Compressible couple-stress fluid permeated with suspended particles heated and soluted from below in porous medium

Abstract

<span style="font-size: 15.0pt;mso-bidi-font-size:8.0pt;font-family:" times="" new="" roman","serif""="">A layer of a compressible couple-stress fluid permeated with suspended particles, heated and soluted from below in a porous medium is considered. For the case of stationary convection, the stable solute gradient and couple-stress have stabilizing effects, whereas the suspended particles and medium permeability have destabilizing effects on the onset or convection in the couple-stress fluid permeated with suspended particles, heated and soluted from below in a porous medium. The effect of compressibility is to postpone the onset of thermosolutal instability. Results are illustrated, graphically, by giving numerical values to the parameters. The system is stable for (<i style="mso-bidi-font-style: normal">c</i>_P/g}β <span style="font-size:15.5pt;mso-bidi-font-size: 8.5pt;font-family:" times="" new="" roman","serif""="">> 1; <i style="mso-bidi-font-style: normal">c</i>_P,<span style="font-size:15.0pt;mso-bidi-font-size: 8.0pt;font-family:" times="" new="" roman","serif""=""> <span style="font-size: 13.0pt;mso-bidi-font-size:6.0pt;font-family:" times="" new="" roman","serif";="" mso-fareast-font-family:hiddenhorzocr"="">β <span style="font-size:15.0pt; mso-bidi-font-size:8.0pt;font-family:" times="" new="" roman","serif""="">and <i><span style="font-size:16.0pt;mso-bidi-font-size:9.0pt;font-family:" times="" new="" roman","serif""="">g </span></i><span style="font-size:15.0pt;mso-bidi-font-size:8.0pt;font-family: " times="" new="" roman","serif""="">denote specific heat at constant pressure, uniform temperature gradient and acceleration due to gravity, respectively. The stable solute gradient is found to introduce oscillatory modes in the system for (<i style="mso-bidi-font-style:normal">c</i>_P/g}β <span style="font-size:15.5pt;mso-bidi-font-size:8.5pt;font-family:" times="" new="" roman","serif""="">> 1<span style="font-size:15.0pt;mso-bidi-font-size:8.0pt;font-family: " times="" new="" roman","serif""="">, which were non-existent in its absence. Sufficient conditions for the non -existence of over-stability are also obtained.

</span></span></span></span></span></span></span></span>