Journal of Applied Nonlinear Dynamics
Unsteady MHD Nanofluid Flow Over Rotating Semi-Infinite Vertical Porous Plate with Soret and Viscous Dissipation Effects
Journal of Applied Nonlinear Dynamics 15(3) (2026) 629--643 | DOI:10.5890/JAND.2026.09.008
Kaspa Sreelatha$^{1,2}$, Siva Reddy Sheri$^{2}$, Gollapalli Shankar$^{3}$
$^{1}$ Department of Mathematics, TSWRDC (W), Markal, Kamareddy 03145, Telangana, India
$^{2}$ Department of Mathematics, GITAM (Deemed to be university), Hyderabad Campus, Medak 502329, Telangana, India
$^{3}$ Department of Mathematics, B V Raju Institute of Technology, Narsapur, Medak, Hyderabad 502313, Telangana, India
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Abstract
The present study examines the unsteady MHD flow of nanofluid consisting of silver and titanium dioxide nanoparticles dispersed in water over a rotating semi-infinite vertically moving permeable plate with magnetic field, buoyancy effect, Dufour effect, viscous dissipation and Soret effect under constant heat source. The core governing relations are made dimensionless with suitable non-dimensionless variables, and the resulting consequent equations are solved by Galerkin FEM. The graphical representations depicting concentration, temperature, and velocity profiles for various different parameters are incorporated. Nusselt number; skin friction, and Sherwood numbers are also tabulated. The velocity profile accounts for increased Dufour effect, Eckert number, and Soret effect, while the trend of decreasing is reversed for increased rotation parameter. Concentration profile enhances for intensified Soret number. The study also reveals that Nusselt number declines for the suction parameter, the Sherwood number appends for the Soret number, & also the chemical reaction parameter. The study of MHD rotating vertical moving plates has potential applications in energy systems, fusion reactors, industrial coolants, and biomedical devices.
References
-
| [1]  | Choi, S.U. and Eastman, J.A. (1995), Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29), Argonne National Lab. (ANL), Argonne, IL (United States).
|
-
| [2]  | Lee, S., Choi, S.S., Li, S.A., and Eastman, J.A. (1999), Measuring thermal conductivity of fluids containing oxide nanoparticles, https://doi.org/10.1115/1.2825978.
|
-
| [3]  | Das, S.K., Choi, S.U., Yu, W., and Pradeep, T. (2007), Nanofluids: science and technology, John Wiley & Sons.
|
-
| [4]  | Makinde, O.D. and Aziz, A. (2011), Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, International Journal of Thermal Sciences, 50(7), 1326-1332, https://doi.org/ 10.1016/j.ijthermalsci.2011.02.019.
|
-
| [5]  | Thumma, T., Chamkha, A., and Sheri, S.R. (2017), MHD natural convective flow of nanofluids past stationary and moving inclined porous plate considering temperature and concentration gradients with suction, International Journal of Numerical Methods for Heat & Fluid Flow, 27(8), 1765-1794, ISSN: 0961-5539.
|
-
| [6]  | Kuznetsov, A.V. and Nield, D.A. (2010), Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49(2), 243-247, https://doi.org/10.1016/ j.ijthermalsci.2009.07.015.
|
-
| [7]  | Gorla, R.S.R. and Chamkha, A. (2011), Natural convective boundary layer flow over a horizontal plate embedded in a porous medium saturated with a nanofluid, Journal of Modern Physics, 2011, http://www.scirp.org/ journal/PaperInformation.aspx?PaperID=4367.
|
-
| [8]  | Li, Q. and Xuan, Y. (2002), Convective heat transfer and flow characteristics of Cu-water nanofluid, Science in China Series E: Technological Science, 45, 408-416, https://doi.org/10.1360/02ye9047.
|
-
| [9]  | Das, S.K., Choi, S.U., and Patel, H.E. (2006), Heat transfer in nanofluids---a review, Heat Transfer Engineering, 27(10), 3-19, https://doi.org/10.1080/01457630600904593.
|
-
| [10]  | Shehzad, S.A., Abbasi, F.M., Hayat, T., and Alsaedi, F. (2015), Model and comparative study for peristaltic transport of water based nanofluids, Journal of Molecular Liquids, 209, 723-728, https://doi.org/10.1016/ j.molliq.2015.05.058.
|
-
| [11]  | Ghaly, A.Y. (2002), Radiation effects on a certain MHD free-convection flow, Chaos, Solitons & Fractals, 13(9), 1843-1850, https://doi.org/10.1016/S0960-0779(01)00193-X.
|
-
| [12]  | Raptis, A. and Massalas, C.V. (1998), Magnetohydrodynamic flow past a plate by the presence of radiation, Heat and Mass Transfer, 34(2), 107-109, https://doi.org/10.1007/s002310050237.
|
-
| [13]  | Shankar, G., Sheri, S.R., Jamshed, W., Ibrahim, R.W., Eid, M.R., and Guedri, K. (2024), Radiative and viscid dissipative flowing influences on heat and mass transfer in MHD Casson fluid employing Galerkin finite element style, International Journal of Modern Physics B, 38(02), 2450022, https://doi.org/10.1142/S021797922450022X.
|
-
| [14]  | Mutuku-Njane, W.N. and Makinde, O.D. (2014), On hydromagnetic boundary layer flow of nanofluids over a permeable moving surface with Newtonian heating, Latin American Applied Research, 44(1), 57-62, ISSN 0327-0793, versión On-line ISSN 1851-8796.
|
-
| [15]  | Shankar, G., Sheri, S.R., and Shehzad, S.A. (2023), Numerical study of transient chemical reactive magnetized Casson fluid flow in the presence of Newtonian heating, International Journal of Modelling and Simulation, 1-12, https://doi.org/10.1080/02286203.2023.2249641.
|
-
| [16]  | Kuznetsov, A.V. and Nield, D.A. (2010), Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences, 49(2), 243-247, https://doi.org/10.1016/ j.ijthermalsci.2013.10.007.
|
-
| [17]  | Nield, D.A. and Kuznetsov, A.V. (2009), The Cheng--Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, International Journal of Heat and Mass Transfer, 52(25-26), 5792-5795, https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.024.
|
-
| [18]  | Bachok, N., Ishak, A., and Pop, I. (2010), Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, International Journal of Thermal Sciences, 49(9), 1663-1668, https://doi.org/10.1016/ j.ijthermalsci.2010.01.026.
|
-
| [19]  | Raptis, A. and Kafousias, N. (1982), Heat transfer in flow through a porous medium bounded by an infinite vertical plate under the action of a magnetic field, International Journal of Energy Research, 6(3), 241-245, https://doi.org/10.1002/er.4440060305.
|
-
| [20]  | Sheri, S.R. and Srinivasa Raju, R. (2016), Transient MHD free convective flow past an infinite vertical plate embedded in a porous medium with viscous dissipation, Meccanica, 51, 1057-1068, https://doi.org/ 10.1007/s11012-015-0285-y.
|
-
| [21]  | Buongiorno, J. (2006), Convective transport in nanofluids, https://doi.org/10.1115/1.2150834.
|
-
| [22]  | Mahapatra, T.R., Mondal, S., and Pal, D. (2012), Heat Transfer due to Magnetohydrodynamic Stagnation-Point Flow of a Power-Law Fluid towards a Stretching Surface in the Presence of Thermal Radiation and Suction/Injection, International Scholarly Research Notices, 2012(1), 465864, https://doi.org/10.5402/ 2012/465864.
|
-
| [23]  | Haroun, N.A., Sibanda, P., Mondal, S., and Motsa, S.S. (2015), On unsteady MHD mixed convection in a nanofluid due to a stretching/shrinking surface with suction/injection using the spectral relaxation method, Boundary Value Problems, 2015, 1-17, https://doi.org/10.1186/s13661-015-0289-5.
|
-
| [24]  | Haroun, N.A., Sibanda, P., Mondal, S., Motsa, S.S., and Rashidi, M.M. (2015), Heat and mass transfer of nanofluid through an impulsively vertical stretching surface using the spectral relaxation method, Boundary Value Problems, 2015, 1-16, https://doi.org/10.1186/s13661-015-0424-3.
|
-
| [25]  | Mondal, S., Haroun, N.A., and Sibanda, P. (2015), The effects of thermal radiation on an unsteady MHD axisymmetric stagnation-point flow over a shrinking sheet in presence of temperature dependent thermal conductivity with Navier slip, PLoS One, 10(9), e0138355, https://doi.org/10.1371/journal.pone.0138355.
|
-
| [26]  | Shankar, G., Sheri, S.R., and Shehzad, S.A. (2023), Numerical study of transient chemical reactive magnetized Casson fluid flow in the presence of Newtonian heating, International Journal of Modelling and Simulation, 1-12, https://doi.org/10.1080/02286203.2023.2249641.
|
-
| [27]  | Agbaje, T.M., Mondal, S., Makukula, Z.G., Motsa, S.S., and Sibanda, P. (2018), A new numerical approach to MHD stagnation point flow and heat transfer towards a stretching sheet, Ain Shams Engineering Journal, 9(2), 233-243, https://doi.org/10.1016/j.asej.2015.10.015.
|
-
| [28]  | Turkyilmazoglu, M. (2012), Exact analytical solutions for heat and mass transfer of MHD slip flow in nanofluids, Chemical Engineering Science, 84, 182-187, https://doi.org/10.1016/j.ces.2012.08.029.
|
-
| [29]  | Hasanuzzaman, M., Labony, M.A., and Hossain, M.M. (2023), Heat generation and radiative effects on time-dependent free MHD convective transport over a vertical permeable sheet, Heliyon, 9(10), https://doi.org/10.1016/j.heliyon.2023.e20865.
|
-
| [30]  | Haroun, N.A., Mondal, S., and Sibanda, P. (2015), Unsteady natural convective boundary-layer flow of MHD nanofluid over a stretching surfaces with chemical reaction using the spectral relaxation method: A revised model, Procedia Engineering, 127, 18-24, https://doi.org/10.1016/j.proeng.2015.11.317.
|
-
| [31]  | Chamkha, A.J., Mohamed, R.A., and Ahmed, S.E. (2011), Unsteady MHD natural convection from a heated vertical porous plate in a micropolar fluid with Joule heating, chemical reaction and radiation effects, Meccanica, 46, 399-411, https://doi.org/10.1007/s11012-010-9321-0.
|
-
| [32]  | Sheri, S.R. and Modugula, P. (2017), Heat and mass transfer effects on unsteady MHD flow over an inclined porous plate embedded in porous medium with Soret--Dufour and chemical reaction, International Journal of Applied and Computational Mathematics, 3, 1289-1306, https://doi.org/10.1007/s40819-016-0177-4.
|
-
| [33]  | Eckert, E.R. and Drake Jr, R.M. (1987), Analysis of heat and mass transfer, OSTI ID:7142648.
|
-
| [34]  | Basant Kumar, J.H.A. and Singh, A.K. (1990), Soret effects on free-convection and mass transfer flow in the stokes problem for a infinite vertical plate, Astrophysics and Space Science, 173, 251-255, https://doi.org/10.1007/BF00643934.
|
-
| [35]  | Sheri, S.R. and Srinivasa Raju, R. (2015), Soret effect on unsteady MHD free convective flow past a semi--infinite vertical plate in the presence of viscous dissipation, International Journal for Computational Methods in Engineering Science and Mechanics, 16(2), 132-141, https://doi.org/10.1080/15502287.2015.1009583.
|
-
| [36]  | Sheri, S.R., Jayaprasad, S., Shankar, G., and Mahendar, D. (2023), Thermo-diffusion and diffusion-thermo effects on an unsteady MHD casson fluid flow past an oscillating vertical plate embedded in a porous medium, in AIP Conference Proceedings (Vol. 2548, No. 1), AIP Publishing, https://doi.org/10.1063/ 5.0119206.
|
-
| [37]  | Sheri, S.R., Jayaprasad, S., and Mahendar, D. (2020), Soret and Dufour effects on MHD free convection flow past an impulsively moving vertical plate in the presence of inclined magnetic field, in AIP Conference Proceedings, 2246(1), AIP Publishing, https://doi.org/10.1063/5.0015575.
|
-
| [38]  | Divya, A., Sheri, S.R., and Suram, A.K. (2023), Finite element analysis of MHD naturally convective flow past an exponentially accelerated plate with viscous dissipation, Numerical Heat Transfer, Part B: Fundamentals, 85(9), 1115-1129, https://doi.org/10.1080/10407790.2023.2274454.
|
-
| [39]  | Shamshuddin, M.D. and Sheri, S.R. (2017), Free convection from a rotating vertical porous plate in a dissipative micropolar fluid with cross diffusion effects, Advances in Modelling and Analysis A, 86, 627-657, https://doi.org/10.18280/mmc_b.860304.
|
-
| [40]  | Venkateswarlu, B. and Satya Narayana, P.V. (2015), Chemical reaction and radiation absorption effects on the flow and heat transfer of a nanofluid in a rotating system, Applied Nanoscience, 5, 351-360, https://doi.org/10.1007/s13204-014-0324-3.
|
-
| [41]  | Kumar, R.K., Prasad, P.D., and Varma, S.V.K. (2016), Thermo-diffusion and chemical reaction effects on free convective heat and mass transfer flow of conducting nanofluid through porous medium in a rotating frame, https://www.researchgate.net/publication/295850124.
|
-
| [42]  | Reddy, J.N. (1993), An introduction to the finite element method, New York, 27, 14.
|
-
| [43]  | Bathe, M. (1998), A fluid-structure interaction finite element analysis of pulsatile (Doctoral dissertation, Massachusetts Institute of Technology).
|
-
| [44]  | Prasad, P.D., Kumar, R.K., and Varma, S.V.K. (2018), Heat and mass transfer analysis for the MHD flow of nanofluid with radiation absorption, Ain Shams Engineering Journal, 9(4), 801-813, https://doi.org/10.1016/ j.asej.2016.04.016.
|
-
| [45]  | Krishna, M.V. and Chamkha, A.J. (2019), Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid past an infinite vertical plate embedded in a porous medium, Results in Physics, 15, Article 102652, https://doi.org/10.1016/j.rinp.2019.102652.
|