Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T01:20:42.588Z Has data issue: false hasContentIssue false

Radiative Flow of Jeffrey Fluid Through a Convectively Heated Stretching Cylinder

Published online by Cambridge University Press:  12 August 2014

T. Hayat
Affiliation:
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
S. Asad*
Affiliation:
Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
A. Alsaedi
Affiliation:
Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
F. E. Alsaadi
Affiliation:
Nonlinear Analysis and Applied Mathematics Research Group, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
*
*Corresponding author ([email protected])
Get access

Abstract

Two-dimensional flow of Jeffrey fluid by an inclined stretching cylinder with convective boundary condition is studied. In addition the combined effects of thermal radiation and viscous dissipation are taken into consideration. The developed nonlinear partial differential equations are reduced into the ordinary differential equations by suitable transformations. The governing equations are solved for the series solutions. The convergence of the series solutions for velocity and temperature fields is carefully analyzed. The effects of various physical parameters such as ratio of relaxation to retardation times, Deborah number, radiation parameter, Biot number, curvature parameter, local Grashof number, Prandtl number, Eckert number and angle of inclination are examined through graphical and numerical results of the velocity and temperature distributions.

Type
Research Article
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.Sakiadis, B. C., “Boundary-Layer Behavior on Continuous Solid Surfaces,” American Institute of Chemind Engineers, 7, pp. 2628 (1961).Google Scholar
2.Crane, L. J., “Flow Past a Stretching Plate,” Zeitschrift Fur Angewandte Mathematik Und Physik, 21, pp. 645647 (1970).Google Scholar
3.Bhattacharyya, K., Hayat, T. and Alsaedi, A., “Analytic Solution for Magnetohydrodynamic Boundary Layer Flow of Casson Fluid Over a Stretching/Shrinking Sheet With Wall Mass Transfer,” Chinese Physics B, 22, p. 024702 (2013).Google Scholar
4.Yasir, K., Abdou, M. A., Naeem, F., Ahmet, Y. and Wu, Q., “Numerical Solution of MHD Flow Over a Nonlinear Porous Stretching Sheet,” Iranian Journal of Chemistry and Chemical Engineering, 63, pp. 125132 (2013).Google Scholar
5.Parsa, A. B., Rashidi, M. M. and Hayat, T., “MHD Boundary-Layer Flow Over a Stretching Surface With Internal Heat Generation or Absorption,” Heat Transfer-Asian Research, DOI: 10.1002/htj.21054 (2013).Google Scholar
6.Turkyilmazoglu, M. and Pop, I., “Exact Analytical Solutions for the Flow and Heat Transfer Near the Stagnation Point on a Stretching/Shrinking Sheet in a Jeffrey Fluid,” International Journal Heat Mass Transfer, 57, pp. 8288 (2013).Google Scholar
7.Mustafa, M., Farooq, A. M., Hayat, T. and Alsaedi, A., “Numerical and Series Solutions for Stagnation-Point Flow of Nanofluid over an Exponentially Stretching Sheet,” PLOS ONE, 5, Doi:10.1371/j.p.0061859 (2013).Google Scholar
8.Hayat, T., Shehzad, A. S., Qasim, M. and Alsaedi, A., “Radiative Flow with Variable Thermal Conductivity in Porous Medium,” Zeitschrift füer Naturforsch, 67a, pp. 153159 (2012).Google Scholar
9.Nadeem, S., Hussain, A., Malik, Y. and Hayat, T., “Series Solutions for the Stagnation Flow of a Second Grade Fluid Over Shrinking Sheet,” Applied Mathematics and Mechanics,” 30, pp. 12551262 (2009).CrossRefGoogle Scholar
10.Aksoy, Y., Pakdemirli, M. and Khalique, M. C., “Boundary Layer Equations and Stretching Sheet Solutions for the Modified Second Grade Fluid,” International Journal Engineering Sciences, 45, pp. 829841 (2007).CrossRefGoogle Scholar
11.Lin, T. H. and Shih, P. Y., “Laminar Boundary Layer Heat Transfer Along Statics and Moving Cylinder,” Journal of the Chinese Institute Engineers, 3, pp. 7379 (1980).Google Scholar
12.Lin, T. H. and Shih, P. Y., “Buoyancy Effects on the Laminar Boundary Layer Heat Transfer Along Vertically Moving Cylinders,” Journal of the Chinese Institute Engineers, 4, pp. 4751 (1981).Google Scholar
13.Wang, Y. C., “Fluid Flow Due to Stretching Cylinder,” Physics Fluids, 31, pp. 466468 (1988).Google Scholar
14.Heckel, J. J., Chen, T. S. and Armaly, B. F., “Mixed Convection Along Slender Vertical Cylinders with Variable Surface Temperature,” International Journal Heat Mass Transfer, 32, pp. 14311442 (1989).CrossRefGoogle Scholar
15.Ishak, A., Nazar, R. and Pop, I., “Magnetohydrodynamic (MHD) Flow and Heat Transfer Due to a Stretching Cylinder,” Energy Conversion and Management, 49, pp. 32653269 (2008).Google Scholar
16.Ishak, A., Nazar, R. and Pop, I., “Uniform Suction/Blowing Effect on Flow and Heat Transfer Due to a Stretching Cylinder,” Applied Mathematics and Modelling, 32, pp. 20592066 (2008).CrossRefGoogle Scholar
17.Ishak, A., “Mixed Convection Boundary Layer Flow Over a Vertical Cylinder with Prescribed Surface Heat Flux,” Journal Physics. A: Mathematical Theoretical, 42, pp. 18 (2009).Google Scholar
18.Fang, T. and Yao, S., “Viscous Swirling Flow Over a Stretching Cylinder,” Chinese Physics Letter, 28, pp. 114702114705 (2011).Google Scholar
19.Rangi, R. R. and Ahmad, N., “Boundary Layer Flow Past a Stretching Cylinder and Heat Transfer with Variable Thermal Conductivity,” Applied Mathematics, 3, pp. 205209 (2012).Google Scholar
20.Mukhopadhyay, S., “Mixed Convection Boundary Layer Flow Along a Stretching Cylinder in a Porous Medium,” Journal of Petroleum Science and Engineering, DOI: 10.1016/j.petrol.2012.08.006 (2012).Google Scholar
21.Rao, B. K., “Heat Transfer to Non-Newtonian Flows over a Cylinder in Cross Flow,” International Journal Heat Fluid Flow, 21, pp. 693700 (2000).Google Scholar
22.Nadeem, S., Rehman, A., Vajravelu, K., Lee, J. and Lee, C., “Axisymmertric Stagnation Flow of a Micropolar Nanofluid in a Moving Cylinder,” Mathematical Problem Engineering, p. 18 (2012).Google Scholar
23.Hayat, T., Ahmed, N. and Ali, N., “Effects of an Endoscope and Magnetic Field on the Peristalsis Involving Jeffrey Fluids,” Communications Nonlinear Science and Numerical Simulation, 13, pp. 15811591 (2008).CrossRefGoogle Scholar
24.Hayat, T., Sajjad, R. and Asghar, S., “Series Solution for MHD Channel Flow of a Jeffrey Fluid,” Communications Nonlinear Science and Numerical Simulation, 15, pp. 24002406 (2010).CrossRefGoogle Scholar
25.Mustafa, M., Hayat, T. and Hendi, A. A., “Influence of Melting Heat Transfer in the Stagnation-Point Flow of a Jeffrey Fluid in the Presence of Viscous Dissipation,” Journal of Applied Mechanics, 79, pp. 15 (2012).Google Scholar
26.Hayat, T., Asad, S., Qasim, M. and Hendi, A. A., “Boundary Layer Flow of a Jeffrey Fluid with Convective Boundary Conditions,” International Journel Numerical Method Fluids, 69, pp. 13501362 (2012).Google Scholar
27.Alsaedi, A., Iqbal, Z., Mustafa, M. and Hayat, T., “Exact Solutions for the Magnetohydrodynamic Flow of a Jeffrey Fluid with Convective Boundary Conditions and Chemical Reaction,” Zeitschrift füer Naturforsch, 67a, pp. 517524 (2012).Google Scholar
28.Liao, S., “An Optimal Homotopy-Analysis Approach for Strongly Nonlinear Differential Equations,” Communication Nonlinear Sciences Numerical Simulation, 15, pp. 20032016 (2010).Google Scholar
29.Liao, J. S., “On the Relationship Between the Homotopy Analysis Method and Euler Transform,” Communication Nonlinear Sciences Numerical Simulation, 15, pp. 14211431 (2010).Google Scholar
30.Abbasbandy, S., Hashemi, M. S. and Hashim, I., “On Convergence of Homotopy Analysis Method and its Application to Fractional Integro-Differential Equations,” Quaestiones Mathematicae, 36, pp. 93105 (2013).Google Scholar
31.Mustafa, M., Hayat, T. and Obaidat, S., “On Heat and Mass Transfer in the Unsteady Squeezing Flow Between Parallel Plates,” Meccanica, 47, pp. 15811589 (2012).Google Scholar
32.Rashidi, M. M., Pour, M. A. S. and Abbasbandy, S., “Analytic Approximate Solutions for Heat Transfer of a Micropolar Fluid Through a Porous Medium with Radiation,” Communication Nonlinear Sciences Numerical Simulation, 16, pp. 18741889 (2011).Google Scholar
33.Turkyilmazoglu, M., “A Note on the Homotopy Analysis Method,” Applied Mathematics Letters, 23, pp. 12261230 (2010).CrossRefGoogle Scholar
34.Turkyilmazoglu, M., “A Homotopy Treatment of Some Boundary Layer Flows,” International Journel Nonlinear Sciences Numerical Simulation, 10, pp. 885889 (2009).Google Scholar
35.Anwar, O., beg, , Rashidi, M. M., Beg, A. T. and Asadi, M., “Simultaneous Effects of Partial Slip and Thermal-Diffusion and Diffusion-Thermo on Steady MHD Convective Flow Due to a Rotating Disk,” Journal of Mechanics in Medicine and Biology, 12, p. 21 (2012).Google Scholar
36.Liao, S. J. and Chwang, A. T., “Apllication of Homotopy Analysis Method in Nonlinear Oscillations,” Journal of Applied Mechanics, 65, pp. 914922 (1998).Google Scholar
37.Alsaadi, F. E., Shehzad, A. S., Hayat, T. and Monaqud, J. S., “Soret and Dufour Effects on the Unsteady Mixed Convection Flow over a Stretching Surface,” Journal of Mechanics, 29, pp. 623632 (2013).Google Scholar
38.Hayat, T., Waqas, M., Shehzad, A. S. and Alsaedi, A., “Mixed Convection Radiative Flow of Maxwell Fluid Near a Stagnation Point with Convective Condition,” Journal of Mechanics, 29, pp. 403409 (2013).Google Scholar