Department of Mathematics

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Mathematics

Cosmological models with time dependent displacement field in the cosmological theory based on Lyra’s geometry have been discussed. Exact solutions have been obtained for a spatially flat FRW model by considering a particular form for the time dependent displacement field. We have also obtained conditions under which the matter-dominated, flat universe undergoes decelerated or accelerated expansions. Accelerated expansion of the Universe is of particular interest in view of the recent observations. © 2020

School of Advanced Sciences

Chennai Campus

African Review of Physics

Cosmological Models in Lyra Geometry with Time-varying Displacement Field

The study of nanofluid flow in porous media is of great interest because of enhanced heat transfer rates of these fluids. In this paper we present a study of mixed convection in a nanofluid flow in a porous medium along a vertical plate. The flow field is subjected to magnetic effects and nonlinear thermal radiation. The study further assumes the effects of heat generation within the boundary layer flow. The transport equations are solved numerically using the fifth-order Runge-Kutta-Fehlberg scheme with a shooting technique and appropriate boundary conditions for different values of physical parameters. The model for the nanofluid flow in the porous medium incorporates the effects of buoyancy ratio parameter and Darcy number. The effects of various physical parameters on the dimensionless velocity, temperature and concentration profiles is investigated. It is observed among other findings that an increase in the Darcy number leads to increase in the velocity profiles. © 2020 by Begell House, Inc.

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Journal of Porous Media

A numerical study of nanofluid flow over a porous vertical plate with internal heat generation and nonlinear thermal radiation

In this paper, we determine the wirelength of embedding complete bipartite graphs K2n-1, 2n-1into 1-rooted sibling tree ST1nand Cartesian product of 1-rooted sibling trees and paths. © 2020 Kansai University. All rights reserved.

Journal of Combinatorial Mathematics and Combinatorial Computing

Embedding complete bipartite graph into sibling trees with optimum wirelength

In a graph G a set S of vertices is called a dominating set of G if every vertex in V (G) − S is adjacent to some vertex in S. Let S be a minimum dominating set G. If V (G) −S contains a dominating set say (Formula presented) of G, then (Formula presented) is called an inverse dominating set with respect to S. A dominating set S of a graph G is non-split dominating set if the induced subgraph V (G) − S is connected. A Wrapped butterfly network WBF(n), n ≥ 3, is obtained by merging the first and last levels of a butterfly network BF(n), n ≥ 3. In this paper we determine the domination, inverse domination and non-split domination numbers of WBF(n). © 2020. All Rights Reserved.

International Journal of Mathematics and Computer Science

Domination and Inverse Domination in Wrapped Butterfly Networks

This communication exploresthe theoretical investigation of induced magnetic field, thermophoresis and Brownian motion on an unsteady, laminar and incompressible nonlinear convective flow of Jeffrey nanofluid through a rectangular channel in presence of thermal radiation and heat source/sink. Further, we also considered double stratification and heat and mass flux conditions at the boundaries. The governing flow field equations are shortened into coupled non-dimensional system ordinary differential equation using an appropriate transformation, then carried out a numerical solution using fifth-order Runge–Kutta–Fehlberg scheme along with shooting technique. The effect of various non dimensional form of the characteristic function of flow, heat and mass transfers, induced magnetic field and skin friction are plotted with respect to the prominent physical parameters and calculated heat and mass transfer rates at the plates. The results so obtained are compared with the existing published work for viscous case which leads a considerable agreement. © 2019, Forum D'Analystes, Chennai.

Journal of Analysis

The combined effects of induced magnetic field, thermophoresis and Brownian motion on double stratified nonlinear convective-radiative Jeffrey nanofluid flow with heat source/sink

We revisit the problem of the weakly nonlinear stability analysis of an immiscible two-fluid viscosity-stratified, density-matched, plane Poiseuille flow (PPF) in a rigid channel. A formal amplitude expansion method, in which the flow variables are expanded in terms of a small amplitude function, is employed to examine the nonlinear development of the uniform wave trains. By employing the Chebyshev spectral collocation method, the linear growth rate and the first Landau coefficient, which determine the weakly nonlinear temporal evolution of a finite amplitude disturbance in the vicinity of linear instability, are computed. The focus is on the parameter regime where the long-waves are stable. The present analysis reveals the existence of both subcritical unstable and supercritical stable bifurcations. It is found that similar to the single fluid PPF, the two-fluid flow remains subcritically unstable at the onset of linear instability. There is a transition from subcritical bifurcation at higher wave numbers to supercritical bifurcation at lower wave numbers. The feedback of the mean flow correction onto the wave is responsible for the subcritical bifurcation. The equilibrium amplitude increases (decreases) as a function of the Reynolds number at a fixed wave number, where the bifurcation is supercritical (subcritical). Similar to the single fluid PPF, there is a reduction in the critical Reynolds number due to even extremely weak but finite amplitude disturbances. Moreover, as the disturbance intensity increases, the percentage reduction in the critical Reynolds number increases. The study helps one to have a better understanding and perspective of the bifurcations that occur close to criticality in the two-fluid interface dominated PPF system. In addition, it calls for devoted experiments supplemented with numerical and theoretical predictions on Poiseuille flow of viscosity and/or density stratified systems that would shed light on the nature of transition. © 2019 Elsevier Ltd

International Journal of Multiphase Flow

Finite amplitude instability in a two-fluid plane Poiseuille flow

Consideration is given to the problem of steady axisymmetric creeping flow of a micropolar fluid around the spherical drop of non-Newtonian liquid shell covered with permeable medium. The field equations of micropolar fluids are presented in terms of velocity vector and microrotation vector. External liquid permeates into the porous layer, but it is not mixed with the liquid located in the internal cavity of a capsule. The flow inside the permeable medium is described by the Brinkman equation. The stream function solution for the external flow field is derived in terms of modified Bessel's function and Gegenbauer's polynomial. The solution is determined by dilating the stream function in terms of the dimensionless parameter S for the internal flow field (Reiner-Rivlin liquid sphere). Analytical expressions for the pressure field, coupling number, microrotation component, viscosity ratio, permeability parameter, and drag force are calculated. The effect of various parameters on the drag force is presented graphically and discussed. It is observed that the drag on a micropolar fluid sphere is more than that on a permeable sphere. Different limiting cases are also considered. © 2020 by Begell House, Inc.

Drag on a reiner-rivlin liquid sphere embedded in a porous region placed in a micropolar fluid

Abstract: Flow around a Reiner–Rivlin non-Newtonian liquid particle, which is surrounded with a Newtonian liquid shell and placed into a permeable medium, is studied. This formulation of the problem is typical for, e.g., studying the motion of an oil droplet surrounded with an aqueous medium (oil-in-water emulsion) in a porous collector under the action of an external pressure drop. An analogous problem is encountered when lymph penetrates into human or animal tissues. The flows inside of the permeable layer, in the region between the Reiner–Rivlin liquid and a porous medium, and inside of the spherical region are described by the Brinkman, Stokes, and Reiner–Rivlin equations, respectively. The general solution for the stream function in the external porous region is written in terms of the modified Bessel function and Gegenbauer polynomials. For the Reiner–Rivlin liquid sphere, the solution is found by expanding the stream function into a power series in terms of small dimensionless parameter S. The boundary problem is solved by conjugating the boundary conditions for all regions. The drag force applied to the Reiner–Rivlin liquid particle placed into the permeable medium is determined. The effects of permeability parameter α, viscosity ratio λ, and dimensionless parameter S on the drag coefficient are studied. Corresponding dependences are represented graphically and discussed. Known particular cases are described using passages to the limits. © 2020, Pleiades Publishing, Ltd.

Colloid Journal

Flow around a Liquid Sphere Filled with a Non-Newtonian Liquid and Placed into a Porous Medium

A effective coloring of the vertices of a graph G starts with an initial subset S of colored vertices, with all residual vertices being uncolored. At each various time interval, a colored vertex with exactly one uncolored adjacent vertex forces this uncolored vertex to be colored. The initial set S is called a forcing set (zero forcing set) of G if, by iteratively applying the forcing process, every vertex in G becomes colored. If the set S has the added property that the subgraph induced by S is a perfect matching or 1-factor, then S is called a 1-factor forcing set of G. The 1-factor forcing number of G, denoted (equation presented), is the minimum cardinality of a 1-factor forcing set of G. In this paper, we introduce this new parameter namely the 1-factor forcing number and obtain the same for certain interconnection networks. © 2020 The Authors. Published by Elsevier B.V.

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Procedia Computer Science

1-factor forcing in certain interconnection networks

In this paper, a novel technique is proposed to solve fuzzy fractional delay differential equations (FFDDEs) with initial condition and source function, which are fuzzy triangular functions. The obtained solution is a fuzzy set of real functions. Each real function satisfies an FFDDE with a specific membership degree. A detailed algorithm is provided to solve the FFDDE. The proposed method has been elucidated in detail through numerical illustrations. Graphs are plotted using MATLAB. © 2010 2020