Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 22, No. 4 (November 2009) 379-404   

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  THERMOSOLUTAL CONVECTION OF MICROPOLAR ROTATING FLUIDS SATURATING A POROUS MEDIUM
 
 
Reena*
Department of Mathematics, Shri K.K. Jain (P.G.) College
Khatauli, Distt. Muzaffarnagar 251001, Uttar Pradesh, India
reena_math@rediffmail.com - m234ragini@gmail.com

U.S. Rana
Department of Mathematics, D.A.V. (P.G.) College
Dehradun 248001, Uttarakhand, India
drusrana@yahoo.co.in

* Corresponding Author
 
 
( Received: March 24, 2008 – Accepted in Revised Form: February 19, 2009 )
 
 

Abstract    Double-diffusive convection in a micropolar fluid layer heated and soluted from below in the presence of uniform rotation saturating a porous medium is theoretically investigated. An exact solution is obtained for a flat fluid layer contained between two free boundaries. To study the onset of convection, a linear stability analysis theory and normal mode analysis method have been used. For the case of stationary convection, the effect of various parameters like medium permeability, solute gradient, rotation and micropolar parameters (i.e. coupling, spin diffusion, micropolar heat conduction and micropolar solute parameters arising due to coupling between spin and solute fluxes) have been analyzed. The critical thermal Rayleigh numbers for various values of critical wave numbers (found by Newton Raphson method) for the onset of instability are determined numerically and depicted, graphically. The oscillatory modes were introduced due to the presence of the micropolar viscous effects, microinertia, rotation and stable solute gradient, which were non-existence in their absence. The principle of exchange of stabilities is found to hold true for the micropolar fluid saturating a porous medium heated from below in the absence of micropolar viscous effect, microinertia, rotation and stable solute gradient. An attempt was also made to obtain sufficient conditions for the nonexistence of overstability.

 

Keywords    Thermosolutal Convection, Porous Medium, Rotation Effect, Micropolar Fluids, Medium Permeability, Stable Solute Gradient, Rayleigh Number

 

چکیده    انتقال حرارت جابجايي پخش دوگانه در يک لايه سيال ميکروقطبي که از پايين تحت حرارت و حلاليت قرار گرفته و با چرخش ثابت، محيطي متخلخل را اشباع مي کند، به طور نظري مطالعه شده است. حل دقيق براي لايه تخت سيال محدود شده بين دو مرز آزاد، به دست آمده است. از تئوري تحليل پايداري خطي و روش تحليل وضعيت نرمال براي مطالعه شروع جابجايي استفاده شده است. تاثير پارامترهاي مختلفي مثل قابليت نفوذ محيط متخلخل، تغييرات حلاليت، چرخش و عوامل ميکرو قطبي (کوپلينگ، نفوذ spin، هدايت حرارتي ميکروقطبي و حلاليت ميکروقطبي که به دليل کوپلينگ بين شار حلاليت و چرخش افزايش مي يابند) بر حالت جابجايي ساکن، تحليل شده است. عدد رايلي حرارتي بحراني و عدد موج بحراني براي شروع ناپايداري به دست آمده و در نمودارها نشان داده شده اند. مشخص شده است که حلاليت پايدار مودهاي نوساني به دليل حضور اثرات ويسکوز ميکروقطبي، ميکرواينرسي، چرخش و گراديان به وجود مي آيند که اين مودها در حالت عدم حضور اين عوامل وجود نداشتند. اصل تبادل پايداري ها براي سيال ميکروقطبي اشباع شده در محيط متخلخل با گرمايش از زير در غياب اثرات ويسکوز ميکروقطبي، ميکرواينرسي، چرخش و گراديان حلاليت پايدار همچنان صادق است. تلاش شد شرايط مناسب براي عدم ايجاد فوق پايداري نيز به وجود آيد.

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