Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

Scaling of free convection heat transfer in a triangular cavity for Pr>1

Unsteady natural convection inside a triangular cavity subject to a non-instantaneous heating on the inclined walls in the form of an imposed temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the flow from start-up to a steady-state has been described based on scaling analyses and direct numerical simulations. The ramp temperature has been chosen in such a way that the boundary layer is reached a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness, then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently. It is seen that the shape of many houses are isosceles triangular cross-section. The heat transfer process through the roof of the attic-shaped space should be well understood. Because, in the building energy, one of the most important objectives for design and construction of houses is to provide thermal comfort for occupants. Moreover, in the present energy-conscious society it is also a requirement for houses to be energy efficient, i.e. the energy consumption for heating or air-conditioning houses must be minimized.

The impact of temperature on mortality in Tianjin, China : a case-crossover design with a distributed lag non-linear model

Background There has been increasing interest in assessing the impacts of temperature on mortality. However, few studies have used a case–crossover design to examine non-linear and distributed lag effects of temperature on mortality. Additionally, little evidence is available on the temperature-mortality relationship in China, or what temperature measure is the best predictor of mortality. Objectives To use a distributed lag non-linear model (DLNM) as a part of case–crossover design. To examine the non-linear and distributed lag effects of temperature on mortality in Tianjin, China. To explore which temperature measure is the best predictor of mortality; Methods: The DLNM was applied to a case¬−crossover design to assess the non-linear and delayed effects of temperatures (maximum, mean and minimum) on deaths (non-accidental, cardiopulmonary, cardiovascular and respiratory). Results A U-shaped relationship was consistently found between temperature and mortality. Cold effects (significantly increased mortality associated with low temperatures) were delayed by 3 days, and persisted for 10 days. Hot effects (significantly increased mortality associated with high temperatures) were acute and lasted for three days, and were followed by mortality displacement for non-accidental, cardiopulmonary, and cardiovascular deaths. Mean temperature was a better predictor of mortality (based on model fit) than maximum or minimum temperature. Conclusions In Tianjin, extreme cold and hot temperatures increased the risk of mortality. Results suggest that the effects of cold last longer than the effects of heat. It is possible to combine the case−crossover design with DLNMs. This allows the case−crossover design to flexibly estimate the non-linear and delayed effects of temperature (or air pollution) whilst controlling for season.

Free convection heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined. The details results will be discussed in the full paper.

Unsteady buoyancy driven flows and heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined.

Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of the non-linear ASDE. The discrete system of equations is obtained by using the meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formulations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode

This article deals with the non-linear oscillations assessment of a distribution static comensator ooperating in voltage control mode using the bifurcation theory. A mathematical model of the distribution static compensator in the voltage control mode to carry out the bifurcation analysis is derived. The stabiity regions in the Thevein equivalent plane are computed. In addition, the stability regions in the control gains space, as well as the contour lines for different Floquet multipliers are computed. The AC and DC capacitor impacts on the stability are analyzed through the bifurcation theory. The observations are verified through simulaation studies. The computation of the stability region allows the assessment of the stable operating zones for a power system that includes a distribution static compensator operating in the voltage mode.

Validation Gating for Non-Linear Non-Gaussian Target Tracking

This paper develops a general theory of validation gating for non-linear non-Gaussian mod- els. Validation gates are used in target tracking to cull very unlikely measurement-to-track associa- tions, before remaining association ambiguities are handled by a more comprehensive (and expensive) data association scheme. The essential property of a gate is to accept a high percentage of correct associ- ations, thus maximising track accuracy, but provide a su±ciently tight bound to minimise the number of ambiguous associations. For linear Gaussian systems, the ellipsoidal vali- dation gate is standard, and possesses the statistical property whereby a given threshold will accept a cer- tain percentage of true associations. This property does not hold for non-linear non-Gaussian models. As a system departs from linear-Gaussian, the ellip- soid gate tends to reject a higher than expected pro- portion of correct associations and permit an excess of false ones. In this paper, the concept of the ellip- soidal gate is extended to permit correct statistics for the non-linear non-Gaussian case. The new gate is demonstrated by a bearing-only tracking example.