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.

&nbsp;

&nbsp;

VIT University

Department of Mathematics

A mathematical model is presented for an optically dense fluid past an isothermal circular cylinder with chemical reaction taking place in it. A constant, static, magnetic field is applied transverse to the cylinder surface. The cylinder surface is maintained at a constant temperature. New variables are introduced to transform the complex geometry into a simple shape and the boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the welltested, efficient, implicit, Crank-Nicolson finite difference scheme. Numerical computations are made and the effects of the various material parameters on the velocity, temperature and concentration as well as the surface skin friction and surface heat and mass transfer rates are illustrated graphs and tables. Increasing magnetohydrodynamic body force parameter (M) is found to decelerate the flow but enhance temperatures. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter. © 2016, Isfahan University of Technology.

School of Advanced Sciences

Vellore Campus

Fulltext

Journal of Applied Fluid Mechanics

Chemical Reaction Effects on an Unsteady MHD Mixed Convective and Radiative Boundary Layer Flow over a Circular Cylinder

An analysis of the thermal radiation effects on MHD boundary layer flow past a permeable exponential stretching surface in the presence of Joule heating and viscous dissipation is presented. Velocity and thermal slips are considered instead of no-slip conditions at the boundary. Stretching velocity and wall temperature are assumed to have specific exponential function forms. The governing system of partial differential equations is transformed into a system of ordinary differential equations using similarity transformations and then solved numerically using the Runge-Kutta fourth order method along with shooting technique. The effects of the various parameters on the velocity, shear stress, temperature and temperature gradient profiles are illustrated graphically and discussed in detail. The influence of the slip parameters causes significant fluctuations in velocity of the flow field. Viscous dissipation characterized by Eckert number enhances the temperature of the fluid, as the heat gets transferred from the sheet to the fluid.

World University root node

Thermal radiation effects on MHD boundary layer slip flow past a permeable exponential stretching sheet in the presence of joule heating and viscous dissipation

The laminar boundary layer flow and heat transfer of Casson non-Newtonian fluid from an inclined (solar collector) plate in the presence of thermal and hydrodynamic slip conditions is analysed. The inclined plate surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite-difference scheme. Increasing velocity slip induces acceleration in the flow near the inclined plate surface. Increasing velocity slip consistently enhances temperatures throughout the boundary layer regime. An increase in thermal slip parameter strongly decelerates the flow and also reduces temperatures in the boundary layer regime. An increase in Casson rheological parameter acts to elevate considerably the velocity and this effect is pronounced at higher values of tangential coordinate. Temperatures are however very slightly decreased with increasing values of Casson rheological parameter.

Non-similar computational solution for boundary layer flows of non-Newtonian fluid from an inclined plate with thermal slip

The present work deals with the free axisymmetric vibrations of circular sandwich plates with core of linearly varying thickness. The face sheets are treated as membranes of equal thickness and the core is assumed to be solid as well as moderately thick. The plate is assumed to be symmetric about the middle surface. Due to linear thickness variation in the core, the face sheets take the shape of conical shell and because of this the face sheet membrane forces contribute to the bending and transverse shear of the core of sandwich plate. The effect of transverse shear and rotatory inertia has been retained in the core. The equations of motion for such a plate have been derived by Hamilton's energy principle. The frequency equations for three different boundary conditions have been obtained by employing differential quadrature method. The effect of various plate parameters such as taper parameter, thickness of the core at the center, face thickness on the natural frequencies has been studied. Comparison of results has been made. © The Author(s) 2014.

JVC/Journal of Vibration and Control

On the use of differential quadrature method in the study of free axisymmetric vibrations of circular sandwich plates of linearly varying thickness

This paper proposes a new concept on transportation problem in which, we maximize the profit and minimize the transportation time while transporting an amount of quantity from a source to the destination. Here, we design two transportation models, in both the models; we maximize the profit and minimize the time of transportation. Here model-I having the unit purchase cost, unit selling price, unit transportation cost and transportation time as trapezoidal interval type-2 fuzzy number, while in model-II all the parameters are trapezoidal interval type-2 fuzzy number. To reduce these model-I and model-II into crisp equivalent, we use the expected value of a trapezoidal interval type-2 fuzzy number. Then the crisp equivalent problems are solved by employing the Interactive fuzzy satisficing method and LINGO 13.0 software to get the optimal solution. A numerical example is provided to demonstrate the models. © 2015, Springer India Pvt. Ltd.

International Journal of Applied and Computational Mathematics

Profit Maximization Solid Transportation Problem with Trapezoidal Interval Type-2 Fuzzy Numbers

A close relation between frames on a separable Hilbert space H and positive invertible bounded operators is known. In this paper, it is shown that for a bounded operator K on H, there is a relationship between K-frames and quotient operators. Results on K-frames have been proved through operator-theoretic results on quotient of bounded operators. © 2016, Sociedad Española de Matemática Aplicada.

SeMA Journal

Frame operators of K-frames

A graceful labeling of a graph G with n edges is an injection f:V(G)→{0,1,2,⋯,n} with the property that the resulting edge labels are also distinct, where an edge incident with vertices u and v is assigned the label |f(u)−f(v)|. A graph which admits a graceful labeling is called a graceful graph. In this paper, inspired by Koh [K.M. Koh, D.G. Rogers and T. Tan, Two theorems on graceful trees, Discrete Math., 25 (1979), 141–148] method, which combines a known graceful trees to obtain a larger graceful trees, we introduced a new method of combining graceful trees called recursive attachment method, and we show that the recursively attached tree Ti=Ti−1⊕TAi−1 is graceful, for i≥1, where T0 is a base tree which is taken as a caterpillar and TAi−1 is an attachment tree which taken as any caterpillar. Here Ti−1⊕TAi−1 represents a tree obtained by attaching a copy of TAi−1 at each vertex of degree at least two in Ti−1, for i≥1. Consequently the graceful tree conjecture is true for every recursively attached caterpillar tree Ti, for i≥1. © 2016 Elsevier B.V.

Electronic Notes in Discrete Mathematics

Generating Graceful Trees from Caterpillars by Recursive Attachment

Sudoku is an interesting number placement puzzle with some simple rules. For some positive integer n, the puzzle involves an n2 × n2 grid partitioned into n2 distinct blocks each of size n × n such that the integers 1 through n2 appear exactly once in each row, each column and each block of the grid. Often some static numbers known as givens are placed according to the difficulty rating in the puzzle and then the rule is to place the numbers from 1 to n2 in the partially filled grid such that the conditions of the puzzle are satisfied. The aim of this paper is to propose a new algorithm for enumerating all possible Sudoku squares of size n2. It is based on the concepts of permutations derived from n2 × n2 S-permutation matrices termed as S-permutations. There is a one-to-one correspondence between Sudoku squares and the set of those S-permutation matrices which are mutually disjoint to each other. The proposed algorithm uses the set of all S-permutations generated by some permutation generation algorithm as input and then enumerates all the subsets of cardinality n2 of all S-permutations which are mutually disjoint to each other. The correctness of the algorithm is established. Its worst-case time complexity is O(wn2 +2logw), where w = (n!)2n. A mathematical formula involving the total number of the sets of (n2-1) mutually disjoint S-permutations is also derived. Experimentally, the proposed algorithm is verified for the Sudoku squares of size 9 × 9. It is observed that our algorithm is more systematic and better in terms of computational efficiency. © 2016 World Scientific Publishing Company.

Discrete Mathematics, Algorithms and Applications

A new algorithm for enumerating all possible Sudoku squares

Mechanical behavior of three-dimensional cellular assembly of graphene foam (GF) presented temperature dependent characteristics evaluated at both low temperature and room temperature conditions. Cellular structure of GF comprised of polydimethyl siloxane polymer as a flexible supporting material demonstrated 94% enhancement in the storage modulus as compared to polymer foam alone. Evaluation of frequency dependence revealed an increase in both storage modulus and tan delta with the increase in frequency. Moreover, strain rate independent highly reversible behavior is measured up to several compression cycles at larger strains. It is elucidated that the interaction between graphene and polymer plays a crucial role in thermo-mechanical stability of the cellular structure. © 2015 Elsevier Ltd.

Carbon

Temperature dependent compressive behavior of graphene mediated three-dimensional cellular assembly

The purpose of this study is to synthesize and characterize nanosized titania (TiO2), zinc oxide (ZnO), and its composite coating on Ti-6Al-4V to enhance its corrosion protection behavior in Ringer's solution. Nanosized powders of TiO2 and ZnO was characterized by Fourier transform infrared spectroscopy (FTIR), powder X-ray diffraction (XRD), and scanning electron microscopy - energy dispersive atomic spectroscopy (SEM-EDAX) analysis. As a result of antibacterial activity, both ZnO and TiO2/ZnO have produce remarkable inhibition zone on Escherichia coli. The antibacterial activity of composites are due to the combined effect of ZnO on TiO2. The adherence and surface uniformity of TiO2/ZnO composite film on titanium implant was examined by optical microscopy and Vickers microhardness test. Corrosion resistant behavior of the coating on titanium implant was investigated by tafel polarization and impedance analysis. The composite coatings on Ti-6Al-4V have produced improved corrosion resistance with a pronounced shift in the anodic corrosion potential (Ecorr) with a corresponding less corrosion current density (Icorr) compared to monophase coating. Similar results have been obtained for impedance analysis which indicated a reduction in double layer capacitance (Cdl) and with enhancement in charge transfer resistance (Rct). These observations suggest improved corrosion resistance property of TiO2/ZnO composite coating on Ti-6Al-4V. Copyright © Taylor & Francis Group, LLC.