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This study focuses on the comprehensive analysis of the thermal characterization of an electrically conducting nanofluid flow containing TiO2 nanoparticles dissolved in two different common liquids (H2O and C2H6O2) and contained within a continuously extending disk. The heat and concentration formulation are modified by incorporating the standard interpretations of the Joule heating, energy source, dissipation, and modified activation energy with binary chemical reactions. The Darcy–Forchheimer addition is used to highlight the significance of porous media. The Brownian dispersion's effects are clearly discernible in the current investigation. Furthermore, as a novelty, special thermophysical models of viscosity and thermal conductivity are included. The obtained differential formulations are tackled through the analytical procedure HAM. The veracity of the finding is verified through a numerical scheme (ND-solve technique). Using several graphs and charts, the perception trends of model factors are evaluated. The influence of C f z , N u z , and S h z are estimated based on flow characteristics. The F ′ (ζ) curve pattern for both nanofluids is declined by the increasing magnitude of M , ϕ , β p * , and F r * , while thermal profile. The drag force and heat transmission rate are shown to optimize with M as well as ϕ in the pictorial simulations produced from the existing model. The Φ (ζ) can also be strengthened by the presence of a high degree N b. The outcomes are validated by previous studies and a good degree of consistency is revealed. [ABSTRACT FROM AUTHOR]

In this article, we use the applications of special functions in the form of Chebyshev polynomials to find the approximate solution of hyperbolic partial differential equations (PDEs) arising in the mathematical modeling of transmission line subject to appropriate symmetric Dirichlet and Neumann boundary conditions. The special part of the model equation is discretized using a Chebyshev differentiation matrix, which is centro-asymmetric using the symmetric collocation points as grid points, while the time derivative is discretized using the standard central finite difference scheme. One of the disadvantages of the Chebyshev differentiation matrix is that the resultant matrix, which is obtained after replacing the special coordinates with the derivative of Chebyshev polynomials, is dense and, therefore, needs more computational time to evaluate the resultant algebraic equation. To overcome this difficulty, an algorithm consisting of fast Fourier transformation is used. The main advantage of this transformation is that it significantly reduces the computational cost needed for N collocation points. It is shown that the proposed scheme converges exponentially, provided the data are smooth in the given equations. A number of numerical experiments are performed for different time steps and compared with the analytical solution, which further validates the accuracy of our proposed scheme. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.compeleceng.2010.04.003 Byline: Nasro Min-Allah (a)(b), Ishtiaq Ali (c), Jiansheng Xing (d), Yongji Wang (b) Keywords: Real-time systems; Fixed-priority scheduling; Preemptive real-time scheduling; Feasibility analysis; Online schedulability Abstract: Due to polynomial time complexity, utilization based tests are desired for online feasibility analysis of periodic task systems. However, the associated disadvantage with these tests is that they propose a bound on system utilization, which trade processor utilization for performance. On the contrary, response time based tests share pseudo-polynomial time complexity, which are very expensive in terms of analysis time and therefore, impractical for analyzing feasibility of online systems. Realizing the advantage of utilization based tests over response time tests, attempts are being made to propose utilization based exact tests that achieve 100% CPU utilization for the system by modifying task parameters such as restricting task periods to be harmonic. We show that in systems where task deadlines are large, better results are obtained by making the task deadlines harmonic. The paper proposes a novel solution to feasibility problem of periodic task system under the assumption of composite deadline by providing a utilization based exact test with an upper bound of 1 and complexity O(n). Author Affiliation: (a) Department of Computer Science, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan (b) Laboratory for Internet Technologies, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China (c) Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan (d) Department of Computer Science, Illinois Institute of Technology, Chicago, IL 60616, USA Article History: Received 9 October 2008; Revised 19 October 2009; Accepted 15 April 2010 Article Note: (footnote) [star] Reviews processed and proposed for publication to the Editor-in-Chief by Associate Editor Dr. F. Sahin.

In this research work, we present an exciting mathematical analysis of a stochastic model, using a standard incidence function, for infectious disease hepatitis C transmission dynamics. In this model, we divided the infected population into three different classes with two different infection stages known as chronic class and acute class while the third is an isolation class. We also presents briefly the Legendre spectral method for the numerical solution to the proposed model. It is observed that the disease-free equilibrium is asymptotically stable, when basic reproduction number R 0 < 1. It is also shown that the proposed model has a stable endemic equilibrium when the reproduction number R 0 > 1. Also, sensitivity analysis is carried out to study and identify the effect of parameters on R0. Moreover, we have performed numerical simulations to study the influence of disease free equilibrium and endemic equilibrium. Legendre polynomial and Legendre weight function are used to solve the proposed stochastic system numerically. Numerical results are compared against the basic reproduction number. [ABSTRACT FROM AUTHOR]