Research Journal of Engineering and Technology

Chander Bhan Mehta ¹, Daleep K. Sharma ², Sanjeev Gangta ³

Affiliations
1 Department of Mathematics, Govt Excellence Degree College Sanjauli, Shimla (H.P)-171207, IN
2 Department of Mathematics, Rajiv Gandhi Govt. College, Shimla-4 (H.P),, IN
3 Department of Mathematics, GSSS(G), Port More, Shimla-1 (H.P), IN

Abstract

The effect of uniform vertical magnetic field and uniform vertical rotation on double-diffusive convection in a layer of an electrically conducting couple-stress fluid heated and soluted from below is considered. For the case of stationary convection, it is clear that stable solute gradient, compressibility, rotation and magnetic field postpone the onset of the convection in compressible couple-stress fluid heated from below in the presence of a magnetic field. Couple-stress parameter has duel character in presence of rotation. While in absence of rotation Couple-Stress parameter has postpones the onset of convection only. Graphs have been plotted by giving numerical values to the parameters to depict the stability characteristics. Further, the solute gradient, magnetic field, rotation is found to introduce oscillatory modes in the systems that were non-existent in their absence. The sufficient conditions for the non-existence of overstability have found, the violation of which does not necessarily imply the occurrence of overstability.

Keywords

Double-Diffusive Convection, Couple-Stress Fluid, Uniform Vertical Magnetic Field and Rotation, Mathematical Classification (AMSC2010):76A05, 76A10, 80A20, 76E06, 76E15, 76E19, 76N20.

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C. B. Mehta ¹, Susheel Kumar ², Sanjeev Gangta ³

Affiliations
1 Department of Mathematics, Govt. College, Sanjauli, Distt. Shimla, IN
2 Department of Mathematics, St. Bedes College Shimla, Distt. Shimla, IN
3 Department of Mathematics, GSSS Portmore Shimla, Distt. Shimla, IN

Abstract

A layer of compressible, elastic-viscous fluid heated and soluted from below in the presence of porous is considered. For the case of stationary convection, the Walters, elastico viscous fluid behaves like an ordinary Newtonion fluid. The presence of solute gradient and magnetic field has a stabilising effect in the presence of compressibility and rotation postpone the onset of convection. The oscillatory modes are not allowed and the principle of exchange of stabilities is satisfied if kinematic viscoelasticity is less than the medium permeability divided by medium porosity. The presence of solute gradient and viscoelasticity introduces oscillatory modes in the presence of rotation. The case of overstability is also studied wherein a sufficient condition for the non-existence of overstability is found.

Keywords

Elastico-Viscous, Magnetic, Overstability, Porous, Compressibility, Rotation, Thermosolutal Convection.

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