Hostname: page-component-745bb68f8f-5r2nc Total loading time: 0 Render date: 2025-01-11T23:42:48.116Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow of a Second Grade Fluid over a Stretching Surface with Newtonian Heating

Published online by Cambridge University Press:  22 March 2012

T. Hayat ,
Z. Iqbal  and
M. Mustafa
T. Hayat
Affiliation:
Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
Z. Iqbal
Affiliation:
Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan
M. Mustafa*
Affiliation:
Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad 44000, Pakistan
*
*Corresponding author (meraj_mm@hotmail.com)
Get access

Abstract

This article describes the boundary layer flow and heat transfer in a second grade fluid over a stretching sheet. Heat transfer analysis is carried out in the presence of a Newtonian heating. The partial differential systems have been transformed into the ordinary differential systems by appropriate relations. Homotopy analysis method (HAM) is used for the solutions. Graphical and tabulated results are presented to see the significance of influential parameters on the velocity and temperature fields. It is seen that temperature profiles and heat transfer rate significantly increase by increasing the conjugate parameter (γ) for Newtonian heating.

Keywords

Heat transferSecond grade fluidNewtonian heatingStretching surface
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 1 , March 2012 , pp. 209 - 216
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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

REFERENCES

1. Tan, W. C. and Masuoka, T., “Stokes Problem for a Second Grade Fluid in a Porous Half Space with Heated Boundary,” International Journal of Nonlinear Mechanics, 40, pp. 515–522 (2005).CrossRefGoogle Scholar
2. Nazar, M., Fetecau, C., Vieru, D. and Fetecau, C., “New Exact Solutions Corresponding to the Second Problem of Stokes for Second Grade Fluids,” Nonlinear Analysis: Real World Applications, 11, pp. 584–591 (2010).Google Scholar
3. Hayat, T., Mustafa, M. and Pop, I., “Heat and Mass Transfer for Soret and Dufour's Effect on Mixed Convection Boundary Layer Flow over a Stretching Vertical Surface in a Porous Medium Filled with a Viscoelastic Fluid,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 1183–1196 (2010).CrossRefGoogle Scholar
4. Fetecau, C. and Fetecau, C., “Starting Solutions for the Motion of a Second Grade Fluid Due to Longitudnal and Torsional Oscillations of a Circular Cylinder,” International Journal of Engineering Science, 44, pp. 788–796 (2006).CrossRefGoogle Scholar
5. Cortell, R., “MHD Flow and Mass Transfer of an Electrically Conducting Fluid of Second Grade in a Porous Medium over a Stretching Sheet with Chemically Reactive Species,” Chemical Engineering Processing, 46, pp. 721–728, (2007).Google Scholar
6. Hayat, T., Iram, S., Javed, T. and Asghar, S., “Shrinking Flow of Second Grade Fluid in a Rotating Frame, an Analytic Solution,” Communications in Nonlinear Science and Numerical Simulation, 15, pp. 2932–2941 (2010).CrossRefGoogle Scholar
7. Hayat, T., Tichler, I. and Brenner, H., “Exact Solutions of Second Grade Fluid Aligned MHD Fluid with Prescribed Vorticity,” Nonlinear Analysis: Real World Applications, 10, pp. 2117–2126 (2009).Google Scholar
8. Hayat, T., Naeem, I., Ayub, M., Asghar, S. and Khalique, C. M., “Exact Solutions of Second Grade Aligned MHD Fluid with Prescribed Velocity,” Nonlinear Analysis: Real World Applications, 10, pp. 2117–2126 (2009).Google Scholar
9. Asghar, S., Hayat, T. and Ariel, P. D., “Unsteady Coutte Flows in a Second Grade Fluid with Variable Material Properties,” Communications in Nonlinear Science and Numerical Simulation, 14, pp. 154 (2009).CrossRefGoogle Scholar
10. Hayat, T., Nawaz, M., Sajid, M. and Asghar, S., “The Effect of Thermal Radiation on the Flow of a Second Grade Fluid,” Computers and Mathematics with Applications, 58, pp. 369–379 (2009).CrossRefGoogle Scholar
11. Mushtaq, M., Asghar, S. and Hossain, M. A., “Mixed Convection Flow of Second Grade Fluid Along a Vertical Stretching Flat Surface with Variable Surface Temperature,” Heat and Mass Transfer, 43, pp. 1049–1061 (2007).Google Scholar
12. Nazar, R. and Latip, N. A., “Numerical Investigation of Three-Dimensional Boundary Layer Flow Due to a Stretching Surface in a Viscoelastic Fluid,” European Journal of Scientific Research, 29, pp. 509– (2009).Google Scholar
13. Hayat, T., Mustafa, M. and Sajid, M., “Influence of Thermal Radiation on Blasius Flow of a Second Grade Fluid,” Zeitschrift Fur Naturforsch, 64a, pp. 827–833 (2009).CrossRefGoogle Scholar
14. Hayat, T. and Nawaz, M., “Magnetohydrodynamic Three-Dimensional Flow of a Second-Grade Fluid with Heat Transfer,” Zeitschrift Fur Naturforsch, 65, pp. 683–691 (2010).CrossRefGoogle Scholar
15. Abel, M. S., Mahesha, N. and Malipatil, S. B., “Heat Transfer Due to MHD Slip Flow of a Second-Grade Liquid Over a Stretching Sheet Through a Porous Medium with Non Uniform Heat Source/Sink,” Chemical Engineering Communications, 198, pp. 191–213 (2011).Google Scholar
16. Merkin, J. H., “Natural-Convection Boundary-Layer Flow on a Vertical Surface with Newtonian Heating,” International Journal of Heat and Fluid Flow, 15, pp. 392–398 (1994).Google Scholar
17. Lesnic, D., Ingham, D. B. and Pop, I., “Free Convection Boundarylayer Flow Along a Vertical Surface in a Porous Medium with Newtonian Heating,” International Journal of Heat and Mass Transfer, 42, pp. 2621–2627 (1999).Google Scholar
18. Lesnic, D., Ingham, D. B. and Pop, I., “Free Convection from a Horizontal Surface in a Porous Medium with Newtonian Heating,” Journal of Porous Media, 3, pp. 227–235 (2000).CrossRefGoogle Scholar
19. Lesnic, D., Ingham, D. B., Pop, I. and Storr, C., “Free Convection Boundary-Layer Flow Above a Nearly Horizontal Surface in a Porous Medium with Newtonian Heating,” Heat and Mass Transfer, 40, pp. 665–672 (2004).Google Scholar
20. Pop, I., Lesnic, D. and Ingham, D. B., “Asymptotic Solutions for the Free Convection Boundary-Layer Flow Along a Vertical Surface in a Porous Medium with Newtonian Heating,” Hybrid Methods in Engineering, 2, p. 31 (2000).Google Scholar
21. Salleh, M. Z., Nazar, R. and Pop, I., “Boundary Layer Flow and Heat Transfer over a Stretching Sheet with Newtonian Heating,” Journal of the Taiwan Institute of Chemical Engineers, 41, pp. 651–655 (2010)Google Scholar
22. Chaudhary, R. C. and Jain, P., “An Exact Solution to the Unsteady Free Convection Boundary Layer Flow Past an Impulsive Started Vertical Surface with Newtonian Heating,” Journal of Engineering Physics, 80, pp. 954–960 (2007).Google Scholar
23. Salleh, M. Z., Nazar, R. and Pop, I., “Forced Convection Boundary Layer Flow at a Forward Stagnation Point with Newtonian Heating,” Chemical Engineering Communication, 196, pp. 987–996 (2009).CrossRefGoogle Scholar
24. Liao, S. J., “Notes on the Homotopy Analysis Method: Some Definitions and Theorems,” Communication Non-linear Science and Numerical Simulation, 14, pp. 983–997 (2009).Google Scholar
25. Liao, S. J., “On the Relationship Between the Homotopy Analysis Method and Euler Transform,” Communication Non-linear Science and Numerical Simulation, 15, pp. 1421–1431 (2010).CrossRefGoogle Scholar
26. Kousar, N. and Liao, S. J., “Series Solution of Non-Similarity Boundary-Layer Flows over a Porous Wedge,” Transport in Porous Media, 83, pp. 397–412 (2010).CrossRefGoogle Scholar
27. Abbasbandy, S. and Shivanian, E., “Prediction of Multiplicity of Solutions of Nonlinear Boundary Value Problems: Novel Application of Homotopy Analysis Method,” Communication Non-linear Science and Numerical Simulation, 15, pp. 3830–3846 (2010).CrossRefGoogle Scholar
28. Abbasbandy, S. and Shirzadi, A., “A New Application of the Homotopy Analysis Method: Solving the Sturm—Liouville Problems,” Communication Non-linear Science and Numerical Simulation, 16, pp. 112–126 (2011).Google Scholar
29. Hashim, I., Abdulaziz, O. and Momani, S., “Homotopy Analysis Method for Fractional IVPs,” Communication Non-linear Science and Numerical Simulation, 14, pp. 674–684 (2009).CrossRefGoogle Scholar
30. Bataineh, A. S., Noorani, M. S. M. and Hashim, I., “On a New Reliable Modification of Homotopy Analysis Method,” Communication Non-linear Science and Numerical Simulation, 14, pp. 409–423 (2009).CrossRefGoogle Scholar
31. Bataineh, A. S., Noorani, M. S. M. and Hashim, I., “Homotopy Analysis Method for Singular Ivps of Emden— Fowler Type,” Communication Non-linear Science and Numerical Simulation, 14, pp. 1121–1131 (2009).CrossRefGoogle Scholar
32. Hayat, T., Qasim, M. and Abbas, Z., “Homotopy Solution for Unsteady Three-Dimensional MHD Flow and Mass Transfer in a Porous Space,” Communication Non-linear Science and Numerical Simulation, 15, pp. 2375–2387 (2010).Google Scholar
33. Hayat, T., Mustafa, M. and Mesloub, S., “Mixed Convection Boundary Layer Flow over a Stretching Surface Filled with a Maxwell Fluid in Presence of Soret and Dufour Effects,” Zeitschrift Fur Naturforsch, 65, pp. 401–410 (2010).CrossRefGoogle Scholar
34. Hayat, T., Mustafa, M. and Asghar, S., “Unsteady Flow with Heat and Mass Transfer of a Third Grade Fluid over a Stretching Surface in the Presence of Chemical Reaction,” Non-linear Analysis: Real World Applications, 11, pp. 3186–3197 (2010).Google Scholar
35. Hayat, T. and Mustafa, M., “Influence of Thermal Radiation on the Unsteady Mixed Convection Flow of a Jeffrey Fluid over a Stretching Sheet,” Zeitschrift Fur Naturforsch, 65, pp. 711–719 (2010).CrossRefGoogle Scholar