Stress concentration effects in micropolar elasticity Technical report no. 8-4

Stress concentration around circular hole in infinite plate subject to axial tensio

Marangoni electroconvection in the presence of an electric field in a fluid heated from above

A poorly electrically conducting fluid, bounded below by a rigid boundary embedded with segmented electrodes and above by a perfectly conducting free surface, convects even when it is heated from above when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. Physically the forces driving such convection are due to the interaction of the applied electric field with space charges that develop in the bulk of the fluid and the surface tension at the free surface. The principle of exchange of stability is established using both moment and energy methods. We find the conditions for both marginal and overstable instabilities in terms of the negative Marangoni number M a , as a function of the dimensionless electric parameter W and the wave number α . The critical values of M a and α for both marginal and overstable states are computed. We found that the effect of W is to suppress Marangoni electroconvection in the neutral as well as in oscillatory states, and this convection sets in earlier in the case of an oscillatory state than in the neutral state

Convection in a viscoelastic fluid-saturated sparsely packed porous layer

The linear stability of a viscoelastic fluid-saturated sparsely packed porous layer heated from below is studied analytically using the Darcy-Brinkman-Jeffreys model with different boundary combinations. The Galerkin technique is employed to determine the criterion for the onset of oscillatory convection. The effects of the viscoelastic parameters, the Prandtl number, and the porous parameter on the critical Rayleigh number, the wave number, and the frequency are analyzed. The results are compared with those obtained for both a Darcy-Jeffrey fluid and a Maxwell fluid. It is shown that under certain conditions for the viscoelastic parameters, the flow is overstable. The possibility of the occurrence of bifurcation is also discussed

Effect of modulation on the onset of thermal convection in a viscoelastic fluid-saturated sparsely packed porous layer

The stability of a Boussinesq viscoelastic fluid-saturated horizontal porous layer, when the boundaries of the layer are subjected to periodic temperature modulation, is analyzed. The Darcy-Forchheimer-Brinkman-Oldroyd model is employed and only infinitesimal disturbances are considered. Three cases of the oscillating temperature field were examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of-phase modulation, and (c) only the bottom wall is modulated. Perturbation solution in powers of the amplitude of the applied field is obtained. The effect of the frequency of modulation on the stability is clearly shown. Possibilities of the occurrence of subcritical instabilities are also discussed. It is shown that an increase in the elastic parameters A<SUB>1</SUB> and A<SUB>2</SUB> has a stabilizing influence. An increase in the Prandtl number destabilizes the system for small values of the frequency but stabilizes the systems for large values of the frequency. It is shown that the system is most stable when the boundary temperatures are modulated out of phase. The maximum range of e when subcritical instabilities exist is also determined

FEDSM2003-45050 ON THE CONVECTIVE STABILITY OF OLDROYD B FLUID SUBJECT TO A HORIZONTAL TEMPERATURE GRADIENT

ABSTRACT The linear convective stability analysis of Oldroyd B fluid with horizontal temperature gradient and thermocapillary effects is carried out. The lower surface of the fluid layer is in contact with an adiabatic rigid plate and the upper face is flat and subject to a temperature dependent surface tension. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and the results are presented for Prandtl numbers 10 and 100. The role of different viscoelastic parameters is discussed