Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T15:58:44.242Z Has data issue: false hasContentIssue false
  • English
  • Français

MHD Natural Convection Heat and Mass Transfer Flow Past a Time Dependent Moving Vertical Plate with Ramped Temperature in a Rotating Medium with Hall Effects, Radiation and Chemical Reaction

Published online by Cambridge University Press:  21 October 2014

G. S. Seth  and
S. Sarkar
G. S. Seth*
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Dhanbad, India
S. Sarkar
Affiliation:
Department of Applied Mathematics, Indian School of Mines, Dhanbad, India
*
* Corresponding author ([email protected]
Get access

Abstract

An investigation of unsteady hydromagnetic natural convection heat and mass transfer flow of an electrically conducting, viscous, incompressible and optically thick radiating fluid past an impulsively moving infinite vertical plate embedded in a uniform porous medium in a rotating system with Hall effects in the presence of homogeneous first order chemical reaction is carried out when temperature of the plate has a temporarily ramped profile. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Expressions for skin friction due to primary and secondary flows and Nusselt number are derived for both ramped temperature and isothermal plates. Expression for Sherwood number is also derived. The numerical values of primary and secondary fluid velocities, fluid temperature and species concentration are displayed graphically whereas those of skin friction are presented in tabular form for various values of pertinent flow parameters. In order to highlight the influence of ramped temperature distribution within the plate on the flow-field, the fluid flow past a ramped temperature plate is compared with the one past an isothermal plate.

Keywords

Hall currentCoriolis forceChemical reactionRamped wall temperature
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 1 , February 2015 , pp. 91 - 104
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Eckert, E. R. and Drake, R. M., Analysis of Heat and Mass Transfer, McGraw Hill, New York (1972).Google Scholar
2.Gebhart, B., Jaluria, Y., Mahajan, R. L. and Sammakia, B., Buoyancy Induced Flow and Transport, CRC Press, New York (1998).Google Scholar
3.Nield, D. A. and Bejan, A., Convection in Porous Media, 3rd Edition, Springer, New York (2006).Google Scholar
4.Pop, I. and Ingham, D. B., Convective Heat Transfer: Mathematical and Computational Modelling of Viscous Fluids and Porous Media, Pergamon, Oxford (2001).Google Scholar
5.Incropera, F. P., Bergman, T. L., Lavine, A. S. and Dewitt, D. P., Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York (2011).Google Scholar
6.Hossain, M. A. and Mandal, A. C., “Mass Transfer Effects on the Unsteady Hydromagnetic Free Convection Flow Past an Accelerated Vertical Porous Plate,” Journal of Physics D: Applied Physics, 18, pp. 163–169 (1985).CrossRefGoogle Scholar
7.Jha, B. K., “MHD Free Convection and Mass Transform Flow through a Porous Medium,” Astrophysics and Space Science, 175, pp. 283–289 (1991).Google Scholar
8.Ibrahim, F. S., Hassanien, I. A. and Bakr, A. A., “Unsteady Magnetohydrodynamic Micropolar Fluid Flow and Heat Transfer over a Vertical Porous Plate through a Porous Medium in the Presence of Thermal and Mass Diffusion with a Constant Heat Source,” Canadian Journal of Physics, 82, pp. 775–790 (2004).CrossRefGoogle Scholar
9.Chamkha, A. J., “Unsteady MHD Convective Heat and Mass Transfer past a Semi-Infinite Vertical Permeable Moving Plate with Heat Absorption,” International Journal of Engineering Science, 42, pp. 217–230 (2004).CrossRefGoogle Scholar
10.Eldabe, N. T. M., Elbashbeshy, E. M. A., Hasanin, W. S. A. and Elsaid, E. M., “Unsteady Motion of MHD Viscous Incompressible Fluid with Heat and Mass Transfer through Porous Medium Near a Moving Vertical Plate,” International Journal of Energy and Technology, 3, pp. 1–11 (2011).Google Scholar
11.Seddeek, M. A., “Effects of Radiation and Variable Viscosity on a MHD Free Convection Flow Past a Semi-Infinite Flat Plate with an Aligned Magnetic Field in the Case of Unsteady Flow,” International Journal of Heat and Mass Transfer, 45, pp. 931–935 (2002).CrossRefGoogle Scholar
12.Viskanta, R. and Grosh, R. J., “Boundary Layer in Thermal Radiation Absorbing and Emitting Media,” International Journal of Heat and Mass Transfer, 5, pp. 795–806 (1962).Google Scholar
13.Raptis, A. and Massalas, C. V., “Magnetohydrody-namic Flow Past a Plate by the Presence of Radiation,” Heat and Mass Transfer, 34, pp. 107–109 (1998).Google Scholar
14.Chamkha, A. J., “Thermal Radiation and Buoyancy Effects on Hydromagnetic Flow over an Accelerating Permeable Surface with Heat Source or Sink,” International Journal of Engineering Science, 38, pp. 1699–1712 (2000).Google Scholar
15.Cookey, C. I., Ogulu, A. and Omubo-Pepple, V. B., “Influence of Viscous Dissipation and Radiation on Unsteady MHD Free Convection Flow Past an Infinite Heated Vertical Plate in a Porous Medium with Time-Dependent Suction,” International Journal of Heat and Mass Transfer, 46, pp. 2305–2311 (2003).Google Scholar
16.Prasad, V. R., Reddy, N. B. and Muthucumaraswamy, R., “Transient Radiative Hydromagnetic Free Convection Flow Past an Impulsively Started Vertical Plate with Uniform Heat and Mass Flux,” Theoretical and Applied Mechanics, 33, pp. 31–63 (2006).CrossRefGoogle Scholar
17.Chandrakala, P. and Bhaskar, P. N., “Thermal Radiation Effects on MHD Flow Past a Vertical Oscillating Plate,” International Journal of Applied Mechanics and Engineering, 14, pp. 379–358 (2009).Google Scholar
18.Sparrow, E. M. and Cess, R. D., Radiation Heat Transfer, Brooks/Cole, Belmont, California (1966).Google Scholar
19.Howell, J. R., Siegel, R. and Mengûç, M. P., Thermal Radiation and Heat Transfer, 5th Edition, CRC Press, New York (2010).CrossRefGoogle Scholar
20.Chambré, P. L. and Young, J. D., “On the Diffusion of a Chemically Reactive Species in a Laminar Boundary Layer Flow,” Physics of Fluids, 1, pp. 48–54 (1958).Google Scholar
21.Das, U. N., Deka, R. K. and 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, pp. 284–287 (1994).Google Scholar
22.Muthucumarswamy, R. and Ganesan, P., “On Impulsive Motion of a Vertical Plate with Heat Flux and Diffusion of Chemically Reactive Species,” Forschung im Ingenieurwesen, 66, pp. 17–23 (2000).CrossRefGoogle Scholar
23.Singh, K. D. and Kumar, R., “Effects of Chemical Reactions on Unsteady MHD Free Convection and Mass Transfer for Flow past a Hot Vertical Porous Plate with Heat Generation/Absorption through Porous Medium,” Indian Journal of Physics, 84, pp. 93–106 (2010).Google Scholar
24.Pal, D. and Talukdar, B., “Combined Effects of Joule Heating and Chemical Reaction on Unsteady Mag-netohydrodynamic Mixed Convection of a Viscous Dissipating Fluid over a Vertical Plate in Porous Media with Thermal Radiation,” Mathematical and Computer Modelling, 54, pp. 3016–3036 (2011).Google Scholar
25.Singh, A. K., “MHD Free Convection Flow Past an Accelerated Vertical Porous Plate in a Rotating Fluid,” Astrophysics and Space Science, 103, pp. 155–163 (1984).Google Scholar
26.Raptis, A. A. and Singh, A. K., “Rotation Effects on MHD Free-Convection Flow Past an Accelerated Vertical Plate,” Mechanics Research Communications, 12, pp. 31–40 (1985).Google Scholar
27.Kythe, P. K. and Puri, P., “Unsteady MHD Free Convection Flows on a Porous Plate with Time-Dependent Heating in a Rotating Medium,” Astrophysics and Space Science, 143, pp. 51–62 (1988).CrossRefGoogle Scholar
28.Tokis, J. N., “Free Convection and Mass Transfer Effects on the Magnetohydrodynamic Flows near a Moving Plate in a Rotating Medium,” Astrophysics and Space Science, 144, pp. 291–301 (1988).Google Scholar
29.Nanousis, N., “Thermal Diffusion Effects on MHD Free Convective and Mass Transfer Flow Past a Moving Infinite Vertical Plate in a Rotating Fluid,” Astrophysics and Space Science, 191, pp. 313–322 (1992).Google Scholar
30.Singh, A. K., Singh, N. P., Singh, U. and Singh, H., “Convective Flow Past an Accelerated Porous Plate in Rotating System in Presence of Magnetic Field,” International Journal of Heat and Mass Transfer, 52, pp. 3390–3395 (2009).Google Scholar
31.Malhotra, C. P., Mahajan, R. L., Sampath, W. S., Barth, K. L. and Enzenroth, R. A., “Control of Temperature Uniformly During Manufacture of Stable Thin-Film Photo-Voltaic Devices,” International Journal of Heat and Mass Transfer, 49, pp. 2840–2850 (2006).Google Scholar
32.Antonopoulos, K. A. and Democritou, F., “Experimental and Numerical Study of Unsteady Non-Periodic Wall Heat Transfer Under Step, Ramp and Cosine Temperature Perturbations,” International Journal of Energy Research, 18, pp. 563–579 (1994).Google Scholar
33.Kuczmarski, M. A. and Gokoglu, S. A., “Buoyancy Suppression in Gases at High Temperature,” International Journal of Heat and Fluid Flow, 28, pp. 496–511 (2007).Google Scholar
34.Schetz, J. A., “On the Approximate Solution of Viscous Flow Problems,” Journal of Applied Mechanics, 30, pp. 263–268 (1963).Google Scholar
35.Kao, T. T., “Laminar Free Convective Heat Transfer Response along a Vertical Flat Plate with Step Jump in Surface Temperature,” Letters in Heat and Mass Transfer, 2, pp. 419–428 (1975).Google Scholar
36.Lee, S. and Yovanovich, M. M., “Laminar Natural Convection from a Vertical Plate with a Step Change in Wall Temperature,” Journal of Heat Transfer, 113, pp. 501–504 (1991).CrossRefGoogle Scholar
37.Chandran, P., Sacheti, N. C. and Singh, A. K., “Natural Convection near a Vertical Plate with Ramped Wall Temperature,” Heat and Mass Transfer, 41, pp. 459–464 (2005).Google Scholar
38.Patra, R. R., Das, S., Jana, R. N. and Ghosh, S. K., “Transient Approach to Radiative Heat Transfer Free Convection Flow with Ramped Wall Temperature,” Journal of Applied Fluid Mechanics, 5, pp. 9–13 (2012).Google Scholar
39.Seth, G. S., Ansari, Md. S. and Nandkeolyar, R., “MHD Natural Convection Flow with Radiative Heat Transfer Past an Impulsively Moving Plate with Ramped Wall Temperature,” Heat and Mass Transfer, 47, pp. 551–561(2011).CrossRefGoogle Scholar
40.Narahari, M., “Transient Free Convection Flow Between Long Vertical Parallel Plates with Ramped Wall Temperature at One Boundary in the Presence of Thermal Radiation and Constant Mass Diffusion,” Meccanica, 47, pp. 1961–1976 (2012).Google Scholar
41.Nandkeolyar, R., Das, M. and Sibanda, P., “Unsteady Hydromagnetic Heat and Mass Transfer Flow of a Heat Radiating and Chemically Reactive Fluid Past a Flat Porous Plate with Ramped Wall Temperature,” Mathematical Problems in Engineering, 2013 Article ID 381806 (2013).Google Scholar
42.Sutton, G. W. and Sherman, A., Engineering Mag-netohydrodynamics, McGraw-Hill, New York (1965).Google Scholar
43.Takhar, H. S., Roy, S. and Nath, G., “Unsteady Free Convection Flow over an Infinite Vertical Porous Plate Due to the Combined Effects of Thermal and Mass Diffusion, Magnetic Field and Hall Currents,” Heat and Mass Transfer, 39, pp. 825–834 (2003).CrossRefGoogle Scholar
44.Saha, L. K., Siddiqa, S. and Hossain, M. A., “Effect of Hall Current on MHD Natural Convection Flow from Vertical Permeable Flat Plate with Uniform Surface Heat Flux,” Applied Mathematics and Mechanics English Edition, 32, pp. 1127–1146 (2011).Google Scholar
45.Seth, G. S., Mahato, G. K. and 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 and Technology, 5, pp. 1–12 (2013).Google Scholar
46.Cramer, K. R. and Pai, S. I., Magnetofluid Dynamics for Engineers and Applied Physicists, McGraw Hill, New York (1973).Google Scholar
47.Symeonidis, V., Karniadakis, G. and Caswell, B., “Schmidt Number Effects in Simulation of Polymer Dissipative Particle Dynamics,” The Journal of Chemical Physics, 125, Article Id: 184902 (2006).CrossRefGoogle ScholarPubMed