Effects of Radiation Absorption, Soret and Dufour on Unsteady MHD Mixed Convective Flow past a Vertical Permeable Plate with Slip Condition and Viscous Dissipation

Document Type : Full Lenght Research Article


Kohima Science College, Jotsoma, Nagaland 797002, India


The objective of current study is to discuss the effects of the Soret and Dufour with radiation absorption, applied heat source and viscous dissipation on an unsteady MHD mixed convective flow with velocity slip condition across a semi-infinite vertical permeable plate in porous medium. A similarity transformation is used to turn the governing partial differential equations with proper boundary conditions into coupled, non-linear ordinary differential equations with variable coefficients. The inbuilt MATLAB solver bvp4c is used to generate numerical solutions. The effects on momentum, thermal and solutal boundary layers for various parametric values are graphically depicted. Skin friction, Nusselt number and Sherwood number are all tabulated and discussed in detail. An improvement in radiation absorption corresponds to enhancement of the heat transfer rate up to 59% while leading to a decline in mass transfer rate around 20%. The momentum, thermal and solutal boundary layers are all found to be boosted when the Soret effect is higher. For higher estimation of slip effect, the skin friction is found to decay around 23%. Also, as more time goes by the thermal and concentration boundary layers are enhanced. Novelty: Results obtained in this studied has also been compared and verified with available scientific literature and is found to be in good agreement, which establishes assurance in the numerical results reported in the study.


Main Subjects

[1]    S. Goldstein, 1965. Modern developments in fluid dynamics. New York, Dover Publications, 1965.
[2]    B. G. S and Joseph D D, 1967. Boundary conditions at a natural permeable wall, Journal of Fluid Mechanics, 30(1), pp. 197–207
[3]    D. Pal and B. Talukdar, 2010. Perturbation analysis of unsteady magnetohydrodynamic convective heat and mass transfer in a boundary layer slip flow past a vertical permeable plate with thermal radiation and chemical reaction, Communications in Nonlinear Science and Numerical Simulation, 15(7), pp. 1813–1830 doi: 10.1016/j.cnsns.2009.07.011.
[4]    D. Ramya, R. S. Raju, J. A. Rao, and A. J. Chamkha, 2018. Effects of velocity and thermal wall slip on magnetohydrodynamics ( MHD ) boundary layer viscous flow and heat transfer of a Nano fluid over a non-linearly-stretching sheet : a numerical study, Propulsion and Power Research, 7(2), pp. 182–195 doi: 10.1016/j.jppr.2018.04.003.
[5]    A. Raptis, 2011. Free convective oscillatory flow and mass transfer past a porous plate in the presence of radiation for an optically thin fluid, Thermal Science, 15(3), pp. 849–857 doi: 10.2298/TSCI101208032R.
[6]    M. A. Hossain and H. S. Takhar, 1996.Radiation effect on mixed convection along a vertical plate with uniform surface temperature, Heat and Mass Transfer, 31(4), pp. 243–248 doi: 10.1007/s002310050052.
[7]    L. Manjula and R. Muthucumaraswamy, 2021. Heat and Mass Transfer Effect on an Infinite Vertical Plate in the Presence of Hall Current and Thermal Radiation with Variable Temperature, International Journal of Applied Mechanics and Engineering, 26(3), pp. 131–140 doi: 10.2478/ijame-2021-0040.
[8]    F. S. Ibrahim, A. M. Elaiw, and A. A. Bakr, 2008. Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi infinite vertical permeable moving plate with heat source and suction, Communications in Nonlinear Science and Numerical Simulation, 13(6), pp. 1056–1066 doi: 10.1016/j.cnsns.2006.09.007.
[9]    G. Sreedevi, R. R. Rao, D. R. V. P. Rao, and A. J. Chamkha, 2016. Combined influence of radiation absorption and Hall current effects on MHD double-diffusive free convective flow past a stretching sheet, Ain Shams Engineering Journal, 7(1), pp. 383–397 doi: 10.1016/j.asej.2015.11.024.
[10]  A. M. Aly, A. J. Chamkha, and Z. A. S. Raizah, 2020. Unsteady coupled heat and mass transfer by free convection from a vertical plate embedded in porous media under impacts of radiation and chemical reaction, Journal of Heat and Mass Transfer Research, 7(2), pp. 95–103 doi: 10.22075/JHMTR.2019.10763.1149.
[11]  S. Matta, B. S. Malga, L. Appidi, and P. P. Kumar, 2021. Radiation and chemical reaction effects on unsteady MHD free convention mass transfer fluid flow in a porous plate, Indian Journal of Science and Technology, 14(8), pp. 707–717 doi: 10.17485/ijst/v14i8.20.
[12]  H. Konwar, 2022. Flow , Heat and Mass Transfer past a Stretching Sheet with Temperature Dependent Fluid Properties in Porous Medium, Journal of Heat and Mass Transfer Research,9, pp. 17–26 doi: 10.22075/jhmtr.2022.25036.1357.
[13]  S. A. Khan, T. Hayat, and A. Alsaedi, 2022. Thermal conductivity performance for ternary hybrid nanomaterial subject to entropy generation, Energy Reports, 8, pp. 9997–10005 doi: 10.1016/j.egyr.2022.07.149.
[14]  S. A. Khan, T. Hayat, A. Alsaedi, and B. Ahmad, 2021. Melting heat transportation in radiative flow of nanomaterials with irreversibility analysis, Renewable and Sustainable Energy Reviews, 140, pp. 110739 doi: https://doi.org/10.1016/j.rser.2021.110739.
[15]  M. Yasir, M. Khan, and A. Ahmed, 2022. Non-linear radiative flow of unsteady Oldroyd-B nanofluid subject to Arrhenius activation energy, Waves in Random and Complex Media, 0(0), pp. 1–15 doi: 10.1080/17455030.2022.2135791.
[16]  S. A. Khan, T. Hayat, and A. Alsaedi, 2022. Entropy optimization for nanofluid flow with radiation subject to a porous medium, Journal of Petroleum Science and Engineering, 217, pp. 110864 doi: https://doi.org/10.1016/j.petrol.2022.110864.
[17]  S. A. Khan, T. Hayat, and A. Alsaedi, 2022. Numerical study for entropy optimized radiative unsteady flow of Prandtl liquid, Fuel, 319, pp. 123601 doi: https://doi.org/10.1016/j.fuel.2022.123601.
[18]  T. Kebede, E. Haile, G. Awgichew, and T. Walelign, 2020. Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids, Journal of Applied Mathematics, 2020(1890972) doi: https://doi.org/10.1155/2020/1890972.
[19]  M. Nemati, M. Sefid, and A. R. Rahmati, 2021. Analysis of the Effect of Periodic Magnetic Field, Heat Absorption / Generation and Aspect Ratio of the Enclosure on Non-Newtonian Natural Convection, Journal of Heat and Mass Transfer Research,8, pp. 187–203 doi: 10.22075/JHMTR.2021.22119.1322.
[20]  E. M. A. Elbashbeshy, H. G. Asker, and B. Nagy, 2022. The effects of heat generation absorption on boundary layer flow of a nanofluid containing gyrotactic microorganisms over an inclined stretching cylinder, Ain Shams Engineering Journal, 13(5), pp. 101690 doi: 10.1016/j.asej.2022.101690.
[21]  M. Khan, M. Yasir, A. Saleh, S. Sivasankaran, Y. Rajeh, and A. Ahmed, 2022. Variable heat source in stagnation-point unsteady flow of magnetized Oldroyd-B fluid with cubic autocatalysis chemical reaction, Ain Shams Engineering Journal, 13(3), pp. 101610 doi: 10.1016/j.asej.2021.10.005.
[22]  M. Yasir, A. Ahmed, M. Khan, Z. Iqbal, and M. Azam, 2022. Impact of ohmic heating on energy transport in double diffusive Oldroyd-B nanofluid flow induced by stretchable cylindrical surface, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 0(0) doi: 10.1177/09544089211064116.
[23]  M. Sheikholeslami, 2022. Numerical investigation of solar system equipped with innovative turbulator and hybrid nanofluid, Solar Energy Materials and Solar Cells, 243, pp. 111786
[24]  W. I. A. Okuyade, T. M. Abbey, and A. T. Gima-laabel, 2018. Unsteady MHD free convective chemically reacting fluid flow over a vertical plate with thermal radiation, Dufour, Soret and constant suction effects, Alexandria Engineering Journal, 57(4), pp. 3863–3871 doi: 10.1016/j.aej.2018.02.006.
[25]  S. Sarma and N. Ahmed, 2022. Dufour effect on unsteady MHD flow past a vertical plate embedded in porous medium with ramped temperature. Nature Publishing Group UK, 2022. Doi: 10.1038/s41598-022-15603-x.
[26]  O. Mopuri, R. Kodi, C. Ganteda, R. Srikakulapu, and G. Lorenzini, 2022. MHD Heat and Mass Transfer Steady Flow of a Convective Fluid Through a Porous Plate in The Presence of Diffusion Thermo and Aligned Magnetic Field, Journal of Advanced Research in Fluid Mechanics and Thermal Sciences,89(1), pp. 62–76 doi: 10.37934/arfmts.89.1.6276.
[27]  C. Sowmiya and B. R. Kumar, 2022. MHD mixed convection flow in a permeable vertical plate with buoyancy and Dufour effects, Journal of Porous Media, 25(11), pp. 71–81 doi: 10.1615/JPorMedia.2022044034.
[28]  M. Venkateswarlu, D. V. Lakshmi, and O. D. Makinde, 2020. Thermodynamic analysis of hall current and Soret number effect on hydromagnetic Couette flow in a rotating system with a convective boundary condition, Heat Transfer Research, 51(1), pp. 83–102 doi: 10.1615/HeatTransRes.2019027139.
[29]  V. Meenakshi, 2021. Dufour and Soret Effect on Unsteady MHD Free Convection and Mass Transfer Flow Past an Impulsively Started Vertical Porous Plate Considering with Heat Generation, Journal of Heat and Mass Transfer Research, 8(2), pp. 257–266 doi: 10.22075/JHMTR.2021.21229.1301.
[30]  B. K. Taid and N. Ahmed, 2022. MHD Free Convection Flow across an Inclined Porous Plate in the Presence of Heat Source, Soret Effect, and Chemical Reaction Affected by Viscous Dissipation Ohmic Heating, Biointerface Research in Applied Chemistry, 12(5), pp. 6280–6296 doi: https://doi.org/10.33263/BRIAC125.62806296.
[31]  M. Yasir, M. Khan, and Z. U. Malik, 2023. Analysis of thermophoretic particle deposition with Soret-Dufour in a flow of fluid exhibit relaxation/retardation times effect, International Communications in Heat and Mass Transfer, 141, pp. 106577 doi: https://doi.org/10.1016/j.icheatmasstransfer.2022.106577.
[32]  S. A. Khan, T. Hayat, and A. Alsaedi, 2022. Simultaneous features of Soret and Dufour in entropy optimized flow of reiner-rivlin fluid considering thermal radiation, International Communications in Heat and Mass Transfer, 137, pp. 106297 doi: https://doi.org/10.1016/j.icheatmasstransfer.2022.106297.
[33]  Y. J. Kim, 2000. Unsteady MHD convective heat transfer past a semi-infinite vertical porous moving plate with variable suction, International Journal of Engineering Science, 38(8), pp. 833–845 doi: 10.1016/S0020-7225(99)00063-4.
[34]  L. Shampine, J. Kierzenka, and M. Reichelt, 2000. Solving boundary value problems for ordinary differential equations in MATLAB with bvp4c, Tutorial Notes, 75275, pp. 1–27 doi: https://classes.engineering.wustl.edu/che512/bvp_paper.pdf.