Radiative Maxwell Fluid Flow with Variable Thermal Conductivity due to a Stretching Surface in a Porous Medium
Publication: Journal of Aerospace Engineering
Volume 27, Issue 5
Abstract
This research examines the thermal radiation effects on the steady flow of Maxwell fluid over a nonisothermal stretched surface. An incompressible fluid fills the semi-infinite porous medium. The thermal conductivity is taken in a time-dependent fashion. Boundary layer approximations are used for the momentum and energy equations. The governing nonlinear partial differential equations are reduced to ordinary differential equations by employing a similarity transformation. The solutions of velocity and temperature are presented by using the homotopy analysis method (HAM). The variations of various interesting embedded parameters of velocity and temperature are displayed and discussed. The values of the local Nusselt number have been compared to the existing numerical solution in a limited sense.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
S. A. Shehzad and T. Hayat are grateful to the Higher Education Commission of Pakistan (HEC) for the financial support.
References
Abbas, Z., Wang, Y., Hayat, T., and Oberlack, M. (2010). “Mixed convection in the stagnation-point flow of a Maxwell fluid towards a vertical stretching surface.” Nonlinear Anal. Real World Appl., 11(4), 3218–3228.
Abbasbandy, S., and Shirzadi, A. (2011). “A new application of the homotopy analysis method: Solving the Sturm-Liouville problems.” Comm. Nonlinear Sci. Num. Simu., 16(1), 112–126.
Ahmad, A., and Asghar, S. (2011). “Flow of a second-grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field.” Appl. Math. Lett., 24(11), 1905–1909.
Cheng, P., and Minkowycz, W. J. (1977). “Free convection about a vertical plate embedded in a porous medium with application to heat transfer from a dike.” J. Geophys. Res., 82(14), 2040–2044.
Chiam, T. C. (1996). “Heat transfer with variable conductivity in a stagnation-point flow towards a stretching sheet.” Int. Commu. Heat Mass Transfer, 23(2), 239–248.
Chiam, T. C. (1998). “Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet.” Acta Mech., 129(1–2), 63–72.
Crane, L. J. (1970). “Flow past a stretching plate.” ZAMP, 21(4), 645–647.
Fetecau, C., Athar, A., and Fetecau, C. (2009). “Unsteady flow of a generalized Maxwell fluid with fractional derivative due to a constantly accelerating plate.” Comput. Math. Appl., 57(4), 596–603.
Ghosh, S. K., and Beg, O. A. (2008). “Theoretical analysis of radiative effects on transient free convection heat transfer past a hot vertical surface in porous media.” Nonlinear Anal. Model. Control, 13, 419–432.
Ghosh, S. K., and Shit, G. C. (2012). “Mixed convection MHD flow of viscoelastic fluid in a porous medium past a hot vertical plate.” World J. Mech., 2(5), 262–271.
Hayat, T., and Qasim, M. (2010). “Influence of thermal radiation and Joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis.” Int. J. Heat Mass Transfer, 53(21–22), 4780–4788.
Hayat, T., Abbas, Z., and Ali, N. (2008). “MHD flow and mass transfer of a upper-convected Maxwell fluid past a porous shrinking sheet with chemical reaction species.” Phys. Lett. A, 372(26), 4698–4704.
Hayat, T., Abbas, Z., Pop, I., and Asghar, S. (2010). “Effects of radiation and magnetic field on the mixed convection stagnation-point flow over a vertical stretching sheet in a porous medium.” Int. J. Heat Mass Transfer, 53(1–3), 466–474.
Hayat, T., Shehzad, S. A., and Qasim, M. (2011). “Mixed convection flow of a micropolar fluid with radiation and chemical reaction.” Int. J. Numer. Meth. Fluids, 67(11), 1418–1436.
Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. (2012). “Radiative flow of Jeffery fluid in a porous medium with power law heat flux and heat source.” Nucl. Eng. Des., 243, 15–19.
Jamil, M., and Fetecau, C. (2010). “Helical flows of Maxwell fluid between coaxial cylinders with given shear stresses on the boundary.” Nonlinear Anal. Real World Appl., 11(5), 4302–4311.
Khan, N. A., Jamil, M., and Ara, A. (2012). “Approximate solutions to time-fractional Schrödinger equation via homotopy analysis method.” Math. Phys., 11.
Lai, F. C. (1991). “Coupled heat and mass transfer by mixed convection from a vertical plate in a saturated porous medium.” Int. Commun. Heat Mass Transfer, 18(1), 93–106.
Layek, G. C., Mukhopadhyay, S., and Samad, A. (2007). “Heat and mass transfer analysis for boundary layer stagnation point flow towards a heated porous stretching sheet with heat absorption/generation and suction/blowing.” Int. Commun. Heat Mass Transfer, 34(3), 347–356.
Liao, S. J. (2003). Beyond perturbation: Introduction to homotopy analysis method, Chapman and Hall, CRC Press, Boca Raton, FL.
Liao, S. J. (2006). “Series solution for unsteady boundary-layer flows over a stretching flat plate.” Stud. Appl. Math., 117(3), 239–263.
Mebine, P., and Adigio, E. M. (2011). “Effects of thermal radiation on transient MHD free convection flow over a vertical surface embedded in a porous medium with periodic boundary temperature.” Math. Aet., 1, 245–261.
Mukhopadhyay, S., and Layek, G. C. (2012). “Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink.” Meccanica, 47(4), 863–876.
Nadeem, S., Hussain, M., and Naz, M. (2010). “MHD stagnation flow of a micropolar fluid through a porous medium.” Mecc., 45(6), 869–880.
Pal, D., and Mondal, H. (2011). “The influence of thermal radiation on hydromagnetic Darcy-Forchheimer mixed convection flow past a stretching sheet embedded in a porous medium.” Mecc., 46(4), 739–753.
Patowary, G. (2012). “Effect of variable viscosity and thermal conductivity of micropolar fluid in a porous channel in presence of magnetic field.” Int. J. Basic Sci. Social Sci., 1, 69–77.
Rashidi, M. M., Pour, S. A. M., and Abbasbandy, S. (2011). “Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation.” Comm. Nonlinear Sci. Num. Simul., 16(4), 1874–1889.
Salleh, M. Z., Mohamed, N., Khiaruddin, R., Khasi’ie, N. S., Nazar, R., and Pop, I. (2012). “Free convection over a permeable horizontal flat plate embedded in a porous medium with radiation effects and mixed thermal boundary conditions.” J. Math. Stat., 8(1), 122–128.
Sharma, P. R., and Singh, G. (2009). “Effects of variable thermal conductivity and heat source/sink on MHD flow near a stagnation point on a linearly stretching sheet.” J. Appl. Fluid Mech., 2, 13–21.
Subhas, A., and Mahesha, N. (2008). “Heat transfer in MHD viscoelastic fluid flow over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation.” Appl. Math. Model., 32(10), 1965–1983.
Subhas, A., Parsad, K. V., and Mahaboob, A. (2005). “Buoyancy force and thermal radiation effects in MHD boundary layer viscoelastic flow over continuously moving stretching surface.” Int. J. Thermal Sci., 44(5), 465–476.
Vyas, P., and Rai, A. (2010). “Radiative flow with variable thermal conductivity over a non-isothermal stretching sheet in a porous medium.” Int. J. Contemp. Math. Sci., 5, 2685–2698.
Vyas, P., and Srivastava, N. (2012). “On dissipative radiative MHD boundary layer flow in a porous medium over a non-isothermal stretching sheet.” J. Appl. Fluid Mech., 5(4), 23–31.
Wang, S., and Tan, W. C. (2008). “Stability analysis of double-diffusive convection of Maxwell fluid in a porous medium heated from below.” Phys. Lett. A, 372(17), 3046–3050.
Yao, B., and Chen, J. (2009). “Series solution to the Falkner--Skan equation with stretching boundary.” Appl. Math. Comput., 208(1), 156–164.
Zierep, J., and Fetecau, C. (2007). “Energetic balance for the Rayleigh--Stokes problem of a Maxwell fluid.” Int. J. Eng. Sci., 45(2–8), 617–627.
Information & Authors
Information
Published In
Journal of Aerospace Engineering
Volume 27 • Issue 5 • September 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Aug 29, 2012
Accepted: Jan 11, 2013
Published online: May 12, 2014
Published in print: Sep 1, 2014
Discussion open until: Oct 12, 2014
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.