

Articles
by
H.R. Nataraja 
Total Records (
3 ) for
H.R. Nataraja 





Swamy N.S.,
,
H.R. Nataraja
,
K.S. Sai
,
S.B. Tiwari
and
B. Nageswara Rao


This study considers the RivlinEricksen constitutive equation for the Cauchy stress in the equation of motion to examine the flow of an incompressible secondgrade fluid with an oscillating rigid moving plate. Simple and reliable numerical procedures are used to obtain the parameters in the analytical expressions for the velocity field and the shearing stress on the moving plate. The Doppler effect is noticed from the increased frequency due to the motion of the plate. The thickness of the boundary layer reduces with an increase in the magnetic interaction parameter. 




S.B. Tiwari
,
B. Nageswara Rao
,
H.R. Nataraja
and
K.S. Sai


This research is concerned primarily with nonlinear oscillations of a modified van der Pol equation. The motion is represented by the harmonic oscillator equation, with the addition of a small nonlinear term. The governing differential equation falls under autonomous category. The solution of the problem is examined utilizing the method of slowly varying amplitude and phase (the KrylovBogoliubovMitropolsky technique). Stationary values of the amplitude are obtained and discussed their stability. It is noted that the stable limitcycles of the differential equation in the higher order averaging method can be identified easily from the time derivative of the amplitude function and the sign of its derivative at the stationary value of the amplitude. 




Sai K.S.,
,
N.S. Swamy
,
H.R. Nataraja
,
S.B. Tiwari
and
B. Nageswara Rao


This study presents an exact solution for the flow of two immiscible fluids under a general oscillatory timedependent pressure gradient in a channel with one porous floor. The oscillatory behavior of the timedependent pressure gradient is expressed in terms of Fourier series. At the interface, continuity of velocities and shear stresses is assumed. Equations governing the flow are solved using the slip condition at the permeable interface whereas the generalized Darcy`s law in the porous region. The unsteady flow depends upon the Reynolds numbers of the fluids, slip parameter and porous parameter. Analytical expressions are provided for the mass flow rate and wall shearing stresses. Numerical results are presented considering water and mercury as the two immiscible fluids for the uniform pressure gradient as well as for the sinusoidal timedependent pressure gradient. Since the formulation of the problem is general, it is possible to examine the unsteady flow of any two immiscible fluids under any specified oscillatory timedependent pressure gradient. This study will be useful in learning how the pressure and viscous forces exert their influence to produce different flow patterns. 





