Hydromagnetic Instability of Viscoelastic Fluids in Blasius Flow

The effect of a fluid's elasticity is investigated on the instability of Blasius flow at the presence of a transverse magnetic field. To determine the critical Reynolds number as a function of the elasticity and magnetic numbers, a two-dimensional linear temporal stability analysis is used assuming that the viscoelastic fluid of interest obeys Walters' B model as its constitutive equation. Neglecting terms nonlinear in the perturbation quantities, an eigenvalue problem is obtained which is solved numerically using the Chebychev collocation method. Based on the results obtained in this work, fluid's elasticity is predicted to have a destabilizing effect on Blasius flow. In contrast, the effect of the magnetic field is predicted to be always stabilizing in Blasius flow, at least in the range of parameters used in this work.