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Triple-diffusive convection in Walters' (Model B') fluid with varying gravity field saturating a porous medium

Kango S. K., Rana G. C., Chand R.

Studia Geotechnica et Mechanica

2013

Vol. 35, nr 3

45--56

The Triple-Diffusive convection in Walters’ (Model B') fluid with varying gravity field is considered in the presence of uniform vertical magnetic field in porous medium. For the case of stationary convection, the magnetic field, varying gravity field and the stable solute gradients have stabilizing effects whereas the medium permeability has destabilizing (or stabilizing) effect on the system under certain conditions. A linear stability analysis theory and normal mode analysis method have been carried out to study the onset convection. The kinematic viscoelasticity has no effect on the stationary convection. The solute gradients, magnetic field, varying gravity field, porosity and kinematic viscoelasticity introduce oscillatory modes in the system, which were non-existent in their absence. The sufficient conditions for the non-existence of overstability are also obtained. The results are also shown graphically.

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.