DARCY-BRINKMAN CONVECTION IN A COUPLE-STRESS FLUID SATURATED ROTATING POROUS LAYER USING THERMAL NON-EQUILIBRIUM MODEL

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Published: Nov 10, 2013

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Sridhar Kulkarni

Abstract

Stability of a rotating couple-stress fluid-saturated rotating porous layer when the fluid and solid phases are not in local thermal equilibrium is analysed. The Darcy -Brinkman model is used for the momentum equation and a two-field model that represents the fluid and solid phase temperature fields separately is used for energy equation. The linear stability analysis is used to obtain the condition for both stationary and oscillatory convection. The effect of thermal non-equilibrium on the onset of both stationary and oscillatory convection is discussed. It is found that inter-phase heat transfer coefficient stabilizes the system. There is a competition between the processes of rotation and thermal diffusion that causes the convection to set in through oscillatory mode rather than stationary. The rotation inhibits the onset of convection in both stationary and oscillatory mode.  Besides, the effect of porosity modified conductivity ratio, Darcy-Prandtl number, couple-stress parameter and the ratio of diffusivities on the stability of the system is investigated.

Keywords: local thermal non-equilibrium, couple-stress fluid, convection, rotation, Rayleigh number.

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Kulkarni, S. (2013). DARCY-BRINKMAN CONVECTION IN A COUPLE-STRESS FLUID SATURATED ROTATING POROUS LAYER USING THERMAL NON-EQUILIBRIUM MODEL. Journal of Global Research in Mathematical Archives(JGRMA), 1(8), 16–33. Retrieved from https://jgrma.com/index.php/jgrma/article/view/100
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Vol. 1 No. 8 (2013): August-2013
Section
Research Paper
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References

] A.K. Goel, S.C. Agarwal (1999): Hydromagnetic stability of an unbounded couple stress binary fluid mixture having vertical temperature and concentration gradients with rotation. Indian J. Appl. Math., 30 (10), 991-1001.

] B.S. Bhadauria and S. Agarwal (2011): Natural convection in a nano fluid saturated rotating porous layer: A non-linear study. Transp. Porous Med, 87, 585-602.

] C.W. Horton and F.T. Rogers (1945): Convective currents in a porous medium, J. Appl. Phys. 16. 367-370.

] D.A. Nield, A. Bejan (2006): Convection in Porous Media, 3rd edn. Springer-Verlag, New York.

] D.A.S. Rees, I. Pop (1999): Free convective stagnation point flow in a porous medium using thermal non-equilibrium model, Int. Commn. Heat Mass Transfer 26, 945 – 954.

] D.A.S. Rees, I. Pop (2000): Vertical free convective boundary layer flow in a porous medium using a thermal non-equilibrium model, J. Porous Media 3, 31 – 44.

] D.B.Ingham, I.Pop (1998): Transport Phenomena in Porous Media: Pergamon, Oxford.

] D.L. Koch, R.J. Hill (2001): Inertial effect in suspension and porous media flows. Annu. Rev. Fluid Mech., 33, 619-647.

] E.R. Lapwood (1948): Convection of a fluid in a porous medium, Proc. Camb. Phil. Soc. 44, 508-521.

] I.S. Shivakumar, M.S.Malashetty and K.B.Chavaraddi (2006): Onset of Convection in a viscoelastic fluid-saturated sparsely packed porous layer using a thermal non-equilibrium model. Can.J.Phys. 84, 973-990.

] I.S.Shivakumar, S.Sureshkumar, and N.Devraju (2011): Coriolis effect on thermal convection in a couple-stress fluid saturated rotating rigid porous layer, Archive of Applied Mechanics 81, 513-530.

] K. Jogendra, A.K. Srivastav and B. S. Bhadauria (2012):Double diffusive convection in a couple stress fluid saturated porous medium using thermal non-equilibrium model. Int. Conference on Modeling and Simulation of Diffusive Processes and Applications. 119-128.

] V.K. Gupta and B.S. Bhadauria (2012): Double diffusive convection in a couple stress fluid saturated sparsely packed porous layer with Soret effect using thermal non-equilibrium model. Int. Conference on Modeling and Simulation of Diffusive Processes and Applications. 89-95.

] Sunil, R.Devi and A.Mahajan (2013): Global Stability of a couple stress fluid in a porous medium using thermal non-equilibrium model. Int. J. of Appl. Math and Mech. 9 (1), 29-49.

] K. Vafai and A. Amiri (1998) : “Non-Darcian effects in combined forced convective flows,†in Transport Phenomenon in Porous Media edited by D. B. Ingham and I. Pop (Pergamon, Oxford, pp 313-329,).

] K. Vafai (2000) : Handbook of Porous Media Marcel Dekker, New York.

] M.S.Malashetty, I.S.Shivakumar, K.Sridhar (2005): The onset of Lapwood-Brinkman convection using a thermal non-equilibrium model. International Journal of Heat and Mass Transfer. 48 (6), 1155-1163.

] M.S.Malashetty, M. Swamy and K. Sridhar (2007): Thermal convection in a rotating porous layer using thermal non-equilibrium model. Phys. Fluids, 19, 1-16.

] M.S. Malashetty and M. Swamy (2010): Effect of rotation on the onset of thermal convection in a sparsely packed porous layer using a thermal non-equilibrium model. International Journal of Heat and Mass Transfer, 53(15), 3088-3101.

] M.S. Malashetty, I.S. Shivakumar, K. Sridhar (2008): The onset of convection in a couple stress fluid saturated porous layer using a thermal non-equilibrium model. Physics Letters A, 373, 781-790.

] N. Banu and D.A.S. Rees (2002): Onset of Darcy-BÑnard convection using a thermal non- equilibrium model, Int. J. Heat and Mass Transfer 45, 2221-2228.

] P.A. Tyvand (2002): Onset of Rayleigh Bénard convection in porous bodies. In Transport Phenomena in Porous Media II, edited by D.B .Ingham and I. Pop (Pergamon, New York), Chap 4, pp. 82-112.

] Nouri-Borujerdi, A.R. Noghrehabadi, D.A.S. Rees (2007): Onset of convection in a horizontal porous channel with uniform heat generation using a thermal non-equilibrium model. Transp Porous Med 69, 343-357.

] R.C. Sharma, M. Sharma (2004): Effect of suspended particles on couple-stress fluid heated from below in the presence of rotation and magnetic field. Indian J. Pure Appl. Math., 35 (8), 973-989.

] S. Govender and P. Vadász (2007): The effect of mechanical and thermal anisotropy on the stability of gravity driven convection in rotating porous media in the presence of thermal non-equilibrium. Transp. in porous Media, 69, 55-66.

] B. Straughan (2006): “Global non-linear stability in porous convection with a thermal non-equilibrium model,†Proc. Roy. Soc. Lond. A 462, 409.

] W.L. Li, H.M. Chu (2004): Modified Reynolds equation for couple stress fluids - A porous media model. Acta Mechanica, 171, 189-202.