Fundamental flows with nonlinear slip conditions: exact solutions

Abstract

In this article, we use nonlinear slip conditions to investigate three fundamental flows. Constitutive equations of the third grade fluid give rise to nonlinear equations. Exact analytic solutions of the nonlinear equations with nonlinear boundary conditions are developed. Numerical values between the dimensionless third grade and slip parameters are tabulated. Graphs are plotted and discussed. (2000). 76B05 · 76P05. Mathematics Subject Classification

Comment on: “Fundamental flows with nonlinear slip conditions: exact solutions”, by R. Ellahi, T. Hayat, F. M. Mahomed and A. Zeeshan, Z. Angew. Math. Phys. 61 (2010) 877–888

“…The inadmissible ranges of d and the possible forms of u obtained above suffice to discuss the results of Ellahi et al [1]. The inadmissible ranges of d and the possible forms of u obtained above suffice to discuss the results of Ellahi et al [1].…”

“…(2) for the integration constant d, Ellahi et al [1] follow the bizarre approach of specifying d as well as other involved parameters and solving for γ. (2) for the integration constant d, Ellahi et al [1] follow the bizarre approach of specifying d as well as other involved parameters and solving for γ.…”

“…With reference to Ellahi et al [1], the solution for the steady generalized Couette flow of a third grade fluid with slip conditions is expressible, in nondimensional form, as follows.…”

“…(1) and (2), are obtained from Eqs. (32) of [1] by U , representing the nondimensional speed of the moving wall, other symbols are as defined in [1]. Apart from replacing a unity on the left hand side of Eq.…”

“…Conditions (30, with unity replaced by U ) and (31) of [1] are recast as Conditions (30, with unity replaced by U ) and (31) of [1] are recast as…”