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Z. Naturforsch. 69a, 1 – 8
(2014)
doi:10.5560/ZNA.2013-0060
Effects of Heat Transfer and Nonlinear Slip on the Steady Flow of Couette Fluid by Means of Chebyshev Spectral Method
1 Department of Mechanical Engineering Bourns Hall, University of California Riverside, 92521 USA
2 Department of Mathematics and Statistics, IIIUI, H-10, 44000, Islamabad, Pakistan
3 Department of Mathematics & Computer Science, University of South Carolina Upstate 800 University Way, Spartanburg, 29303, USA
Received April 16, 2013 / revised August 7, 2013 / published online November 21, 2013
Reprint requests to: R. E.; E-mail:
rellahi@engr.ucr.edu
This article is concerned with the study of heat transfer and nonlinear slip effects on the Couette flow of a third-grade fluid. Numerical solutions are obtained by solving nonlinear differential equations using the higher-order Chebyshev spectral method. The results for no slip and no thermal slip become special cases of this study. Moreover, the results for Poiseuille flow can be obtained as a special case from the generalized Couette flow analysis by setting the plate velocity to zero. Graphical results for involved pertinent parameters are sketched and examined.
Key words: Third-Grade Fluid; Couette Flow; Nonlinear Slip Boundary Conditions; Heat Transfer; Chebyshev Spectral Method.