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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CASE STUDY OF HYDROMAGNETIC STABILITY OF A FLOW THROUGH A POROUS SUBSTANCE 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
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and f represents density of the fluid. An investigation
Abstract
was carried out suggesting that the applied magnetic field induces in the fluid a certain level of rigidity along with certain degree of elasticity which enables it to send out disturbances by new modes of propagation known as transverse waves (Bullared, 1949 and Batchelor, 1950). Moreover Lehnert (1954) concluded that the fluid having conducting nature behaves differently in the absence and in the presence of a magnetic field. These are some of the interesting features associated with magnetic field, which have attracted the research workers towards the study of this subject.
In this paper, I am going to discuss the various scenarios of stability problems when a fluid undergoes the effect of magnetic field, fluid passes through a porous substance or when heat is applied to flow of fluid. Instability of fluids under magnetic field is of great importance in physical sense in various phenomena related to atmospheric and oceanic activities. Investigation of stability of fluid flowing through porous media provides crucial information which is applied in various branches of engineering and technology. The fluid flowing with suspended particles are quite sensitive to variations in temperature. The study of these flows is very important in several industrial applications and in
Therefore, the stability of such flows is of great physical importance. Many researchers have done investigations on the stability of different types of flows under the influence of magnetic field and they have shown that the application of magnetic field is a key technique to examine the dawn of instability.
atmospheric sciences. Keywords: thermal instability, atmospheric sciences, interface, visco-elastic.
1. HYDROMAGNETIC INSTABILITY
2. STABILITY OF A HETEROGENEOUS FLOW WITH SHEAR FORCE
The subject of hydromagnetics associates itself with the ways in which the magnetic field may impact the fluid behaviour. A number of research workers have explored the stability of different types of flows under the impact of magnetic field to check the arrival of instability. The impact of magnetic field on the hydro magnetic Benard's problem is taken care of and the results show that the magnetic field induces the fluid stable (Chandrasekhar,1954). It is discussed how the flow of fluid between two plates placed parallel to each other and acted upon by magnetic field force behaves. Lundquist (1952) showed that how important the hydro magnetic flows are provided the dimensional less number
(e * m )
The stability of a heterogeneous shear flow of an incompressible, having almost zero viscosity, nonconducting fluid having zero electrical resistivity when a uniform magnetic field is applied in the streaming direction when the system is statically stable is discussed in detail (Agrawal & Agrawal,1969).
3. STABILITY OF NON-DISSIPATIVE HETEROGENEOUS SHEAR FLOW Agrawal and Agrawal in 1970 carried out analysis of the stability patterns of heterogeneous shear flow having nondissipative nature impacted by magnetic field having uniform intensity and acting in the direction of the flow. During the analysis, the density of the fluid is assumed to be the function of vertical co-ordinate and it increases in vertically upward direction.
1/2
Bmf * L ch *
f
exceeds 1, where Bmf is the
magnetic field, L ch is the characteristic length, e the electrical conductivity, m denotes magnetic permeability
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