Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T03:11:35.889Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical Solution for Variable Viscosity and Internal Heat Generation Effects on Boundary Layer Flow Over an Exponentially Stretching Porous Sheet with Constant Heat Flux and Thermal Radiation

Published online by Cambridge University Press:  22 May 2014

A. M. Megahed
A. M. Megahed*
Affiliation:
Department of Mathematics, Faculty of Science, Benha University, Egypt
*
*[email protected]
Get access

Abstract

A numerical study has been carried out to analyze the constant heat flux, internal heat generation, variable viscosity and thermal radiation effects on the flow and heat transfer of a Newtonian fluid over an exponentially stretching porous sheet. Using a similarity transformation, the governing partial differential equations are transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by using an efficient Chebyshev spectral method. The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl number on velocity and temperature are discussed by using graphical approach. Moreover, numerical results indicate that in the presence of constant heat flux, the skin-friction coefficient as well as Nusselt number is strongly affected by the viscosity parameter, suction parameter, radiation parameter and the internal heat generation parameter.

Keywords

Newtonian fluidExponentially stretching sheetNumerical solutionVariable viscosityThermal radiationConstant heat flux
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 4 , August 2014 , pp. 395 - 402
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.Crane, L. J., “Flow Past a Stretching Plate,” Zeitschrift für angewandte Mathematik und Physik, 21, pp. 645–647 (1970).Google Scholar
2.Gupta, P. S. and Gupta, A. S., “Heat and Mass Transfer on a Stretching Sheet with Suction and Blowing,” The Canadian Journal of Chemical Engineering, 55, pp. 744–746 (1977).Google Scholar
3.Chen, C. K. and Char, M. I., “Heat Transfer of a Continuous Stretching Surface with Suction or Blowing,” Journal of Mathematical Analysis and Applications, 135, pp. 568–580 (1988).Google Scholar
4.Pop, I. and Na, T. Y., “Unsteady Flow Past a Stretching Sheet,” Mechanics Research Communications, 23, pp. 413–422 (1996).CrossRefGoogle Scholar
5.Cortell, R., “Viscous Flow and Heat Transfer over a Nonlinearly Stretching Sheet,” Applied Mathematics and Computation, 184, pp. 864–873 (2007).CrossRefGoogle Scholar
6.Hayat, T., Abbas, Z. and Javed, T., “Mixed Convection Flow of a Micropolar Fluid over a Non-Linearly Stretching Sheet,” Physics Letters A, 372, pp. 637–647 (2008).Google Scholar
7.El-Aziz, M. A., “Radiation Effect on the Flow and Heat Transfer over an Unsteady Stretching Sheet,” International Communications in Heat and Mass Transfer, 36, pp. 521–524 (2009).Google Scholar
8.Akyildiz, F. T. and Siginer, D. A., “Galerkin-Legendre Spectral Method for the Velocity and Thermal Boundary Layer over a Non-Linearly Stretching Sheet,” Nonlinear Analysis: Real World Applications, 11, pp. 735–741 (2010).Google Scholar
9.Megahed, A. M., “Variable Viscosity and Slip Velocity Effects on the Flow and Heat Transfer of a Power-Law Fluid over a Non-Linearly Stretching Surface with Heat Flux and Thermal Radiation,” Rheologica Acta, 51, pp. 841–847 (2012).CrossRefGoogle Scholar
10.Magyari, E. and Keller, B., “Heat and Mass Transfer in the Boundary Layers on an Exponentially Stretching Continuous Surface,” Journal of Physics D: Applied Physics, 32, pp. 577–585 (1999).CrossRefGoogle Scholar
11.ELbashbeshy, E. M. A., “Heat Transfer over an Exponentially Stretching Continuous Surface with Suction,” Archives of Mechanics, 53, pp. 643–651 (2001).Google Scholar
12.Partha, M. K., Murthy, and Rajasekhar, G. P., “Effects of Viscous Dissipation on the Mixed Convection Heat Transfer from an Exponentially Stretching Surface,” Heat and Mass Transfer, 41, pp. 360–366 (2005).CrossRefGoogle Scholar
13.Sajid, M. and Hayat, T., “Influence of Thermal Radiation on the Boundary Layer Flow Due to an Exponentially Stretching Sheet,” International Communications in Heat and Mass Transfer, 35, pp. 347–356 (2008).Google Scholar
14.Bidin, B. and Nazar, R., “Numerical Solution of the Boundary Layer Flow over an Exponentially Stretching Sheet with Thermal Radiation,” European Journal of Scientific Research, 33, pp. 710–717 (2009).Google Scholar
15.Nadeem, S., Zaheer, S. and Fang, T., “Effects of Thermal Radiation on the Boundary Layer Flow of a Jeffrey Fluid over an Exponentially Stretching Surface,” Numerical Algorithms, 57, pp. 187–205 (2011).CrossRefGoogle Scholar
16.Bhattacharyya, K., “Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet,” Chinese Physics Letters, 28, pp. 074701–1-074701-4 (2011).CrossRefGoogle Scholar
17.Rohni, A. M., Ahmad, S., Ismail, A. I. Md. and Pop, I., “Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Vertical Sheet with Suction,” International Journal of Thermal Sciences, 64, pp. 264–272 (2013).Google Scholar
18.Raptis, A., “Flow of a Micropolar Fluid Past a Continuously Moving Plate by the Presence of Radiation,” International Journal Heat and Mass Transfer, 41, pp. 2865–2866 (1998).Google Scholar
19.Raptis, A., “Radiation and Viscoelastic Flow,” International Communications Heat and Mass Transfer, 26, pp. 889–895 (1999).CrossRefGoogle Scholar
20.Dandapat, B. S., Santra, B. and Vajravelu, K., “The Effects of Variable Fluid Properties and Thermocapillarity on the Flow of a Thin Film on an Unsteady Stretching Sheet,” International Journal Heat and Mass Transfer, 50, pp. 991–996 (2007).Google Scholar
21.Mahmoud, M. A. A. and Megahed, A. M., “MHD Flow and Heat Transfer in a Non-Newtonian Liquid Film over an Unsteady Stretching Sheet with Variable Fluid Properties,” Canadian Journal of Physics, 87, pp. 1065–1071 (2009).Google Scholar
22.El-Gendi, S. E., “Chebyshev Solution of Differential, Integral and Integro-Differential Equations,” Computer Journal, 12, pp. 282–287 (1969).CrossRefGoogle Scholar
23.Magyari, E. and 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 Heat and Mass Transfer, 38, pp. 554–556 (2011).Google Scholar
24.Mostafa, A. A.Mahmoud, and Ahmed, , Megahed, M., “Non-Uniform Heat Generation Effect on Heat Transfer of a Non-Newtonian Power-Law Fluid over a Non-Linearly Stretching Sheet,” Meccanica, 47, pp. 1131–1139 (2012).Google Scholar