MHD OSCILLATING FLOW OF GENERALIZED JEFFREY FLUID PASSING THROUGH A RECTANGULAR DUCT FILLED WITH POROUS MEDIUM
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This article presents some new exact solutions corresponding to unsteady magnetohydrodynamic flow of generalized Jeffrey fluid in a rectangular duct, filled with a porous medium oscillating parallel to its length. The exact solutions are established by means of the double finite Fourier sine transform and discrete Laplace transform. The series solution of velocity field, associated shear stress, and volume flow rate in terms of Fox H-function, satisfying all imposed initial and boundary conditions, have been obtained. Also, the obtained results are analyzed graphically through various pertinent parameters.Viscous flow
Viscous liquid
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Exact solutions are obtained for the thermal decay of a metastable state for two different forms of the potential and for uniform and localized boundary conditions by using the Laplace transform method. The exact inverse Laplace transforms are found for a symmetric case, and the results are compared with other calculations and with the Kramers rate.
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The thermal gradie nt and withdrawal rate are two important solidification parameters during directional solidification.Using Vc++ and Fluent software,the magnetic fluid flow was simulated under different thermal gradients and withdrawal rates.The simulation results show that with the increase of thermal gradient,the thermoelectric magnetohydrodynamic effect can be enhanced under weak magnetic field.However,with the increase of withdrawal rate,the thermoelectric magnetohydrodynamic effect reduces relatively.
Temperature Gradient
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Exact one-dimensional solutions of the magnetohydrodynamic equations of an incompressible fluid are considered. It is shown that one class of plane wave solutions of the linearized equations is also a possible class of solutions of the general equations including the effect of displacement current. A similar result is also established for the solutions for a horizontally stratified fluid. For the particular case when the viscosity is equal to the magnetic diffusivity an exact solution is obtained for the magnetohydrodynamic Rayleigh problem for a semi-infinite plate. It is shown that this solution may be employed directly to give the solution for liquids of small, but not necessarily equal, viscosity and magnetic diffusivity.
Magnetic diffusivity
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This paper analyzes the system of partial differential equations (PDEs) describing the absorption of solar energy via a solar collector utilizing nanofluids. Obtaining exact solution of any system of PDEs is a challenge, however, the current system is effectively solved by means of the Laplace transform (LT). To simplify our procedure, some preliminary theoretical aspects are derived for the inverse LT of some complex expressions and then invested to establish the exact solution. Explicit exact forms are obtained for the involved phenomena in terms of the complementary error function. Moreover, the exact solutions at different special cases are evaluated. Four different kinds of nanofluids are considered to extract the numerical results and physically discussed/interpreted.
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The present study carries out three-dimensional numerical simulations of fluid dynamics and electrodynamics in a cylindrical and a rectangular shaped Faraday-type MHD generator with continuous electrodes under strong MHD interaction. An analytical condition is based on the experimentally operating condition of the pulsed MHD generator “Pamir-3U” with rectangular cross section. Numerical results show that the electric power output of cylindrical shaped MHD generator is almost the same as that of rectangular shaped MHD generator under low voltage condition. Under high voltage condition, the electric power output of cylindrical shaped MHD generator is larger than that of rectangular shaped MHD generator. The eddy current appears near insulating wall on cross section of cylindrical shaped MHD generator. Under the high voltage condition, the eddy current is caused by the difference of the electric field between the side of electrode edge and the others. Under the low voltage condition, the eddy current is due to the electromotive force directed opposite to the core current flow in the boundary-layer separation region.
Magnetohydrodynamic generator
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Concise summary of magnetohydrodynamic (MHD) theory, history, and future trends presented in report. Worldwide research on MHD covered, and selected data from key research projects included. Magnetohydrodynamic generator produces electric current by passing fluid at high speed through strong magnetic field. Fluid ionized gas, plasma, or liquid metal. Magnetohydrodynamic generators offer potential for high efficiency, low power cost, and cleaner emissions.
Magnetohydrodynamic generator
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The multi-dimensional hyperviscous magnetohydrodynamic equations are considered in this paper. The well-posedness of the multi-dimensional hyperviscous magnetohydrodynamic equations is proved. Global attractor of the multi-dimensional hyperviscous magnetohydrodynamic equations is proved in H12+n4×H12+n4 and H1+n2×H1+n2.
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