Effect of Rarefactions and Convective Heat Change on Free Convective Unsteady MHD Flow in a Slip-Flow Regime Past a Vertical Wall with Convective Surface Boundary Condition
Abstract
The study investigates the unsteady free convective two-dimensional MHD flow past a vertical porous plate with convective surface boundary condition in porous medium in slip flow regime under the action of variable suction velocity. Analytical solutions are obtained for the system using perturbation technique that converts non-linear coupled governing partial differential equations into non-dimensional form of ordinary differential equations. Effects of variable suction velocity, rarefactions parameter and heat change parameter are analysed and discussed graphically for various values of effective physical parameter such as Grasshof number, Magnetic field parameter, Prandtl number, Permeability parameter on fluid velocity and temperature, skin friction, and heat transfer.
Downloads
References
O.G. Martynenko, A.A. Berezovsky, and Y.A. Sokovishin, “Laminar free convection from of a vertical plate,” Int. J. Heat Mass Transfer. 27, 869-881 (1984), https://doi.org/10.1016/0017-9310(84)90008-5
U.N. Das, R.K. Deka, and V.M. Soundalgekar, “Transient free convection flow past an infinite vertical plate with periodic temperature variation,” J. Heat Transfer, (ASME), 121, 1091-1094 (1999). https://doi.org/10.1115/1.2826063
M.A. Hossain, S. Hussain, and D.A. Rees, “Influence of fluctuating surface temperature and concentration on natural convection flow from a vertical flate plate,” Z. angew. Math. Mech. 81, 699-709, (2001). https://doi.org/10.1002/1521-4001(200110)81
P.K. Sahoo, N. Datta, and S. Biswal, “Magneto hydrodynamics unsteady free convection flow past an infinite vertical plate with constant suction and heat sink,” Ind. J. Pure Appl. Math. 34, 145-155 (2003).
M.M. Abdelkhalek, “Heat and mass transfer in MHD free convection from a moving permeable vertical surface by a perturbation technique,” Commun. Nonlinear Sci. Numer. Simulat. 14, 2091-2012 (2009). https://doi.org/10.1016/j.cnsns.2008.06.001
P.K. Sharma, and R.C. Chaudhary, “Effect of variable suction on transient free convection viscous incompressible flow past a vertical plate with periodic temperature variations in slip-flow regime,” Emirates Journal for Engineering Research, 8, 33-38 (2003).
A.R.A. Khaled, and K. Vafai, “The effect of the slip condition on stokes and couette flows due to an oscillatory wall: exact solution,” Int. J. Nonlinear Mech. 39, 795-809 (2004). https://doi.org/10.1016/s0020-7462(03)00043-X
A. Mehmood, and A. Ali, “The effect of slip condition on unsteady MHD oscillatory flow of a viscous fluid in a planer channel,” Rom. Journ. Phys. 52, 85-91 (2007).
R.C. Chaudhary, and A.K. Jha, “Effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip flow regime,” Appl. Math. Mech. Engl. Ed, 29, 1179-1194 (2008). https://doi.org/10.1007/s10483-008-0907-x
T. Hayat, T. Javed, and Z Abbas, “Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous sheet,” International Journal of Heat and Mass Transfer, 51, 4528-4534 (2008). https://doi.org/10.1016/j.ijheatmasstransfer.2007.12.022
O.D. Makinde, “Effect of variable viscosity on thermal boundary layer over a permeable flat plate with radiation and a convective surface boundary condition,” Journal of Mechanical Science and Technology, 26, 1615-1622 (2012). https://doi.org/10.1007/s12206-012-0302-1
K. Gangadhar, N.B. Reddy, and P.K. Kameshwaran, “Similarity solution of hydro magnetic heat and mass transfer over a vertical plate with a convective surface boundary condition and chemical reaction,” International Journal of Nonlinear Science, 13(3), 298-307 (2012).
P. Olanrewaju, T. Anake, O.T. Arulogun, and D. Ajadi, “Further results on the effects of variable viscosity and magnetic field on flow and heat transfer to a continuous flat plate in the presence of heat generation and radiation with a convective boundary condition,” American Journal of Computational and Applied Mathematics, 2, 42-48 (2012). https://doi.org/10.5923/j.ajcam.20120202.08
P. Garg, G.N. Purohit, and R.C. Chaudhary, “Similarity solutions for combined free-forced convection past a vertical porous plate in a porous medium with a convective surface boundary condition,” Int. J. of Applied Mechanics and Engineering, 21(4), 827-836 (2016). https://doi.org/101515/ijame-2016-0048
P. Garg, G.N. Purohit, and R.C. Chaudhary, “Free convective unsteady MHD flow in slip flow Regime past a vertical plate with a convective surface boundary condition,” Journal of Informatics and Mathematical sciences, 10, 261 270 (2018). https://dx.doi.org/10.26713/jims.v10i1-2.1050
N. Kalita, R.K. Deka, and R.S. Nath, “Unsteady flow Past an accelerated vertical plate in presence of chemical reaction,” East Eur. J. Phys. (3), 223-232 (2023). https://doi.org/10.26565/2312-4334-2023-3-49
S. Sarma, N. Ahmed, “Dufour effect on unsteady MHD flow past a vertical plate embedded in porous medium with ramped temperature,” Sci. Rep. 12(1), 13343 (2022). https://doi.org/10.1038/s41598-022-15603-x
A. Selvaraj, S.D. Jose, R. Muthucumaraswamy, and S. Karthikeyan, “MHD-Parabolic flow past an accelerated isothermal vertical plate with heat and mass diffusion in the presence of rotation,” Material Today Proc. 46, 3546 3549 (2021). https://doi.org/10.1016/j.matpr.2020.12.499
M.V. Krishna, “Hall and ion slip impacts on unsteady MHD free convective rotating flow of Jeffreys fluid with ramped wall temperature,” Int. Commun. Heat. Mass. Transfer, 119, 104927 https://doi.org/10.1016/j.icheatmasstransfer,2020.104927
P.K. Pattnaik, S. Mishra, A. Barik, and A. Mishra, “Influence of chemical reaction on magnetohydrodynamic flow over an exponential stretching sheet: a numerical study,” Int. J. Fluid Mech. Res. 47(3), (2020). https://doi.org/10.1615/InterJFluidMechRes.2020028543
R.S. Nath, and R.K. Deka, “Theoretical study of Thermal and Mass Stratification Effects on MHD Nanofluid past an Exponentially Accelerated Vertical Plate in a Porous Medium in Presence of Heat Source, Thermal Radiation and Chemical Reaction,” Int. J. Appl. Comput. Math. (2024). https://doi.org/10.1007/s40819-024-01721-9
Copyright (c) 2024 Hemant Agarwal, Shyamanta Chakraborty
![Creative Commons License](http://i.creativecommons.org/l/by/4.0/88x31.png)
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).