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2 International Journal of Applied Mechanics and Engineering

2 Khan S. K.

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Boundary layer viscoelastic fluid flow over an exponentially stretching sheet

Khan S. K.

International Journal of Applied Mechanics and Engineering

2006

Vol. 11, no 2

321-335

In the present paper, a viscoelastic boundary layer fluid flow over an exponentially stretching continuous sheet has been examined. The flow is assumed to be generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x. Approximate analytical similarity solutions (zero and first order) of the highly non-linear boundary layer equation are obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving that sequentially. The first-order solution is derived in the form of confluent hypergeometric Whittaker functions. The solutions are verified at the boundary sheet. These solutions (zero and first order) involve an exponential dependence of the similarity variable, the stretching velocity and the stream function on the axial coordinate. The accuracy of the analytical solutions is also verified by the numerical solutions obtained by employing the Runge-Kutta fourth order method with shooting. The effects of various physical parameters on the velocity profile and skin-friction coefficient are also discussed in this paper.

Boundary layer MHD flow of a viscoelastic fluid over a porous quadratic stretching sheet

Khan S. K.

International Journal of Applied Mechanics and Engineering

2005

Vol. 10, no 2

267-279

A mathematical analysis on the boundary layer MHD flow of a viscoelastic fluid over a porous stretching sheet has been presented in this paper. A typical choice of quadratic stretching of the boundary, which generates a quadratic part in velocity parallel to the boundary sheet and a linear mass flux part in the velocity normal to the stretching sheet, has been assumed. Streamline patterns and skin friction coefficients are discussed for various values of nondimensional physical parameters. The result of the analysis reveals that the combined effect of the non-dimensional viscoelastic parameter and Hartmann number is to increase significantly the values of skin friction coefficient, whereas, the combined effect of the nondimensional constant mass flux parameter and modified linear mass flux parameter is to reduce largely the values of skin friction coefficient. For positive values of the linear mass flux parameter the stream functions attain a positive slope away from the origin while they attain a negative slope everywhere for zero value. The limiting cases of our results yield the results of Andersson (1992) and Kumaran and Ramanaiah (1996).