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2 International Journal of Applied Mechanics and Engineering

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Oblique stagnation flow of a thermodynamically-valid Walters' B liquid: a series solution

Mortazavi N., Sadeghy K., Alikbar V., Alizadeh-Pahlavan A.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 3

829-852

A thermodynamically-valid exact solution was found for laminar, two-dimensional, oblique stagnation point flow of a Walters' B fluid above a stretching sheet. To circumvent the problem with the extra boundary condition, and also to be able to obtain results at large elasticity numbers, use will be made of the homotopy analysis method in order to find an analytical solution. The analytical solution so obtained shows that the behavior of fluids with a negative elasticity number is completely different from those with a positive elasticity number. For example, while for the wall shear stress is increased by an increase in the elasticity number, for it is predicted to decrease when the elasticity number is increased. A comparison of the results obtained using the homotopy analysis method with those obtained using the perturbation method (Mahapatra et al., 2007) suggests that the perturbation method may not be so reliable when addressing viscoelastic fluids.

Blasius flow of viscoelastic fluids: a numerical approach

Sadeghy K., Sharifi M.

International Journal of Applied Mechanics and Engineering

2004

Vol. 9, no 2

399-411

The effects of a fluid elasticity on the characteristics of a boundary layer in a Blasius flow are investigated for a second-grade fluid, and also for a Maxwell fluid. Boundary layer approximations are used to simplify the equations of motion which are finally reduced to a single ODE using the concept of similarity solution. For the second-grade fluid, it is found that the number of boundary conditions should be augmented to match the order of the governing equation. A combination of finite difference and shooting methods are used to solve the governing equations. Results are presented for velocity profiles, boundary layer thickness, and skin friction coefficient in terms of the local Deborah number. An overshoot in velocity profiles is predicted for a second-grade fluid but not for a Maxwell fluid. The boundary layer is predicted to become thinner for the second-grade fluid but thicker for the Maxwell fluid, the higher the Deborah number. By an increase in the level of fluid elasticity, a drop in wall skin friction is predicted for the second-order fluid but not for the Maxwell fluid.