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.

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VIT University

Department of Mathematics

Reducing carbon emissions plays a significant role in developing sustainable inventory systems. In a seller-buyer relationship, an allowable delay in payment is considered for the buyer to manage the stock and simulate the demand. Deteriorating items that usually have specific maximum lifetimes have become a challenge for most firms. Contrary to the importance of these issues, very little research has studied the impact of carbon emissions on deteriorating inventory systems. This paper provides a price-dependent demand for perishable items when carbon cap-and-trade regulation fills the mentioned gap. This model provides a carbon reduction investment scheme and illustrates this investment’s effect on the inventory system. This paper determines the optimal replenishment cycle and selling price, in which: (a) perishable items have specific maximum lifetimes, (b) a specific period of delay in payment is allowed for the buyer to accumulate revenue, (c) carbon is emitted due to ordering and storage operations and carbon cap and trade is regulated along with allowable carbon reduction investment. After developing the model, optimal values are obtained from necessary and sufficient conditions of optimality. Numerical experiments are proposed to validate the model. By developing an algorithm, the optimal values of replenishment cycle, selling price, and carbon reduction technology investment are obtained, and the impact of carbon emissions and efforts to control emissions are outlined. Finally, some managerial applications are mentioned, and future research directions are exposed. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.

World University root node

School of Advanced Sciences

Vellore Campus

Fulltext

Mathematics

Joint pricing and inventory model for deteriorating items with maximum lifetime and controllable carbon emissions under permissible delay in payments

This paper deals with an economic production quantity (EPQ) inventory model for deteriorating items under preservation technology. The preservation technology is used to protect the items from deterioration. Three different production levels are considered. It is assumed that initially the production rate is at a lower rate and it increases gradually over the period. This is just in order to reduce the holding cost by avoiding the larger stock quantity at the beginning of the production cycle. The shortages are permitted and fully backordered. The objective of the production inventory model is to determine the optimal production policy which minimizes the manufacturer's total cost. Theoretical results are established in order to demonstrate the existence of the optimal solution and a proper solution procedure is presented. A numerical example and sensitivity analysis are presented to validate the theoretical results. Also, some managerial insights are provided. © EDP Sciences, ROADEF, SMAI 2021.

RAIRO - Operations Research

Production inventory model for controllable deterioration rate with shortages

The main aim of this study is to analyze the dynamical properties of hepatitis B-type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable during the activation of immune response and time taken to infect the healthy cells. Mathematically, the qualitative analyses such as stability, bifurcation, and stabilization analysis are performed to explore the dynamical characteristics of HBV over the period of time. The significance of the model parameters is revealed through Hopf-type bifurcation analysis and the global stability analysis of the proposed model. With the help of data set values that are extracted from the literature, the efficiency of the derived theoretical results is explored. © 2021 John Wiley & Sons, Ltd.

Chennai Campus

Mathematical Methods in the Applied Sciences

Stability and bifurcation analysis of hepatitis B-type virus infection model

This article is mainly focusing on the existence and uniqueness of nonlocal fractional delay differential systems of order 1 &lt; r &lt; 2 in Banach spaces. By using the theoretical concepts related to the fractional calculus, cosine, and sine functions of operators and fixed point approach, we prove our main results. By using Kranoselskii's fixed point theorem, we discuss the existence of the mild solution and by applying the Banach contraction principle, we prove the existence and uniqueness of the mild solution of nonlocal fractional delay differential system. Finally, we provide an example to illustrate the obtained theoretical results. © 2020 Wiley Periodicals LLC

Numerical Methods for Partial Differential Equations

A new study on existence and uniqueness of nonlocal fractional delay differential systems of order 1 &lt; r &lt; 2 in Banach spaces

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (103–106), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity. © 2021 Wiley Periodicals LLC

Heat Transfer

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

In this manuscript, we investigate an electrically conducting, laminar and an incompressible 2D (two-dimensional) Casson fluid above a nonlinear permeable sheet in the occurrence of Newtonian heating and heat source. The nonlinear coupled arrangement of typical differential conditions are acquired through appropriate changes and after that figured by utilizing R-K method including shooting technique. The behaviour of dimensionless parameters is presented graphically and discussed velocity and temperature distributions along with friction aspect coefficient and rate of heat transfer concerning Nusselt number. It is discovered that the Casson and Newtonian warming parameters increase the grinding factor coefficient and heat transfer rates. © 2021, Springer Nature Singapore Pte Ltd.

Lecture Notes in Mechanical Engineering

MHD Casson Fluid Flow Past a Stretching Sheet with Convective Boundary and Heat Source

Abstract: Evaluating the entropy generation is essential in thermal systems to avoid the unnecessarily wasted thermal energy during the thermal processes. Nowadays, researchers are greatly fascinated to scrutinize the entropy generation in a human system because it is utilized as a thermodynamic approach to understand the heat transfer characteristics of cancer systems or wounded tissue and their accessibility status. Further, numerous nanoparticles have been employed as an agent to control the heat transfer of blood and wounded tissue. As a result, the present model manifests the entropy generation, flow characteristics and heat transport of Ag/Fe3O4-blood flow of a nanofluid in a permeable circular tube with the influence of variable electrical conductivity and linear radiation. Nonlinear transport equations are converted into ordinary differential equations by suitable similarity variables which are solved with weighted residual method. Significant parameters like Reynolds number, dimensionless permeability parameter, extending/contracting parameter, Eckert number and Hartmann number on the radial pressure, axial velocity, radial velocity and temperature are explored through graphs. The obtained results show that temperature distribution of Fe3O4 nanoparticles is higher than Ag nanoparticle, in case of suction. The dimensionless permeability parameter has an opposite nature on the radial pressure for the suction and injection cases. Growing values of Hartmann number enhance the total entropy generation for the cases of suction and injection. Graphic Abstract: [Figure not available: see fulltext.] © 2021, The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature.

European Physical Journal E

Exploring the heat transfer and entropy generation of Ag/Fe 3 O 4 -blood nanofluid flow in a porous tube: a collocation solution

The present paper is on 2D Casson magnetohydrodynamic flow through exponentially shrinking surface. The set of nonlinear PDEs are established into ODEs by using R-K scheme connected by shooting methodology. Some of the physical quantities are implemented to demonstrate the effects of exponential, Eckert number, Casson and radiation parameters on temperature and velocity distributions. The constraint of Eckert numbers decelerates the rate of heat transfer in both and cases. © 2021, Springer Nature Singapore Pte Ltd.

Unsteady Casson MHD Flow Due to Shrinking Surface with Suction and Dissipation

We propose to investigate the solutions of system of functional-integral equations in the setting of measure of noncompactness on real-valued bounded and continuous Banach space. To achieve this, we first establish some new Darbo type fixed and coupled fixed point results for µ-set (ω, ϑ)-contraction operator using arbitrary measure of noncompactness in Banach spaces. An example is given in support for the solutions of a pair of system of functional-integral equations. © 2021, Semnan University, Center of Excellence in Nonlinear Analysis and Applications. All rights reserved.