EFFECTS OF TRANSVERSE ELECTRIC FIELD AND HETEROGENEITY OF A POORLY ELECTRICALLY CONDUCTING FLUID SATURATED NANOPOROUS ZEOLITES ACQUIRING SMART MATERIAL PROPERTIES

N. Rudraiah^{1}, G. Ranganna^{2} and P. Shilpa^{3}

^{1} National Research Institute for Applied Mathematics, 7th Block (West), Jayanagar, Bangalore, India

^{1,2} UGC-CAS for Fluid Mechanics, Department of Mathematics, Central College campus Bangalore, India

^{3} Department of Mathematics, R.L. Jalappa Institute of Technology, Doddaballapur, Bangalore, India

**Abstract.** In this paper we explain a Mathematical Model involving Darcy linear drag,
Forchheimer quadratic drag, horizontal density gradient and the variation of electrical
conductivity due to organic substances dissolved in a heterogeneous Boussinesq poorly
conducting couple stress fluid flow (PCPCSFF) through Nano Porous Zeolites regarded
as densely packed porous media. Initially, the flow is at rest and set in motion due to
initial piecewise horizontal concentration gradient.

Analytical solutions, for electric potential using the Maxwell field equations and
for velocity and density using nonlinear Darcy – Forchheimer equation in the presence of
couple stress and electric force are obtained using the method of time series evolution.
The analytical solutions for streamlines and density are computed for different values of
time, t, for a particular value of electric number W_{1} and couple stress parameter β and the
results are depicted graphically in figures 1 and 2. From these figures we found that the
streamlines are closer in the region of x<0 than that of x>0 and the density profiles are
concentrated in the lower region and develop curvature in the presence of electric field
and couple stress parameter. The physical reason for the nature of streamlines and density
profiles are given in the last section and some important conclusions are drawn.