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In this article, the non-fragile finite-time H ∞ state estimation problem of neural networks is discussed with distributed time-delays. Based on a modified Lyapunov–Krasovskii functional and the linear matrix inequality (LMI) technique, a novel delay-dependent criterion is presented such that the error system is finite-time boundedness with guaranteed H ∞ performance. In order to obtain less conservative results, Wirtingers integral inequality and reciprocally convex approach are employed. The estimator gain matrix can be achieved by solving the LMIs. Finally, Numerical examples are given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Nonlinear stability theory is used to investigate free convection arising in a particular class of Horton–Rogers–Lapwood (HRL) problem. Time periodic modulation is imposed on either the temperature at the bounding surfaces or the gravitational field permeating the medium. The Brinkman model and the Boussinesq approximation govern the fluid flow. The energy formulation is followed and the Galerkin method is used to determine the relevant threshold for arbitrary values of the modulational amplitude and frequency. In general it is found that an increase in the modulational amplitude encourages convection ensuing at the threshold. The existence of a subcritical region is predicted and the importance of the nonlinear theory is established. [ABSTRACT FROM AUTHOR]

The present investigation deals with the combined effect of natural convection and surface radiation in an air filled square cavity with a nonuniformly heated thin plate placed horizontally or vertically at its center. The non-uniform heating is due to the non-linearly varying temperature of the plate. The vertical walls of the two dimensional cavity are cooled while the horizontal ones are insulated. The resulting coupled equations were solved using the finite volume method on a uniformly staggered grid system. Numerical simulations were carried out for a wide range of values of non-uniform heating, plate length and surface emissivity at a Rayleigh number of Ra = 10 7 . It is found that the surface radiation makes the entire cavity thermally active with a good homogenization of the temperature field for both uniform and nonuniform heating of the plate. The heat transfer rate for a vertically placed plate is always higher than that of a horizontally oriented one. The increase of emissivity always enhances the heat transfer within the cavity, while the plate length can have both augmenting and dampening effects. The non-uniform heating results in a dual effect depending on the plate length and emissivity. The effect of uniform and non-uniform heating of the plate on the total and convective heat transfer rates is presented and discussed. [ABSTRACT FROM AUTHOR]

Abstract: Thermorheological effect on the sufficient conditions for the onset of natural convection in a fluid saturated porous medium with uniformly distributed internal heat sources is studied. The flow through the medium is governed by Brinkman’s equation. The constituent phases of the medium are assumed lack thermal equilibrium. A nonlinear temperature dependent viscosity is considered. The resulting eigenvalue problem is solved using the Galerkin weighted residual method. Results indicate that the temperature dependence of viscosity and the presence of heat sources produce effects that are favourable for convection to set in. A possible application of this study in a practical situation is highlighted. [Copyright &y& Elsevier]

Abstract: The effect of gravity modulation on the onset of convection in a horizontal fluid saturated porous layer in which the applied temperature gradient is opposite to that of gravity is investigated. The flow through the porous layer is governed by an extended form of Darcy’s law incorporating Brinkman’s boundary layer correction. The permeability and thermal conductivity of the medium are assumed to be transversely anisotropic. A stability analysis based on the method of small perturbations is performed using normal mode assumption. The study is focussed on low amplitude gravity modulation and the thresholds are found using Mathieu’s functions. The emergence of instability via the synchronous and subharmonic modes and the transition between them are discussed as a function of the physical parameters of interest. [Copyright &y& Elsevier]

An internal natural convective flow arising in a closed square cavity due to the presence of two orthogonal and differentially heated plates is studied numerically. The flow is assumed to be laminar and two-dimensional. The Alternating Direction Implicit technique in association with the Successive Over Relaxation method is used to solve the coupled nonlinear governing equations. The heat and fluid flow interactions are studied for various combinations of plate–plate and plate–wall temperature ratios and different positions of the heated plates. When there are two plates with high temperature contrast the heat transfer mechanism inside the cavity is mainly ruled by the hotter one. In general convection heat transfer becomes strengthened when the vertical plate is hotter. [ABSTRACT FROM AUTHOR]

Abstract This paper discusses about Markovian (s , Q) inventory-queueing system with server interruptions of two heterogeneous servers. Matrix method is applied to obtain the steady state joint probability distribution of customers level in the queue, retrial group, status of the servers and stock level of heterogeneous system. This paper studies the significant effect of heterogeneous system (each server work with different service rate) as compared with homogeneous system (all servers work with same service rate). Performance measures are derived for heterogeneous system and homogeneous system. Appropriate cost functions for both models are defined. Numerical examples are used to compare the total expected cost rates of both systems. Heterogeneous system yields the minimum total expected cost value and therefore the heterogeneous system is effective. Highlights • This paper investigates the Markovian (s , Q) inventory system with server interruptions and two heterogeneous servers. • One important feature is that our paper makes comparison of the systems with homogeneous servers and heterogeneous servers with server interruptions and obtained the heterogeneous system to be better than the corresponding homogeneous system. • Our paper gives the better solution for heterogeneous servers based on the numerical examples corresponding to the homogeneous system. • Mr.V.P.Singh (1970) in his paper "Two Server Markovian queues with Balking: Heterogeneous Vs Homogeneous", Operations Research Vol. 18, 1, 145–149, had obtained solution to Queueing system (without Inventory) with two heterogeneous servers and had compared the heterogeneous servers with the corresponding homogeneous servers and obtained results under which the queueing system with heterogeneous servers is better than the corresponding homogeneous system. Our result with inventory is consistent with the result of Mr. V.P. Singh. [ABSTRACT FROM AUTHOR]