Effects of Thermal and Mass Stratification on Unsteady MHD Flow Past an Oscillating Vertical Plate Embedded in a Porous Medium with Variable Surface Conditions
Abstract
oscillating vertically in its own axis in which it is embedded in a porous medium with variable heat and mass diffusion. For concentration, temperature and velocity fields, the non-dimensional governing equations are solved using the Laplace transform method for the unitary Prandtl and Schmidt numbers, when the plate is oscillating in its own plane harmonically. Numerical computations are carried out and presented in graphs for different physical parameters like thermal Grashof number, phase angle, mass Grashof number, stratification
parameter and time on concentration, velocity, temperature, plate heat flux, mass flux and skin friction. The findings of this study can be utilized to enhance comprehension of MHD flow on vertical oscillating plate in combined stratified environments. Significant findings arising from the mass and thermal stratification are compared to the scenario in which stratification is absent.
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References
V.M. Soundalgekar, U.N. Das, and R.K. Deka, ”Free convection effects on MHD flow past an infinite vertical oscillating plate with constant heat flux,” Indian J. Math. 39, 195-202 (1997).
J.S Park, and J.M. Hyun, ”Transient behavior of vertical buoyancy layer in a stratified fluid,” Intl. J. Heat Mass Transfer, 41, 4393-4397 (1998). https://doi.org/10.1016/S0017-9310(98)00175-6
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, 121, 1091-1094 (1999). https://doi.org/10.1115/1.2826063
J.S. Park, ”Transient buoyant flows of a stratified fluid in a vertical channel,” KSME. Intl. J. 15, 656-664 (2001). https://doi.org/10.1007/BF03184382
A. Shapiro, and E. Fedorovich, ”Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid,” J. Fluid Mech. 498, 333-352 (2004). https://doi.org/10.1017/S0022112003006803
E. Magyari, I. Pop, and B. Keller, ”Unsteady free convection along an infinite vertical flat plate embedded in a stably stratified fluid- saturated porous medium,” Transport in Porous Media, 62, 233-249 (2006). https://doi.org/10.1007/s11242-005-1292-6
C.Y. Cheng, ”Double-diffusive natural convection along a vertical wavy truncated cone in non-newtonian fluid saturated porous media with thermal and mass stratification,” Int. Commun. Heat Mass Transf. 35(8), 985–990 (2008). https://doi.org/10.1016/j.icheatmasstransfer.2008.04.007
R.C. Chaudhary, and A. Jain, ”MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium,” Theoret. Appl. Mech. 36(1), 1-27 (2009). http://dx.doi.org/10.2298/TAM0901001C
C.Y. Cheng, ”Combined heat and mass transfer in natural convection flow from a vertical wavy surface in a power-law fluid saturated porous medium with thermal and mass stratification,” Int. Commun. Heat Mass Transf. 36(4), 351–356 (2009). http://dx.doi.org/10.1016/j.icheatmasstransfer.2009.01.003
B.C. Neog, and R.K. Deka, ”Unsteady natural convection flow past an accelerated vertical plate in a thermally stratified fluid,” Theoret. Appl. Mech. 6(4), 261-274 (2009). https://doi.org/10.2298/TAM0904261D
S. Gurminder, P.R. Sharma, and A.J. Chamkha, ”Effect of thermally stratified ambient fluid on MHD convective flow along a moving nonisothermal vertical plate, Intl. J. Phy. Sci. 5(3), 208-215 (2010). https://doi.org/10.5897/IJPS.9000199
R.K. Deka, and A. Bhattacharya, ”Magneto-Hydrodynamic (MHD) flow past an infinite vertical plate immersed in a stably stratified fluid,” International Journal of the Physical Sciences, 6(24), 5831-5836 (2011). https://doi.org/10.5897/IJPS11.011
R. Muthucumaraswamy, and V. Visalakshi, ”Radiative flow past an exponentially accelerated vertical plate with variable temperature and mass diffusion,” Int. J. of Enng. Annals. of Faculty Engineering Hunedoara, 9, 137-140 (2011). https://annals.fih.upt.ro/pdf-full/2011/ANNALS-2011-2-26.pdf
A.G.V. Kumar, S.V.K. Varma, and R. Mohan, ”Chemical reaction and radiation effects on MHD free convective flow past an exponentially accelerated vertical plate with variable temperature and variable mass diffusion,” Annals of the Faculty of Engineering Hunedoara, 10(2), 195 (2012). https://annals.fih.upt.ro/pdf-full/2012/ANNALS-2012-2-32.pdf
R.K. Deka, and A. Paul, ”Convectively driven flow past an infinite moving vertical cylinder with thermal and mass stratification,” Pramana, 81, 641–665 (2013). http://dx.doi.org/10.1007/s12043-013-0604-6
H. Kumar, and R.K. Deka, ”Thermal and mass stratification effects on unsteady flow past an accelerated infinite vertical plate with variable temperature and exponential mass diffusion in porous medium,” East European Journal of Physics, (4), 87-97 (2023). https://doi.org/10.26565/2312-4334-2023-4-09
R.S. Nath, and R.K. Deka, ”Thermal and mass stratification effects on unsteady parabolic flow past an infinite vertical plate with exponential decaying temperature and variable mass diffusion in porous medium,” ZAMM-Journal of Applied Mathematics and Mechanics/Zeitschrift f¨ur Angewandte Mathematik und Mechanik, 104(6), e202300475 (2024). http://dx.doi.org/10.1002/zamm.202300475
R.S. Nath, R.K. Deka, ”Thermal and mass stratification effects on MHD nanofluid past an exponentially accelerated vertical plate through a porous medium with thermal radiation and heat source,” Int J Mod Phys B, 2550045. In press (2024). https://doi.org/10.1142/S0217979225500456
R.S. Nath, 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, 10(2), 92 (2024). https://doi.org/10.1007/s40819-024-01721-9
P. Das, R.K. Deka, ”Thermal and mass stratification effects on unsteady MHD parabolic flow past an infinite vertical plate with variable temperature and mass diffusion through porous medium,” East European Journal of Physics, 2: 181-191 (2024). https://doi.org/10.26565/2312-4334-2024-2-17
D. Sahu, R.K. Deka, ”Thermal and mass stratification effects on MHD flow past an accelerated vertical plate with variable temperature and exponential mass diffusion embedded in a porous medium,” East European Journal of Physics, 2: 161-171 (2024). https://doi.org/10.26565/2312-4334-2024-2-15
D. Sahu, R.K. Deka, ”Influences of thermal stratification and chemical reaction on MHD free convective flow along an accelerated vertical plate with variable temperature and exponential mass diffusion in a porous medium,” Heat Transfer, 2024; 1-24 (2024). https://doi.org/10.1002/htj.23106
R.B. Hetnarski, ”An algorithm for generating some inverse Laplace transforms of exponential form,” ZAMP, 26, 249-253 (1975). https://doi.org/10.1007/BF01591514
M. Abramowitz, I.A. Stegun, and R.H. Romer, ”Handbook of mathematical functions with formulas, graphs, and mathematical tables,” American Journal of Physics, 56(10), 958 (1988). https://doi.org/10.1119/1.15378
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