iosr-Jm   Volume-2 ~ Issue-1

Abstract: Analytical solutions are obtained for one-dimensional advection-diffusion equation with variable coefficients in longitudinal semi-infinite homogeneous porous medium for uniform flow. The solute dispersion parameter is considered temporally dependent while the velocity of the flow is considered uniform. The first order decay and zero-order production terms are considered inversely proportional to the dispersion coefficient. Retardation factor is also considered in present paper. Analytical solutions are obtained for two cases: former one is for uniform input point source and latter case is for increasing input point source where the solute transport is considered initially solute free. The Laplace transformation technique is used. New space and time variables are introduced to get the analytical solutions. The solutions in all possible combinations of increasing or decreasing temporally dependence dispersion are compared with each other with the help of graph. It is observed that the concentration attenuation with position and time is the fastest in case of decreasing dispersion in accelerating flow field.
Keywords: Advection, Diffusion, First-order Decay, Zero-order Production, Retardation Factor, Homogeneous Medium.

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Abstract: Effect of magnetic field on transient free convection flow past an electrically conducting fluid over an oscillating vertical plate with chemical reaction is studied here. Exact solutions obtained by Laplace Transform methods are presented graphically for different values of physical parameters. It is observed that chemical reaction parameter and magnetic parameter influence the velocity and concentration profiles significantly.
Keywords: Free Convection, MHD, Oscillating Plate, Chemical Reaction AMS 2000 subject classification: 76R10, 76W05, 80A20, 80A32

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Abstract: We define a Cap-coset a ^ S of a subset S in an Artex space A over a Bi-monoid M and a Cup-coset a v S of a subset S in an Artex space A over a Bi-monoid M. We prove a ^ S need not be equal to S even when S is a SubArtex Space of A and a ϵ S. We prove if a ϵ S, then a ^ S C S. We prove that for a,b ϵ S a ≤ b implies a ^ S C b ^ S. We also prove that a v S need not be equal to S even when S is a SubArtex Space of A and a ϵ S. We prove if a ϵ S, then a v S C S. We prove that for a,b ϵ S a ≤ b implies b v S C a v S.
Keywords: Artex spaces, Cap-cosets, Cup-cosets, SubArtex Spaces.

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