International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 05 | May 2023
p-ISSN: 2395-0072
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IMPACT OF PRESENCE OF SUSPENDED PARTICLES IN STRATIFIED FLUID AND STABILITY UNDER INFLUENCE OF TEMPERATURE N.K. Gaur1, Vivek Parkash2 1Professor & Head, Department of Mathematics, M.M.College, Modinagar, Ghaziabad (U.P), India 2Assistant Professor of Mathematics, Dyal Singh College, Karnal (Haryana), India
------------------------------------------------------------------------***----------------------------------------------------------------------2. CASE WHEN DUST PARTICLES ARE ABSTRACT SUFFICIENTLY FINE IN SIZE Stratified fluid flows are the flows through a gravitational field whose origin lies in the changes in density within the field. The atmosphere and the oceans are both examples of stratified medium. The stratification of atmosphere is due to thermal reasons and the salinity induces stratification in oceans. If the fluid is not heterogeneous, the gravity has no effect on the flow of the fluid, in turn it is only responsible for hydrostatic pressure. Heterogeneity will also have minute effects even when force of gravity is absent. But the presence of both heterogeneity and the force of gravity is responsible for very strange and complicated things happening. One such situation is reflected in the instability of RayleighTaylor configuration. Moreover presence of suspended particles in fluid flows makes the fluid much more sensitive to variations and deflections in temperature. The study of these flows is very crucial in several industrial applications and in atmospheric sciences. Moreover, the study of thermal instability of fluid layers with suspended particles is very essential for knowing the nature of these flows.
Saffman[1] discussed the case when the dust particles are sufficiently fine, so that the relaxation time is much smaller than the characteristic-time scale of the disturbances. The dust particles move in the gas roughly with the same velocity as that of the gas, so that the effect of the dust particles is simply to increase the density of the gas. He also discussed the case of coarse dust particles i.e. the case when the relaxation time is comparable or greater than the characteristic time of the disturbances. The physical explanation is that the disturbance has to flow round the particles, and the energy is dissipated. The kinetic energy present in the disturbances is responsible for this energy. This results in decrease in the amplitude of the perturbations. Thus the presence of dust particles, makes the system stable. It is also noted that the stabilizing action of the coarse dust depends only on the parameter f d where f is proportional to the fraction of' dust d fd s particles and f d s is the size of the dust particles.
Keywords and Phrases: heterogeneity, relaxation time, kinetic energy, thermohaline convections.
Thus, if f d is kept constant, then an increase in the size of
1. CASE OF THERMAL INSTABILITY OF FLUID LAYERS HAVING SUSPENDED PARTICLES
coarse and irregular shaped dust particles decreases the value and hence reduces the stabilizing effect.
Admirable work in this field was done by Saffman1 and Veronis. Saffman[1] did a considerable good work in this direction. He investigated the effect of the dust particles in terms of two parameters, namely the contribution of dust particles in its motion and the relaxation time . Relaxation time denotes the rate of adjustment of velocity of dust particles with respect to the gas velocity change and is a function of size of the each particle individually.
Sharma & Sharma[2] studied the problem of thermal instability of a horizontal fluid layer through a porous medium in the presence of suspended particles. They proved that the effect of suspended particles as well as medium permeability was to destabilize the fluid layer. They also investigated the thermal instability of the layer in the presence of rotation and suspended particles. It was found that the rotation has a stabilizing effect but then PES is not valid. Finally, they examined the problem of thermosolutal convection in a layer of fluid heated form below
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3. THERMAL INSTABILITY OF A HORIZONTALLY FLOWING FLUID
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