Volume 23, Issue 2

A multistage system refers to a system contains multiple components or stages which are necessary to finish the final product or service. To analyze these problems, the first step is model building and the other is optimization. Response surfaces are used to model multistage problem as an efficient procedure. One regular approach to estimate a response surface using experimental results is the ordinary least squares (OLS) method. OLS method is very sensitive to outliers, so some multivariate robust estimation methods have been discussed in the literature in order to estimate the response surfaces accurately such as multivariate M-estimators. In optimization phase, multi-response optimization methods such as global criterion (GC) method and ε -constraints approaches are different methods to optimize the multi-objective-multistage problems. An example of the multistage problem had been estimated considering multivariate robust approaches, besides applying multi-response optimization approaches. The results show the efficiency of the proposed approaches.

A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10 −4 ≤ Da ≤ 10 −1 ), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10 −4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10 −1 . The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

The problem of unsteady magnetohydrodynamics (MHD) free convection flow of nano-fluid past an oscillation moving vertical semi-infinite permeable flat plate with constant heat source and vertical variable thermal boundary condition in a rotating frame of reference is studied theoretically. The boundary layer has the oscillatory type of solution because slip velocity is assumed to oscillate in time with constant frequency. The governing equations are solved using small perturbation approximation. For this investigation, we use two types of nano-particles in base fluid, namely Cu (copper) and Al 2 O 3 (aluminium oxide). The effect of various types of suspended metallic nano-particles and non-dimensional physical parameters on the fluid flow and heat transfer rate are presented and discussed through the graphs.

Coastal lagoons are high value productive and important systems for different projects. For example, aquaculture, fisheries and tourism are few of them. The quality of coastal waters in the ecosystems of lagoons can be greatly influenced by the growth of unwanted elements, e.g., excessive fisheries, tourism, etc. In this paper, a mathematical model is proposed and analysed to study the general and simplified form of an ecosystem of Chilika Lake, India. Chilika Lake (19°28′N–19°54′N and 85°06′E–85°36′E) is the largest wintering ground for migrating water fowl found anywhere on the Indian sub-continent. These migratory birds utilize the Chilika Lake for feeding, resting and breeding. The interaction of birds and small fish in the Chilika Lake is considered to be Leslie–Gower Holling type II. Since big fish are being sourced as income for local fishermen and the population of big fish is highly variable, and hence birds and small fishes are mainly the two types of biomass considered for this study. It must be noted that, in this study, we have considered the case of Chilika lake theoretically only and no practical data is collected for this study, and the name of Chilika is used only for better ecological understanding. Therefore, this theoretical study maybe linked to any such ecosystem. Their interaction is found mathematically, a two-dimensional continuous-time dynamical system modeling a simple predator–prey food chain. The dynamical system is represented in the form of two nonlinear coupled ordinary differential equation (ODE) systems. The main mathematical results are given in terms of boundedness of solutions, existence of equilibria, local and global stability of the coexisting interior point. An ecosystem in Indian coastal lagoons may suffer immediate environmental perturbations, such as depressions, tropical cyclones, earthquakes, epidemics, etc. To model such situations, the ODE model is further extended to a stochastic model driven by L e ́ $\check{d}{e}$ vy noise. The stochastic analysis includes the existence of the unique global solution, stability in mean, and extinction of the population. The proposed model is numerically simulated with the help of an assumed set of parameters for the possible pictorial behavior of the theoretical model. The proposed model may be used for planning purposes by using the data on meteorological and weather shocks such as heavy rainfall, heat-waves, cold-waves, depressions, tropical cyclones, earthquakes, etc. from India Meteorological Department (IMD).

The equations, modelling a nonlinear resistive-capacitive-inductance shunted Josephson junction (NRCLJJ) subjected to various signal shapes of the electrical current, are simulated experimentally using the Arduino Uno-type microcontroller that takes benefit of its simplicity, lost cost, high precision, ease of implementation, and stability compared to the voltage-controlled oscillators (VCO) circuitry. Real time electrical signals are observed presenting various dynamics. Shapiro steps (SS) from the IV -characteristics are also obtained. These real electrical signals are then used to power an electromechanical pendulum in the second part of this work. Bifurcation diagram shows that the pendulum exhibits periodic and chaotic dynamics.

We present a level set based adaptive mesh method for solving the drag minimization problem of incompressible flow governed by Stokes equations. Shape sensitivity analysis of the cost functional is derived. During the optimization process, two levels of meshes are adopted. A uniform coarse mesh for evolving the level set function is defined over the whole computational domain. The level set function also serves as the refinement indicator with an easy strategy. The coarse mesh that contains the interfaces then further divided into a uniform fine mesh and the computation is mainly near the interfaces. Therefore, the computational cost is significantly reduced compared with the uniform mesh over the whole domain that achieves the same resolution. Above all, the value of the shape derivative on the boundary can be obtained implicitly, which is a very difficult task in classical optimal shape design problems. The overall optimization procedure is presented and verified with benchmark examples.

In this paper we present callocation method for solving the problems in the calculus of variation (CV) using multiquadratic radial basis functions (MQRBFs). In this method we use the Gauss quadrature rule for approximating the integral in CV problems. The effects of the shape parameter of MQRBFs on the convergence of the method have been discussed. Illustrative examples are included to evaluate the capability of the proposed method.

This article deals with the heat transfer enhancement due to buoyancy force in a partially heated square enclosure filled with nanofluids. The model is developed to analyse the behaviour of nanofluids taking into account of volume fraction and stretching parameter, when square horizontal walls are moving in opposite directions to each other. Implicit alternate direct finite difference method has been used to solve the governing equations of vorticity, energy, and kinematics. Graphically investigated the effect of physical pertinent controlling parameters on the dimensionless velocity, streamlines, isothermal, and Nusselt number. The obtained numerical solution achieves the best configuration for Rayleigh number 10 3 ≤ Ra ≤ 10 5 , stretching parameter 0 ≤ τ ≤ 2.5, and volume fraction 0 ≤ ϕ ≤ 0.2. It is found that the stretching parameter and direction of moving walls affect the fluid flow, flow strength, and heat transfer in the cavity.

In this paper, we propose and study a fractional Caputo-difference map based on the 2D generalized Hénon map. By means of numerical methods, we use phase plots and bifurcation diagrams to investigate the rich dynamics of the proposed map. A 1D synchronization controller is proposed similar to that of Pecora and Carrol, whereby we assume knowledge of one of the two states at the slave and replicate the second state. The stability theory of fractional discrete systems is used to guarantee the asymptotic convergence of the proposed controller and numerical simulations are employed to confirm the findings.