyptian Mathematical Society, 23(2): 451–456, 2015, doi: 10.1016/j.joems.2014.06.014.

Badr A., Subhas A.M., MHD boundary layer flow over a nonlinear stretching sheet in a nanofluid with convective boundary condition, Journal of Computational and Theoretical Nanoscience, 12(12): 6020–6027, 2015, doi: 10.1166/jctn.2015.4753.

Rahman M.M., Eltayeb I.A., Radiative heat transfer in a Hydromagnetic nanofluid past a non-linear stretching surface with convective boundary condition, Meccanica, 48(3): 601–615, 2013, doi:10.1007/s11012-012-9618-2.

Mustafa M., Khan J.A., Hayat T., Alsaedi A., Boundary layer flow of nanofluid over a nonlinearly stretching sheet with convective boundary condition, IEEE Transactions on Nanotechnology, 14(1): 159–168, 2015, doi: 10.1109/TNANO.2014.2374732.

Hamad M.A.A., Pop I., Ismail A.M., Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate, Nonlinear Analysis: Real World Applications, 12(3): 1338–1346, 2011, doi: 10.1016/j.nonrwa.2010.09.014.

Bala Anki Reddy P., Suneetha S., Bhaskar Reddy N., Numerical study of MHD boundary layer slip flow of a Maxwell nanofluid over an exponentially stretching surface with convective boundary condition, Propulsion and Power Research, 6(4): 259–268, 2017, doi: 10.1016/j.jppr.2017.11.002.

Daniel Y.S., Aziz Z.A., Ismail Z., Salah F., Effects of slip and convective conditions on MHD flow of nanofluid over a porous nonlinear stretching/shrinking sheet, Australian Journal of Mechanical Engineering, 16(3): 1–17, 2017, doi: 10.1080/14484846.2017.1358844.

Hayat T., Ullah I., Alsaed I A., Farooq M., MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness, Results in Physics, 7: 189–196, 2017, doi: 10.1016/j.rinp.2016.12.008.

Uddin M.J., Sohail A., Anwar Bég O., Ismail A.I. Md., Numerical solution of MHD slip flow of a nanofluid past a radiating plate with Newtonian heating: A Lie group approach, Alexandria Engineering Journal, 57(4): 2455–2462, 2018, doi: 10.1016/j.aej.2017.03.025.

Rana P., Dhanai R., Kumar L., Radiative nanofluid flow and heat transfer over a nonlinear permeable sheet with slip conditions and variable magnetic field: Dual solutions, Ain Shams Engineering Journal, 8(3): 341–352, 2017, doi: 10.1016/j.asej.2015.08.016.

Lu D., Ramzan M., ul Huda N., Chung J. D., Farooq U., Nonlinear radiation effect on MHD Carreau nanofluid flow over a radially stretching surface with zero mass flux at the surface, Scientific Reports, 8: 3709, 2018, doi:10.1038/s41598-018-22000-w.

Zaib A., Rashidi M.M., Chamkha A.J., Mohammad N.F., Impact of nonlinear thermal radiation on stagnation-point flow of a Carreau nanofluid past a nonlinear stretching sheet with binary chemical reaction and activation energy, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 232(6): 962–972, 2018, doi: 10.1177/0954406217695847.

Magyari E., Pantokratoras A., Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows, International Communications in Heat and Mass Transfer, 38(5): 554–556, 2011, doi: 10.1016/j.icheatmasstransfer.2011.03.006.

Afify A.A., The influence of slip boundary condition on Casson nanofluid flow over a stretching sheet in the presence of viscous dissipation and chemical reaction, Mathematical Problems in Engineering, 1–12, Article ID 3804751, 2017, doi: 10.1155/2017/3804751.

Reddy C.S., Kishan N., MHD boundary layer flow of Casson nanofluid over a nonlinear stretching sheet with viscous dissipation and convective condition, Journal of Nanofluids, 5(6): 870–879, 2016, doi: 10.1166/jon.2016.1271.

Khan U., Ahmed N., Asadullah M., Mohyud-Din S.T., Effects of viscous dissipation and slip velocity on two-dimensional and axisymmetric squeezing flow of Cuwater and Cu-kerosene nanofluids, Propulsion and Power Research, 4(1): 40–49, 2015, doi: 10.1016/j.jppr.2015.02.004.

Navier C., Dissertation on the laws of fluid movement [in French: Memoire sur les lois du mouvement des fluids], Memoires de l’Academie Royale des Sciences de l’Institut de France, 6: 389–440, 1823.

Shaw S., Kameswaran P.K., Sibanda P., Effects of slip on nonlinear convection in nanofluid flow on stretching surfaces, Boundary Value Problems, 2016: 2, 2016, doi: 10.1186/s13661-015-0506-2.

Oyelakin I.S., Mondal S., Sibanda P., Unsteady Casson nanofluid flow over a stretching sheet with thermal radiation, convective and slip boundary conditions, Alexandria Engineering Journal, 55(2): 1025–1035, 2016, doi: 10.1016/

Khan N.A., Sultan F., MHD flow of a Williamson fluid over an infinite rotating disk with anisotropic slip, Journal of Engineering Physics and Thermophysics, 92(6): 1625–1636, 2019, doi:10.1007/s10891-019-02083-6.

Khan N.A., Naz F., Sultan F., Entropy generation analysis and effects of slip conditions on micropolar fluid flow due to a rotating disk, Open Engineering, 7(1): 185–198, 2017, doi:10.1515/eng-2017-0025.

Ramya D., Srinivasa Raju R., Anand Rao J., Rashidi M.M., Boundary layer viscous flow of nanofluids and heat transfer over a nonlinearly isothermal stretching sheet in the presence of heat generation/absorption and slip boundary conditions, International Journal of Nanoscience and Nanotechnology, 12(4): 251–268, 2016,

Suneetha S., Bhaskar Reddy N., Ramachandra Prasad V., Radiation and mass transfer effects on MHD free convective dissipative fluid in the presence of heat source/sink, Journal of Applied Fluid Mechanics, 14(1): 107–113, 2011.

Reddy S.R.R., Anki Reddy P.B., Suneetha S., Magnetohydrodynamic flow of blood in a permeable inclined stretching viscous dissipation, non-uniform heat source/sink and chemical reaction, Frontiers in Heat and Mass Transfer, 10(22): 2018, doi: 10.5098/hmt.10.22.

Eckert E.R.G., Drake R.M., Analysis of Heat and Mass Transfer, Mc-Graw Hill, New York, 1972.

Yirga Y., Shankar B., MHD Flow and heat transfer of nanofluids through a porous media due to a stretching sheet with viscous dissipation and chemical reaction effects, International Journal for Computational Methods in Engineering Science and Mechanics, 16(5): 275–284, 2015, doi: 10.1080/15502287.2015.1048385.

Ram Reddy Ch., Murthy P.V.S.N., Rashad A.M., Chamkha Ali J., Soret effect on stagnation-point flow past a stretching/shrinking sheet in a nanofluid-saturated non-Darcy porous medium, Special Topics & Reviews in Porous Media – An International Journal, 7(3): 229–243, 2016,doi: 10.1615/SpecialTopicsRevPorousMedia.v7.i3.20.

Mishra S.R., Baag S., Mohapatra D.K., Chemical reaction and Soret effects on hydromagnetic micropolar fluid along a stretching sheet, Engineering Science and Technology, an International Journal, 19 (4): 1919–1928, 2016, doi: 10.1016/j.jestch.2016.07.016.

Freidoonimehr N., Rashidi M.M., Mahmud S., Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid, International Journal of Thermal Sciences, 87: 136–145, 2015, doi: 10.1016/j.ijthermalsci.2014.08.009.

Buongiorno J., Convective transport in nanofluids, ASME Journal of Heat Transfer, 128(3): 240–250, 2006, doi: 10.1115/1.2150834.

Rohni A.M., Ahmad S., Ismail A.I.M., Pop I., Flow and heat transfer over an unsteady shrinking sheet with suction in a nanofluid using Buongiorno’s model, International Communications in Heat and Mass Transfer, 43: 75–80, 2013, doi: 10.1016/j.icheatmasstransfer.2013.02.001.

Kuznetsov A.V., Nield D.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49(2): 243–247, 2010, doi: 10.1016/j.ijthermalsci.2009.07.015.

Khan W.A., Pop I., Boundary-layer flow of a nanofluid past a stretching sheet, International Journal of Heat and Mass Transfer, 53(11–12): 2477–2483, 2010, doi: 10.1016/j.ijheatmasstransfer.2010.01.032.

Seth G.S., Mishra M.K., Analysis of transient flow of MHD nanofluid past a nonlinear stretching sheet considering Navier’s slip boundary condition, Advanced Powder Technology, 28(2): 375–384, 2017, doi:10.1016/j.apt.2016.10.008.

DOI: 10.24423/EngTrans.925.20200601