i-manager's Journal on Mathematics (JMAT)

Research Paper

Abstract

The Maxwell model is considered to be the simplest of rate type fluids model of viscoelastic fluid, the model describes the blood flow in small vessels. And also the response of some polymeric liquids. The focus of this work is derivation of magneto-hydrodynamic of Maxwell model in cylindrical co-ordinates (r;θ; z), basic equations (equation of continuity and momentum), and the Maxwell model were changed from the vector form to deferential form to derive the model in cylindrical co-ordinates (r; θ ; z). The Maxwell equation has been derived and system of partial differential equations was obtained under effect of magnetic field.

Research Paper

Abstract

Markov chain is a powerful technique employed to forecast the variations in the sharemarket, customer behaviour, marketing, customers' brand loyalty, weather, game of golf, weather report, gold rate, conversion of currency rate, etc. This study focuses on research discrete-time Markov chain. Some significant properties of Markov chains are evoked and then the research and knowledge gained on Markov chains is applied to predict Eid al-Fitr day for the succeeding years and also in the long run. The Eid al-Fitr day for each year depends only on the previous year Eid al-Fitr day and not on its previous years' Eid al-Fitr days. The authors have also justified is study that the application of Markov chain is an appropriate process in predicting Eid al-Fitr day in Oman.

Research Paper

Abstract

This paper deals with non-steady radial flow of a viscous, incompressible liquid in the porous medium around a radially oscillating time dependent spherical surface. The momentum equation considered for the flow through the porous medium takes care of the fluid inertia and the Newtonian stresses in addition to the classical Darcy's friction. Expressions for the pressure and velocity distributions have been derived in terms of the expansion rate of sphere radius using analytical method and effects of variation of pressure, velocity of a viscous, incompressible, and homogeneous fluid flow in a porous medium are reported and the results are presented graphically for the two special cases of radius of the sphere.

Research Paper

Abstract

Let Fn =(M, L) be an n-dimensional Finsler manifold, and Let L and L be the two Finsler metrics. For a differential one form β(x,dx)=bi(x)dxi on M, G. Randers, in 1941, introduced a special Finsler space defined by the change L =L+β, where L is i Riemannian, to consider a unified field theory. For a β-change of Finsler metric, the differential one-form β plays a very important role. With the above observations, in this article, the authors have tried to study the necessary and sufficient n condition for Finsler space Fn which is transformed by a b-change of Finsler space Fn with (α, β)-metric to be of Douglas type. And also we are discussing the different classes of (α, β)-metrics of Finsler spaces Fn are discussed, which is obtained by a β-change of a Finsler space Fn is of Douglas type. The terminology and notations are referred to the Matsumoto's monograph (Matsumoto, 1992).

Research Paper

Abstract

In this paper, the effect of solid particle concentration and flow velocity of nanofluid with and without superimposed vibration at the wall were numerically investigated. For this purpose, non-newtonian nanofluid containing Al2O3 and aqueous CMC solution as a single phase with an average particle size of 25 nm and four particle concentration of 0.0, 0.5, 1.0, and 1.5% were used. Effects of volume concentration on convective heat transfer coefficient were investigated in different Reynolds number for different vibration parameters. The results showed that in a steady flow, with Reynolds number, dispersion of nanoparticles causes the thermal boundary layer to grow rapidly than that of base fluid in axial direction and vibration act as a catalyst; at a given concentration much enhancement results than steady state. The ratio of convective heat transfer coefficient of unsteady state to a steady state flow of nanofluid with an increase of Reynolds number and increases with concentration. Vibration effects reduce in significance as frequency increases, and that they are more sensitive to amplitude to frequency. The largest increase of about 300% was observed under the condition of vibrational flow of nanofluid compared with a steady flow of base fluid.