Oscillatory Free Convective Flow of Viscoelastic Fluid Through Porous Medium in a Rotating Vertical Channel
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Oscillatory Free Convective Flow of Viscoelastic Fluid Through Porous Medium in a Rotating Vertical Channel Khem Chand • K. D. Singh • Sanjeev Kumar
Received: 26 September 2012 / Revised: 20 April 2013 / Accepted: 18 July 2013 / Published online: 24 August 2013 Ó The National Academy of Sciences, India 2013
Abstract A theoretical analysis of an oscillatory viscoelastic, incompressible and electrically conducting fluid in an infinite vertical porous channel is presented. The entire system rotates about the axis normal to the plane of the plate with uniform angular velocity X. A closed form solution for the velocity, temperature and skin friction are obtained. Results are presented through graphs and table for the various values of rotation, viscoelastic, permeability and frequency of oscillation parameter and discussed in detail. Keywords Viscoelastic Oscillatory Porous medium Rotating vertical channel
Greek symbols a Modulus of rigidity b Coefficient of volume expansion Small positive constant j Thermal conductivity l Coefficient of viscosity m Kinematic viscosity x Frequency of oscillations q Density of the fluid * Represent the dimensional variable
Introduction List of Symbols Variables Cp g K* K0 p* t* T (u, v, w)
Specific heat at constant pressure Acceleration due to gravity Permeability of the medium Viscoelastic parameter Modified pressure Time Temperature Fluid velocity along x, y, z-axis
K. Chand (&) S. Kumar Department of Mathematics & Statistics, H. P. University, Shimla, India e-mail: [email protected] S. Kumar e-mail: [email protected] K. D. Singh Department of Mathematics (ICDEOL), H. P. University, Shimla, India e-mail: [email protected]
The phenomenon of hydrodynamics free convection flow of a rotating viscoelastic fluid has received a considerable attention of many researchers because of its application in geophysical science, atmosphere and oceanic circulations, nuclear reactor, power transformers, petroleum technology, in chemical engineering for the purification and filtration process and in the cases like drug permeation through human skin. The principle of this subject is very useful in recovering the water for drinking and irrigation purpose. The knowledge of flows through porous medium is also useful to study the movement of natural gas and water through the reservoirs. A series of investigation have been made by different scholars where the porous medium is either bounded by horizontal, vertical surface or parallel porous plates. Raptis and Perdikis [1] studied the problem of free convective flow through porous medium bounded by the vertical porous plate with constant suction when the free stream velocity oscillates in time about a constant mean value. Singh and Mathew [2] also investigated the effect of permeability and the injection/suction on an
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oscillatory free convective flows of the viscous incompressible fluid through highly porous medium bounded between two infinite vertical porous plate where the entire system rotates about
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