The Stability Study Of Double Diffusive Convection In A Viscoelastic Fluid-Saturated Porous Layer

The problem of convection in a viscoelastic fluid-saturated porous layer has at-tracted considerable interest during the last few decades because of its wide range of applications,including the disposal of waste material,oil exploitation,food processing and other.lt has a typical nonlinear characteristics. Enhance understanding of the non-linear phenomena and do further studies, not only improve the scientific understanding of the phenomenon, but also facilitate more effective control of the phenomenon.The onset of double diffusive convection in a viscoelastic fluid-saturated infinite horizontal porous layer is studied using linear and weakly non-linear stability analysis. The modified Darcy-Maxwell model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained using linear stability analysis, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.lt is found that the increasing relaxation time increases the elas-ticity of a viscoelastic fluid thus causing instability,and the increasing porosity modified conductivity ratio,Lewis number also cause instability.But the increasing heat transfer coefficient and solute Rayleigh number make the system more stability.The non-linear theory based on the truncated representation of Fourier series method. The effect of various parameters on transient heat and mass transfer is also brought out.It is found that:the effect of relaxation time,porosity modified conductivity ratio and Vadasz number are to advance the onset of double diffusive convection,and then enhance the heat and mass transport. The increasing heat transfer coefficient and solute Rayleigh number suppress the heat and mass transport, and Lewis number suppressed the heat transfer while it enhances the mass transport.