Flow and heat transfer along a plane wall with periodic suction

Summary The three-dimensional incompressible laminar boundary layer past a flat plate is investigated, when suction with a slightly sinusoidal transverse suction velocity distribution at the wall is applied. For the asymptotic flow conditions far downstream the components of the wall shear stress and the heat transfer including its dependence on Prandtl number are determined.

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Zusammenfassung Es wird die dreidimensionale inkompressible, laminare Grenzschicht an der längsangeströmten Platte behandelt, bei der mit einer in Querrichtung schwach sinusförmigen Geschwindigkeitsverteilung an der Wand abgesaugt wird. Für den asymptotischen Zustand weit stromabwärts werden die Komponenten der Wandschubspannung sowie der Wärmeübergang mit dessen Abhängigkeit von der Prandtl-Zahl bestimmt.

     

Multiscale computational method for nonstationary integrated heat transfer problem in periodic porous materials

This article discusses multiscale analysis and numerical algorithm for the nonstationary integrated heat transfer problem with rapidly oscillating coefficients. The multiscale asymptotic expansion of the solution for this kind of problems is presented first. Then, error estimates of the multiscale approximate solution are derived, and a numerical algorithm based on the multiscale method for temperature field is introduced. Finally, using some numerical models, we verify the validity and relevancy of the proposed algorithm. The numerical results show that the algorithm is effective to predict the heat transfer performance of porous materials, and support the convergence theorem reported in this article. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 510–530, 2016     

Temperature fields in machining processes and heat transfer models

This paper deals with the modelling of the heat transfer process with special attention to the characterization of the thermal field during turning processes. Specifically, the measurement of the thermal field and the selection of the proper heat transfer models are dealt with. The analysis is developed in view of the solution of direct and inverse problems.     

Asymptotic transport models for heat and mass transfer in reactive porous media

We propose an approach for deriving in a rigorous but formal way a family of models of mass and heat transfer in reactive porous media. At a microscopic level we set a model coupling the Boltzmann equation in the gas phase, the heat equation on the solid phase and appropriate interface condititons. An asymptotic expansion leads to a system of coupled diffusion equations where the effective diffusion tensors are defined from the microscopic geometry of the material through auxiliary problems. The ellipticity of the diffusion operator is addressed. To cite this article: P. Charrier, B. Dubroca, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

小周期复合材料热传导问题的双尺度渐近展开及收敛性分析

利用双尺度渐近展开和均匀化思想讨论了小周期复合材料的热传导问题,得到了具有高阶震荡系数的抛物型方程的渐近展开式,并证明了当Ω为R~2中的光滑的区域时渐近展开式在空间L~2(0,T;H~1(Ω))中具有较好的收敛性.     

Investigation of surface destruction of construction materials under intense periodic heat transfer

The study simulates the surface destruction of structural steel elements in power installations as a result of interaction with periodic high-temperature chemically active flows. The system of equations of thermoelasticity with two spatial observations is used. The existence of high tangential and axial compressive stresses is established in a thin layer near the metal-gas interface. Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 115–118.     

New integral transforms in boundary-value problems for laminated composites with a periodic structure

An elliptic equation for a layered regularly inhomogeneous (composite) material serves as an example for the introduction of new integral transforms that enable boundary-value problems to be solved in quadratures, without the need to solve boundary-layer problems. These integral transforms are used to solve simple boundary-value problems for a layered composite and to obtain a fundamental solution of an elliptic equation in an infinite two-dimensional laminar medium.     

Lattice-Boltzmann Models for heat transfer

A multispeed heat transfer lattice Boltzmann model is presented. The model possesses the perfect gas state equation with arbitrary special heat ratio. The macroscopic conservation equations are derived by the Chapman-Enskog method. The one dimensional simulation for the sinusoidal energy distributions are compared with the theoretical results, showing good agreement. The theoretical conductivity in the energy equation is in accordance with the simulations.     

Population models in almost periodic environments

We establish the basic theory of almost periodic sequences on ?₊. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.     

Symmetry analysis of a heat conduction model for heat transfer in a longitudinal rectangular fin of a heterogeneous material

We consider a heat conduction model arising in transient heat transfer through longitudinal fins of a heterogeneous (functionally graded) material. In this case, the thermal conductivity depends on the spatial variable. The heat transfer coefficient depends on the temperature and is given by the power law function. The resulting nonlinear partial differential equation is analyzed using both classical and nonclassical symmetry techniques. Both the transient state and the steady state result in a number of exotic symmetries being admitted by the governing equation. Furthermore, nonclassical symmetries are also admitted. Both classical and nonclassical symmetry analysis results in some useful reductions and some remarkable exact solutions are constructed.     

A non-conforming finite element for limit analysis of periodic composites

In this work, a non-conforming three-dimensional finite element coupled with direct methods and homogenization technique is presented for the limit analysis of periodic metal-matrix composites. Using this element, which is constructed from bilinear shape functions and enriched by internal second-order polynomials, limit analysis of composite material can be efficiently carried out. Accuracy and overall performance are illustrated through comparison with different structural solid elements in the context of direct as well as incremental methods. It is shown that the limit domain of periodic composites for different fiber distributions and volume fractions provides a foundation for the structural design. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of stochastic heat transfer in a solid

The unsteady partial differential equations for expectation and correlation distributions of the stochastic temperature distribution in a solid are obtained, when the coefficients and the source term in the stochastic heat transfer equations are white Gaussian processes. Some solutions of the unsteady partial differential equations for expectation and correlation distributions of stochastic heat transfer are presented.     

A look at a problem in heat transfer

Consideration and careful investigation of a simple physical problem in heat transfer shows that even such a problem may not always have solutions and meaningful solutions exist only under restricted conditions. In other words, not all physical problems are well posed. The analysis given here shows that in many practical problems in fluid mechanics and heat transfer the question ‘how well posed is it?’ is non-trivial.     

The periodic unfolding method for the heat equation in perforated domains

We study the heat equation with non-periodic coefficients in periodically perforated domains with a homogeneous Neumann condition on the holes. Using the time-dependent unfolding method, we obtain some homogenization and corrector results which generalize those by Donato and Nabil(2001).     

Shakedown and limit analysis of periodic composites

The optimization of fiber distribution is analyzed in order to improve the strength performance of metal-matrix composite material, which is submitted to two variable independent loads by coupling homogenization and shakedown theories. Numerical Direct Methods are applied to acquire the shakedown domain of three-dimensional heterogeneous elastic-perfectly plastic fiber-reinforced composite for optimal design. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weighted least absolute deviations estimation for periodic ARMA models

This paper investigates the weighted least absolute deviations estimator (WLADE) for causal and invertible periodic autoregressive moving average (PARMA) models. Asymptotic normality of the estimator is derived under a fractional moment condition. A simulation study is given to assess the performance of the proposed WLADE.