×
Khan, Arshad; Khan, Ilyas; Ali, Farhad; Khalid, Asma; Shafie, Sharidan

Exact solutions of heat and mass transfer with MHD flow in a porous medium under time dependent shear stress and temperature. (English) Zbl 1433.76182

Abstr. Appl. Anal. 2015, Article ID 975201, 16 p. (2015).
Summary: This paper aims to study the influence of thermal radiation on unsteady magnetohydrodynamic (MHD) natural convection flow of an optically thick fluid over a vertical plate embedded in a porous medium with arbitrary shear stress. Combined phenomenon of heat and mass transfer is considered. Closed-form solutions in general form are obtained by using the Laplace transform technique. They are expressed in terms of exponential and complementary error functions. Velocity is expressed as a sum of thermal and mechanical parts. Corresponding limiting solutions are also reduced from the general solutions. It is found that the obtained solutions satisfy all imposed initial and boundary conditions and reduce to some known solutions from the literature as special cases. Analytical results for the pertinent flow parameters are drawn graphically and discussed in detail. It is found that the velocity profiles of fluid decrease with increasing shear stress. The magnetic parameter develops shear resistance which reduces the fluid motion whereas the inverse permeability parameter increases the fluid flow.

MSC:

76W05 Magnetohydrodynamics and electrohydrodynamics
76S05 Flows in porous media; filtration; seepage
80A19 Diffusive and convective heat and mass transfer, heat flow
Cite Review PDF
Full Text: DOI
OA License

References:

[1] Singh, J., Flow of elasto-viscous fluid past an accelerated porous plate, Astrophysics and Space Science, 106, 1, 41-45, (1984) · Zbl 0546.76015 · doi:10.1007/BF00653912
[2] Narahari, M., Effects of thermal radiation and free convection currents on the unsteady Couette flow between two vertical parallel plates with constant heat flux at one boundary, WSEAS Transactions on Heat and Mass Transfer, 5, 1, 21-30, (2010)
[3] Narahari, M.; Nayan, M. Y., Free convection flow past an impulsively started infinite vertical plate with Newtonian heating in the presence of thermal radiation and mass diffusion, Turkish Journal of Engineering and Environmental Sciences, 35, 3, 187-198, (2011) · doi:10.3906/muh-1101-15
[4] Narahari, M.; Ishak, A., Radiation effects on free convection flow near a moving vertical plate with newtonian heating, Journal of Applied Sciences, 11, 7, 1096-1104, (2011) · doi:10.3923/jas.2011.1096.1104
[5] Chaudhary, R. C.; Jain, P., Unsteady free convection boundary-layer flow past an impulsively started vertical surface with Newtonian heating, Romanian Journal of Physics, 51, 911, (2006)
[6] Das, U. N.; Deka, R.; Soundalgekar, V. M., Effects of mass transfer on flow past an impulsively started infinite vertical plate with constant heat flux and chemical reaction, Forschung im Ingenieurwesen, 60, 10, 284-287, (1994) · doi:10.1007/BF02601318
[7] Soundalgekar, V. M.; Birajdar, N. S.; Darwhekar, V. K., Mass-transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux, Astrophysics and Space Science, 100, 1-2, 159-164, (1984) · doi:10.1007/BF00651593
[8] Muthucumaraswamy, R.; Ganesan, P.; Soundalgekar, V. M., On flow and heat transfer of a viscous incompressible fluid past an impulsively started vertical isothermal plate, International Journal of Thermal Sciences, 40, 3, 297-302, (2001) · Zbl 0989.76013 · doi:10.1016/S1290-0729(00)01219-9
[9] Muthucumaraswamy, R.; Ganesan, P.; Soundalgekar, V. M., Heat and mass transfer effects on flow past an impulsively started vertical plate, Acta Mechanica, 146, 1-2, 1-8, (2001) · Zbl 0989.76013 · doi:10.1007/BF01178790
[10] Das, S. S.; Biswal, S. R.; Tripathy, U. K.; Das, P., Mass transfer effects on unsteady hydromagnetic convective flow past a vertical porous plate in a porous medium with heat source, Journal of Applied Fluid Mechanics, 4, 4, 91-100, (2011)
[11] Toki, C. J.; Tokis, J. N., Exact solutions for the unsteady free convection flows on a porous plate with time-dependent heating, Zeitschrift für Angewandte Mathematik und Mechanik, 87, 1, 4-13, (2007) · Zbl 1122.76081 · doi:10.1002/zamm.200510291
[12] Senapati, N.; Dhal, R. K.; Das, T. K., Effects of chemical reaction on free convection MHD flow through porous medium bounded by vertical surface with slip flow region, American Journal of Computational and Applied Mathematics, 2, 124-135, (2012)
[13] Khan, I.; Fakhar, K.; Shafie, S., Magnetohydrodynamic free convection flow past an oscillating plate embedded in a porous medium, Journal of the Physical Society of Japan, 80, 10, (2011) · doi:10.1143/JPSJ.80.104401
[14] Khan, A.; Khan, I.; Ali, F.; Ulhaq, S.; Shafie, S., Effects of wall shear stress on unsteady MHD conjugate flow in a porous medium with ramped wall temperature, PLoS ONE, 9, 3, (2014) · Zbl 1407.76176 · doi:10.1371/journal.pone.0090280
[15] Hussanan, A.; Ismail, Z.; Khan, I.; Hussein, A. G.; Shafie, S., Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating, The European Physical Journal Plus, 129, article 46, (2014) · doi:10.1140/epjp/i2014-14046-x
[16] Barik, R. N.; Dash, G. C.; Kar, M., Free convection heat and mass transfer MHD flow in a vertical porous channel in the presence of chemical reaction, Journal of Fluids, 2013, (2013) · doi:10.1155/2013/297493
[17] Chandran, P.; Sacheti, N. C.; Singh, A. K., Natural convection near a vertical plate with ramped wall temperature, Heat and Mass Transfer, 41, 5, 459-464, (2005) · doi:10.1007/s00231-004-0568-7
[18] Narahari, M.; Beg, O. A.; Ghosh, S. K., Mathematical modelling of mass transfer and free convection current effects on unsteady viscous flow with ramped wall temperature, World Journal of Mechanics, 1, 176-184, (2011) · doi:10.4236/wjm.2011.14023
[19] Rajesh, V., Chemical reaction and radiation effects on the transient MHD free convection flow of dissipative fluid past an Infinite vertical porous plate with ramped wall temperature, Chemical Industry & Chemical Engineering Quarterly, 17, 2, 189-198, (2011) · doi:10.2298/CICEQ100829003R
[20] Patra, R. R.; Das, S.; Jana, R. N.; Ghosh, S. K., Transient approach to radiative heat transfer free convection flow with ramped wall temperature, Journal of Applied Fluid Mechanics, 5, 2, 9-13, (2012)
[21] Seth, G. S.; Mahatoo, G. K.; Sarkar, S., Effects of Hall current and rotation on MHD natural convection flow past an impulsively moving vertical plate with ramped temperature in the presence of thermal diffusion with heat absorption, International Journal of Energy & Technology, 5, 1-12, (2013)
[22] Samiulhaq; Khan, I.; Ali, F.; Shafie, S., MHD free convection flow in a porous medium with thermal diffusion and ramped wall temperature, Journal of the Physical Society of Japan, 81, 4, (2012) · doi:10.1143/JPSJ.81.044401
[23] Ghara, N.; Das, S.; Maji, S. L.; Jana, R. N., Effect of radiation on MHD free convection flow past an impulsively moving vertical plate with ramped wall temperature, American Journal of Scientific and Industrial Research, 3, 6, 376-386, (2012) · doi:10.5251/ajsir.2012.3.6.376.386
[24] Das, S.; Mandal, C.; Jana, R. N., Effects of radiation on unsteady Couette flow between two vertical parallel plates with ramped wall temperature, International Journal of Computer Applications, 39, 34-42, (2012)
[25] Navier, C. L. M. H., Sur les lois dee mouvement des fluids, Mémoires de l’Académie Royale des Sciences de l’Institut de France, 6, 389-440, (1827)
[26] Fetecau, C.; Fetecau, C.; Rana, M., General solutions for the unsteady flow of second-grade fluids over an infinite plate that applies arbitrary shear to the fluid, Zeitschrift für Naturforschung—Section A: Journal of Physical Sciences, 66, 12, 753-759, (2011) · doi:10.5560/ZNA.2011-0044
[27] Hayat, T.; Khan, I.; Ellahi, R.; Fetecau, C., Some MHD flows of a second grade fluid through the porous medium, Journal of Porous Media, 11, 4, 389-400, (2008) · doi:10.1615/JPorMedia.v11.i4.50
[28] 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
[29] David Maxim Gururaj, A.; Anjali Devi, S. P., MHD boundary layer flow with forced convection past a nonlinearly stretching surface with variable temperature and nonlinear radiation effects, International Journal of Development Research, 4, 75-80, (2014)
[30] Fetecau, C.; Rana, M.; Fetecau, C., Radiative and porous effects on free convection flow near a vertical plate that applies shear stress to the fluid, Zeitschrift für Naturforschung—Section A: Journal of Physical Sciences, 68, 1-2, 130-138, (2013) · doi:10.5560/ZNA.2012-0083
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.