Starting solutions for the motion of second grade fluids due to oscillating shear stresses

Nonlinear engineering: Modeling and application

article

Muhammad Jamil¹ 

[1] Department of Mathematics, NED University of Engineering and Technology

关键词: Second grade fluid;    exact solutions;    velocity field;    oscillating shear stresses;    Laplace and finite Hankel transforms;   

DOI  :  10.1515/nleng-2015-0011

来源: De Gruyter

【 摘 要 】

Exact analytic solutions for the motion of second grade fluid between two infinite coaxial cylinders are established. The motion is produced by the inner cylinder that at time t = 0+ applies torsional and longitudinal oscillating shear stresses to the fluid. The exact analytic solutions, obtained with the help of Laplace and finite Hankel transforms, and presented as a sum of the steady-state and transient solutions, satisfy both the governing equations and all associate initial and boundary conditions. In the special case when a1 to 0 they reduce to those for a Newtonian fluid. Finally, the effect of various parameters of interest on transient parts of velocity components, velocity profiles as well as comparison between second grade and Newtonian fluids is discussed through graphical illustration.

【 授权许可】

Unknown