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1

Span-wise fluctuating MHD convective flow of a viscoelastic fluid through a porous medium in a hot vertical channel with thermal radiation

Singh K. D.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 3

667--681

EN

An unsteady mixed convection flow of a visco-elastic, incompressible and electrically conducting fluid in a hot vertical channel is analyzed. The vertical channel is filled with a porous medium. The temperature of one of the channel plates is considered to be fluctuating span-wise cosinusoidally, i.e., [...]. A magnetic field of uniform strength is applied perpendicular to the planes of the plates. The magnetic Reynolds number is assumed very small so that the induced magnetic field is neglected. It is also assumed that the conducting fluid is gray, absorbing/emitting radiation and non-scattering. Governing equations are solved exactly for the velocity and the temperature fields. The effects of various flow parameters on the velocity, temperature and the skin friction and the Nusselt number in terms of their amplitudes and phase angles are discussed with the help of figures.

2

Oscillatory MHD convective flow of second order fluid through porous medium in a vertical rotating channel in slip-flow regime with heat radiation

Garg B. P., Singh K. D., Bansal A. K.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 1

33--52

EN

An analysis of an oscillatory magnetohydrodynamic (MHD) convective flow of a second order (viscoelastic), incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter […], Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation […].

3

Estimation of Seismic Site Coefficient and Seismic Microzonation of Imphal City, India, Using the Probabilistic Approach

Pallav K., Raghukanth S. T. G., Singh K. D.

Acta Geophysica

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2015

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Vol. 63, no. 5

1339--1367

EN

Seismic site coefficients (Fs) for Imphal city have been estimated based on 700 synthetically generated earthquake time histories through stochastic finite fault method, considering various combinations of magnitudes and fault distances that may affect Imphal city. Seismic hazard curves and Uniform Hazard Response Spectra (UHRS) are presented for Imphal city. Fs have been estimated based on site response analyses through SHAKE-91 for a period range of engineering interest (PGA to 3.0 s), for 5% damping. Fs were multiplied by UHRS values to obtain surface level spectral acceleration with 2 and 10% probability of exceedance in 50 year (~2500 and ~500 year) return period. Comparison between predicted mean surface level response spectra and IS-1893 code shows that spectral acceleration value is higher for longer periods (i.e., > 1.0 s), for ~500 year return period, and lower for periods shorter than 0.2 s for ~2500 year return period.

4

Exact solution of MHD mixed convection periodic flow in a rotating vertical channel with heat radiation

Singh K. D.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

853--869

EN

Magnetohydrodynamic (MHD) mixed convection flow of a viscous, incompressible and electrically conducting fluid in a vertical channel is analyzed analytically. A magnetic field of uniform strength is applied perpendicular to the planes of the channel walls. The fluid is acted upon by a periodic variation of the pressure gradient in the vertically upward direction. The temperature of one of the plates is non-uniform and the temperature difference of the walls of the channel is high enough to induce heat transfer due to radiation. The fluid and the channel rotate in unison with an angular velocity about the axis normal to the plates of the channel. An exact analytical solution of the problem is obtained. Two cases of small and large rotation have been considered to assess the effects of different parameters involved in the flow problem. The velocity field, the amplitude and the phase angle of the shear stress are shown graphically and discussed in detail. During analysis it is found that the flow problem studied by Makinde and Mhone (2005) is incorrect physically and mathematically.

5

Effect of slip condition on viscoelastic MHD oscillatory forced convection flow in a vertical channel with heat radiation

Singh K. D.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

1237--1248

EN

In this paper an oscillatory flow of a viscoelastic, incompressible and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel plates is discussed. One of these plates is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel oscillates with time. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature difference of the two plates is also assumed high enough to induce heat transfer due to radiation. A closed form analytical solution to the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters entering into the problem. A number of particular cases have been shown by dotted curves in the figures. During the analysis it is found that the physical and the mathematical formulations of the problems by Makinde and Mhone (2005), Mehmood and Ali (2007), Kumar et al. (2010) and Choudhury and Das (2012) are not correct. The correct solutions to all these important oscillatory flow problems are deduced.

6

Heat and mass transfer effects on an oscillatory mhd convective flow through porous medium in a rotating porous channel with heat radiation

Singh K. D., Pathak R.

International Journal of Applied Mechanics and Engineering

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2012

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Vol. 17, no. 4

1309-1326

EN

An oscillatory MHD convective and mass transfer flow of an electrically conducting, viscous, incompressible fluid in a rotating porous channel filled with a porous medium has been analyzed. Effects of radiation and chemical reaction are also considered. The two porous plates are subjected to a constant injection and suction. It is considered that the influence of the uniform magnetic field acts normal to the flow. The entire system rotates about an axis normal to the planes of the plates with uniform angular velocity [...]. Expressions for velocity, temperature, concentration, and amplitude and phase angle of skin-friction, the Nusselt number and Sherwood number are obtained. The results obtained for velocity are discussed for small (...) and large (...) rotation of the channel with the help of graphs.

7

Exact solution of an oscillatory MHD flow in a channel filled with porous medium

Singh K. D.

International Journal of Applied Mechanics and Engineering

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2011

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Vol. 16, no 1

277-283

EN

An exact solution of an oscillatory MHD flow of a viscous, incompressible and electrically conducting fluid in an infinite horizontal channel is presented. The channel is filled with a porous medium and a magnetic field is applied perpendicular to the plates of the channel. During the analysis it is found that the mathematical formulation and the solution obtained of the problem by Makinde and Mhone (2005) are both wrong. Equations (2.1) to (2.4) do not govern the flow problem shown geometrically in their Fig.1. This important flow problem is again formulated mathematically in the present paper and a fresh and a correct closed form analytical solution is obtained. The validity and correctness of the present solution is verified by the limiting case for H=s=0. In this case of oscillatory flow in the absence of a magnetic field and through ordinary medium the solution reduces to the well known result obtained by Schlichting and Gersten (2001). The results are discussed in detail with the help of graphs for the variations of different flow parameters.