\r\nof convection in a mechanically anisotropic fluid saturated porous

\r\nmedium of infinite horizontal extent are determined. The medium

\r\nis heated from below and its bounding surfaces are subjected to

\r\ntemperature modulation which consists of a steady part and a

\r\ntime periodic oscillating part. The Brinkman model is employed

\r\nin the momentum equation with the Bousinessq approximation.

\r\nThe stability region is found for arbitrary values of modulational

\r\nfrequency and amplitude using the energy method. Higher order

\r\nnumerical computations are carried out to find critical boundaries

\r\nand subcritical instability regions more accurately.","references":"[1] Y. Shu, B.Q. Li, B.R. Ramaprian, Convection in modulated thermal\r\ngradients and gravity: experimental measurements and numerical\r\nsimulations, International Journal of Heat and Mass Transfer, Vol. 48,\r\npp. 145-160, 2005.\r\n[2] G. Venezian, Effect of modulation on the onset of thermal convection,\r\nJournal of Fluid Mechanics, Vol. 35, pp. 243-254, 1969.\r\n[3] S. Rosenblat, D.M. Herbert, Low-frequency modulation of thermal\r\ninstability, Journal of Fluid Mechanics, Vol. 43, pp. 385-398, 1970.\r\n[4] S. Rosenblat, G.A. Tanaka, Modulation of thermal convection instability,\r\nPhysics of Fluids, Vol. 14, pp. 1319 -1322, 1971.\r\n[5] C.S. Yih, C.H. Li, Instability of unsteady flows or configurations. Part\r\n2. Convective instability, Journal of Fluid Mechanics, Vol. 54, pp. 143\r\n-152, 1972.\r\n[6] G.M. Homsy, Global stability of time-dependent flows. Part 2.\r\nModulated fluid layers, Journal of Fluid Mechanics, Vol. 62, pp.\r\n387-403, 1974.\r\n[7] R.G. Finucane, R.E. Kelly, Onset of instability in a fluid layer heated\r\nsinusoidally from below, International Journal of Heat and Mass\r\nTransfer, Vol. 19, pp. 78 -85, 1976.\r\n[8] J.P. Caltagirone, Stability of a horizontal porous layer under periodical\r\nboundary conditions, International Journal of Heat and Mass Transfer,\r\nVol. 19, pp. 815-820, 1976.\r\n[9] B. Chhuon, J.P. Caltagirone, Stability of a horizontal porous layer with\r\ntimewise periodic boundary conditions, Journal of Heat Transfer, Vol.\r\n101, pp. 244-248, 1979.\r\n[10] N. Rudraiah, P.V. Radhadevi, P.N. Kaloni, Effect of modulation on the\r\nonset of thermal convection in a viscoelastic fluid-saturated sparsely\r\npacked porous layer, Canadian Journal of Physics, Vol. 68, pp. 214-221,\r\n1980.\r\n[11] M.S. Malashetty, V.S. Wadi, Rayleigh-Benard convection subject to time\r\ndependent wall temperature in a fluid-saturated porous layer, Fluid\r\nDynamics Research, Vol. 24, pp. 293-308, 1999.\r\n[12] B.S. Bhadauria, Thermal modulation of Rayleigh-Benard convection in\r\na sparsely packed porous medium, Journal of Porous Media, Vol. 10,\r\npp. 1-14, 2007. [13] J. Singh, E. Hines, D. Iliescu, Global stability results for temperature\r\nmodulated convection in ferrofluids, Applied Mathematics and\r\nComputation, Vol. 219, pp. 6204-6211, 2013.\r\n[14] G. Castinel, M. Combarnous, Critere dapparition de la convection\r\nnaturelle dans une couche poreuse anisotrope horizontal, Comptes\r\nrendus de l\u2019Acadmie des Sciences, Vol. 278, pp. 701-704, 1974.\r\n[15] J.F. Epherre, Criterion for the appearance of natural convection in an\r\nanisotropic porous layer, International Journal of Chemical Engineering,\r\nVol. 17, pp. 615-616, 1977.\r\n[16] L. Storesletten, Effects of anisotropy on convective flow through\r\nporous media, Transport Phenomena in Porous Media, Elsevier, Oxford,\r\n261-284, 1998.\r\n[17] M.S. Malashetty, D. Basavaraja, Rayleigh-Benard convection subject to\r\ntime dependent wall temperature\/gravity in a fluid-saturated anisotropic\r\nporous medium, Heat and Mass Transfer, Vol. 38, pp. 551-563, 2002.\r\n[18] F. Capone, M. Gentile, A.A. Hill, Penetrative convection via\r\ninternal heating in anisotropic porous media, Mechanics Research\r\nCommunications, Vol. 37, pp. 441-444, 2010.\r\n[19] F. Capone, M. Gentile, A.A. Hill, Double-diffusive penetrative\r\nconvection simulated via internal heating in an anisotropic porous layer\r\nwith throughflow, International Journal of Heat and Mass Transfer, Vol.\r\n54, pp. 1622-1626, 2011.\r\n[20] S. Saravanan, T. Sivakumar, Thermovibrational instability in a fluid\r\nsaturated anisotropic porous medium, Journal of Heat Transfer, Vol.\r\n133, pp. 1-9, 2011.\r\n[21] P.G. Siddheshwar, R.K. Vanishree, A.C. Melson, Study of heat transport\r\nin Benard-Darcy convection with g-jitter and thermo-mechanical\r\nanisotropy in variable viscosity liquids, Transport in Porous Media, Vol.\r\n92, pp. 277-288, 2012.\r\n[22] B.S. Bhadauria, Palle Kiran, Heat transport in an anisotropic porous\r\nmedium saturated with variable viscosity liquid under temperature\r\nmodulation, Transport in Porous Media, Vol. 100, pp. 279-295, 2013.\r\n[23] S. Saravanan, T. Sivakumar, Onset of filtration convection in a vibrating\r\nmedium: The Brinkman model, Physics of Fluids, Vol. 22, pp. 1-15,\r\n2010.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 124, 2017"}