The a main class of problems which helps

The theory of Rayleigh-B´enard convection of a horizontal liquid layer with upper freesurface over a heated plate has many important applicatios in a number of engineeringproblem such as extraction of oil from porous medium etc. The gravitational field on theearth is not constant. It is always fluctuating, this fluctuating gravitational field is calledas g-jitter or Gravity modulation. So, convecion under the fluctuating gravitational field1is a main class of problems which helps us to study convection problem in a microgravitycondition. Variation of the gravitational field affects the stability of the system eventhough basic temperature gradient is identical.The effect of Gravity modulation on a stable convection configuration can affect thestability of the system under consideration may be by increasing or decreasing the rateof convection. In general, a distribution of stratifying agency that is convectively stableunder constant gravity conditions can be destabilized when a time-dependent componentof the gravity field is introduced certain combinations of thermal gradients, physicalproperties and modulation parameters may lead to parametric resonance and hence,to the stability of the system. Bhadauria and Kiran1, Gresho and Sani2, P. Kiran3, Malashetty and Basavaraja4, Siddheshwar and Abraham9 and Siddheshwar andPranesh 10 have studied the effects of gravity modulation on the onset of convectionin various types of Newtonian and non-Newtonian fluids. P. G. Siddheshwar and B. R.Revathi12 studied the effect of Gravity Modulation on weakly non-linear stability ofstationary convection in a dielectric fluid. It is reported in the literature that vibrationscan either substantially enhance or retard heat transfer and thus drastically affect theconvection.Couple stress theory of fluids was developed by Stokes13 and represents the simplestgeneralization of the classical theory which allows for polar effects such as the presence ofcouple stresses and body couples. The study of flow of couple stress fluid has been greatinterest in research field due to its wide range of types and their scientific applications.Use of couple stress in fluid in the study of mechanism of lubrications one of the mainfrontapplication in the field of mechanical engineering, medicine etc. S. Pranesh and SameenaTarannum5 studied the effect of gravity modulation in weak electrically conductingcouple stress fluid with saturated porous layer. S. Pranesh and Sangeetha george6studied effect of imposed time periodic boundary temperature in a dielectric couple stressfluid. Few authors I.S. Shivakumara8, P.G. Siddeshwar and S. Pranesh11 and manymore have considered couple stress fluid in investigating Rayleigh-B´enard convectionunder different situations.In most part of the last century the engineering applications of fluid mechanicswere restricted to systems in which electric and magnetic fields played no role. Inrecent years, the study of the interaction of electromagnetic fields with fluids startedgaining attention with the promise of applications in areas like nuclear fusion, chemicalengineering, medicine and high speed noiseless printing. Onset of natural convectionin the presence of an external electric field has been studied by Rudraiah et al.7,Siddheshwa and Abraham9 and Takashima and Gosh15.2The main objective of this paper is to study the effects of fluctuating gravity andelectric field in a weak electrically conducting couple stress fluid with a saturated porouslayer on the onset of Rayleigh-B´enard convection.