78 The effect of temperature modulation on the onset of Darcy ferroconvection in a horizontal porous layer heated from below is investigated. The analysis is based on the assumption that the amplitude of the temperature modulation is small enough compared with the imposed steady temperature difference. The effect of the oscillating temperature field is treated by a perturbation expansion in powers of the amplitude of the applied field. The effect of magnetic parameters, Vadasz number and temperature modulation in the cases of symmetric, asymmetric and bottom wall modulation, were discussed. The study divulges that subcritical motion exists for symmetric temperature modulation for low frequency. In the case of asymmetric and bottom wall modulation only supercritical motion exists. Keywords: Ferrofluid, porous media, magnetic field, temperature modulation 1.0 Introduction T hermo-mechanical interactions in fluids make the possible onset of convection induced by externally applied temperature gradients. The theory of thermal instability in a horizontal fluid layer heated from below was investigated by Lord Rayleigh (Rayleigh, 1916) and termed that phenomenon of buoyancy-induced instability as Rayleigh Bénard convection. The Rayleigh Bénard convection that occur in fluids with magnetic particles is named as ferroconvection. Ferrofluids are colloidal suspensions of surfactant-coated magnetic particles in a liquid medium, where the sizes of the particles are of several nanometers. They exhibit a variety of unusual properties, for instance, these fluids exhibit increased viscosity and apparent density in magnetic field gradients. Due to its wide range of applications in aerospace, industrial equipment designs, loudspeaker audio, biomedicals etc. (Papell, 1964) and (Scherer and Neto, 2005) a great effort has been devoted to the study of ferroconvection during the past three decades. The convective instability of a ferromagnetic fluid for a fluid layer heated from below in the presence of uniform vertical magnetic field has been first investigated by Finlayson (Finlayson, 1970). Gupta and Gupta (Gupta, 1979), Gotoh and Yamada (Gotoh and Yamada, 1982), Stiles and Kagan (Stiles and Kagan, 1990) Russell et al (Russell et al, 1995) extended the pioneering work of Finalyson (Finlayson, 1970) to deal with the influence of a strong magnetic field and large wave number convection. Maruthamanikandan (2003) employed the Rayleigh-Ritz technique to examine the problem of onset of Bénard convection in a horizontal layer of a radiating ferromagnetic fluid. The effect of viscosity variation on non-Darcy ferroconvection was paid attention by Soya Mathew and Maruthamanikandan (2018) and Maruthamanikandan et al. (2018). The motivation for the study of convection in a fluid saturated a porous medium has rich technological applications in chemical engineering, geothermal activities, oil recovery techniques and biological processes. Darcy (Darcy, 1856), Muskat (Muskat, 1937), Hubbert (Hubbert, 1956), Whitaker (Whitaker, 1966) has developed the flow of fluids through porous media and the equations pertaining to it. In many systems, such as charges in electrostatic field and ferromagnetic resonance, modulation of a suitable parameter can have marked effects on the motion and can result in increased stability of the system. Venezian (Venezian, 1969) investigated the stability of a horizontal layer of fluid heated from below when, in addition a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. He showed that at low frequencies the equilibrium state becomes unstable because at that frequency the disturbances grow to a sufficient size so that the inertia effect becomes important. Malashetty and Wadi (Malashetty and Wadi, 1999) investigated the stability of a Boussinesq fluid saturated horizontal porous layer with time-dependent wall temperatures. It is shown that the system is most stable when the boundary temperature is modulated out of phase. Nisha Mary and Maruthamanikandan (Nisha and Maruthamanikandan, 2018) used regular perturbation Effect of time-dependent sinusoidal boundary temperatures on the onset of ferroconvection in a porous medium NISHA MARY THOMAS SOYA MATHEW and S MARUTHAMANIKANDAN Ms. Nisha Mary Thomas, Department of Sciences and Humanities, School of Engineerng and Technology, Christ (Deemed to be University), Ms. Soya Mathew, Department of Mathematics, Kristu Jayanti College, Kothanur and Mr. S Maruthamanikandan, Department of Mathematics, School of Engineering, Presidency University, Bengaluru 560064, India. E-mail: nisha.mary@christuniversity.in / soyamathew@kristujayanti.com / maruthamanikandan@presidencyuniversity.in