Mixed convection in vertical channels with a discrete heat source

Two dimensional laminar mixed convection flow in vertical channels with a discrete heat source was numerically analyzed. An isoflux discrete heating element was located on the left wall, while the isothermal conditions were imposed on the other wall. The governing equations were solved using a finite difference method based on the control volume approach. The mean Nusselt number was calculated and the maximum component temperature was determined. The computations were carried out for different Grashof number, Reynolds number, heater locations and the channel width. It was observed that the location of the heating element does not play a considerable role on the flow. At low Reynolds numbers (Re<50), the mean Nusselt number and the maximum temperature are mainly controlled by the Grashof number. However, at higher Reynolds numbers, the Reynold number plays an important role on the flow. It was also found that at low Reynolds numbers, cooling is more effective when the channel width is large (W/H>1). However, at high Reynolds numbers more effective cooling is obtained in narrow channels.

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Mischkonvektion in vertikalen Kanälen mit einer lokalen Wärmequelle

Zusammenfassung Die zweidimensionale laminare Mischkonvektion in vertikalen Kanälen mit einer lokalen Wärmequelle wird numerisch untersucht. Ein Heizelement konstanter Wärmeleistung befindet sich auf der linken Kanalwand, die rechte hat konstante Temperatur. Die Lösung der Grundgleichung erfolgte mit Hilfe der auf dem Kontrollvolumenprinzip basierenden Finitdifferenzenmethode. Die mittlere Nusselt-Zahl sowie die Maximaltemperatur des Heizelementes wurden berechnet, und zwar unter Variation der Grashof-Zahl, der Reynolds-Zahl, der Lage des Heizelements und der Kanalbreite. Letztere hatte nur geringen Einfluß auf den Strömungsverlauf. Bei kleinen Reynolds-Zahlen (Re<50) werden Nusselt-Zahl und Maximaltemperatur vorrangig durch die Grashof-Zahl bestimmt, während bei hohen Reynolds-Zahlen letztere den Strömungsvorgang beherrscht. Ferner zeigte sich, daß bei niedrigen Reynolds-Zahlen die Kühlung für große Kanalbreite (W/H>1) effektiver wird und bei hohen Reynolds-Zahlen die Verhältnisse gerade umgekehrt liegen.

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Nomenclature g gravitational acceleration - Gr Grashof number (Gr=gqH ⁴/v²k) - H heater hight - k thermal conductivity of fluid - L height of the channel - Nu Nusselt number - P pressure - Pr Prandtl number - Re Reynolds number (Re=V ₀H/v) - S position of heater center - T temperature - T _c cold wall temperature - T ₀ inlet temperature - u velocity component inx-direction - U dimensionless velocity component inx-direction (U=u/V ₀) - x horizontal axis - X dimensionless horizontal axis (x/H) - v velocity component iny-direction - V dimensionless velocity component iny-direction (V=v/V ₀) - V ₀ inlet velocity - W width of the channel - y vertical axis - Y dimensionless vertical axis (y/H) Greek symbols a thermal diffusivity - thermal expansion coefficient - density of fluid - kinematic viscosity - dimensionless temperature (=(T–T _c)/[qH/k])     

Simulation studies on multi-mode heat transfer from an open cavity with a flush-mounted discrete heat source

Prominent results of a simulation study on conjugate convection with surface radiation from an open cavity with a traversable flush mounted discrete heat source in the left wall are presented in this paper. The open cavity is considered to be of fixed height but with varying spacing between the legs. The position of the heat source is varied along the left leg of the cavity. The governing equations for temperature distribution along the cavity are obtained by making energy balance between heat generated, conducted, convected and radiated. Radiation terms are tackled using radiosity-irradiation formulation, while the view factors, therein, are evaluated using the crossed-string method of Hottel. The resulting non-linear partial differential equations are converted into algebraic form using finite difference formulation and are subsequently solved by Gauss–Seidel iterative technique. An optimum grid system comprising 111 grids along the legs of the cavity, with 30 grids in the heat source and 31 grids across the cavity has been used. The effects of various parameters, such as surface emissivity, convection heat transfer coefficient, aspect ratio and thermal conductivity on the important results, including local temperature distribution along the cavity, peak temperature in the left and right legs of the cavity and relative contributions of convection and radiation to heat dissipation in the cavity, are studied in great detail.     

锆金属粉尘云的爆炸特性

采用20 L近球形爆炸实验系统对锆粉尘云的爆炸特性开展了实验研究,分别分析了初始点火能量、点火延迟时间、粉尘云浓度3种因素对锆粉尘云爆炸强度的影响,揭示了锆粉尘云在密闭容器中的爆炸特性。在本实验条件下,结果表明:初始点火能量对锆粉尘云最大爆炸压力有显著影响,锆粉尘云最大爆炸压力随初始点火能量的增大而增大;随点火延迟时间的增加,锆粉尘云最大爆炸压力先增大后减小,存在最佳点火延迟时间;随粉尘云浓度的增大,锆粉尘云最大爆炸压力先增大后减小,存在最佳锆粉尘云浓度,得到锆粉尘云的爆炸下限为18~20 g/m3。     

State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

In this work,a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed.The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions.The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity.The inverse Laplace transforms are computed numerically,and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.     

The unsteady heat transfer due to a heat source in an MHD stretching sheet flow

The time evolution in the temperature field resulting from the sudden introduction of a heat source into the already fully established steady MHD flow of an electrically conducting fluid past a linearly stretching isothermal surface is considered. The problem is shown to be fully described by two dimensionless parameters, a modified magnetic field strength ?? and a heat source strength Q. Numerical solutions of the initial-value problem show that there is a critical value Q _c of the parameter Q, dependent on ??, such that, for Q<Q _c , the solution approaches a steady state at large times and, for Q>Q _c , the solutions grows exponentially large as time increases. This growth rate is determined through an eigenvalue problem which also determines the critical value Q _c . The limits of Q _c for both small and large values of ?? are discussed.     

煤粉尘爆炸过程中火焰的传播特性

为了揭示煤粉尘爆炸过程中火焰传播特征,采用2种不同质量分数挥发分的煤粉在半封闭竖直燃烧管中进行实验。分别使用高速摄影装置和红外热成像装置记录火焰传播过程和空间的温度分布情况,并分析2种煤粉尘云的火焰传播速度和温度曲线。结果表明:在同等条件下,火焰在挥发分质量分数高的煤粉尘云中的传播速度和火焰温度要高于其在挥发分质量分数较低的煤粉尘云中的。煤粉尘云的体积质量和点火能量也影响着火焰的传播过程,随着煤粉尘云体积质量的增大,火焰的传播速度和火焰温度整体上呈现先增大后减小的趋势,在传播的后半段火焰速度出现震荡现象;随着点火能量的增大,火焰在煤粉尘云中的传播速度和最高温度也相应升高。通过大量的实验数据计算得到特定条件下火焰传播速度和温度的经验公式。     

镁粉尘云最低着火温度的实验测试

采用标准装置Godbert-Greenwald恒温炉测试了不同条件下镁粉尘云最低着火温度。实验测试结果显示:D50为6、47、104、173 m时镁粉尘云最低着火温度分别为480、520、620、700 ℃;选取D50为6 m的镁粉,在分散压力恒定为0.1 MPa时,镁粉浓度由424 g/m3变化到5 085 g/m3,粉尘云最低着火温度由600 ℃降低到480 ℃;而粉尘质量恒定为0.3 g时,分散压力从0.1 MPa增加到0.2 MPa,粉尘云最低着火温度由540 ℃升高到580 ℃。还分析了镁粉粒径、浓度及分散压力对粉尘云最低着火温度的影响。     

瓦斯煤尘共存条件下的煤尘云爆炸下限

近年来瓦斯煤尘共存条件下的爆炸事故呈多发趋势。运用20 L爆炸特性测试系统,对瓦斯煤尘共存复合体系的爆炸特性进行实验研究,得到了瓦斯在不同点火能量、静止及湍流状态下的爆炸下限,以及不同条件下煤尘的爆炸下限。结果表明:随着瓦斯浓度的增加,煤尘的爆炸下限呈指数衰减;瓦斯浓度存在某临界点,高于此临界点,复合体系爆炸过程中瓦斯起主导作用,表现为"强瓦斯"性,反之,煤尘起主导作用,表现为"强煤尘"性。研究结论为有效预防煤矿井下瓦斯煤尘共存爆炸事故提供重要的理论依据。     

An alternative approach to the heat equation

The technique of conformal transformations of the metric, widely used in general relativity and in cosmology, is applied to the analysis of heat conduction in an anisotropic medium, in which the thermal conductivity is described by a tensor instead of a scalar. The anisotropic medium is reduced to an effective equivalent one, which is isotropic. The simplification is achieved for a particular conformal factor of the transformation, uniquely determined under physically reasonable assumptions on the thermal conductivity, density, and specific heat of the medium. Another application consists in the formal elimination of source or sink terms from the heat equation by using a suitable conformal transformation.

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Nodal predictive error model and Bayesian approach for thermal diffusivity and heat source mapping

This article aims at solving a two-dimensional inverse heat conduction problem in order to retrieve both the thermal diffusivity and heat source field in a thin plate. A spatial random heat pulse is applied to the plate and the thermal response is analysed. The inverse approach is based on the minimisation of a nodal predictive error model, which yields a linear estimation problem. As a result of this approach, the sensitivity matrix is directly filled with experimental data, and thus is partially noisy. Bayesian estimators, such as the Maximum A Posteriori and a Markov Chain Monte Carlo approach (Metropolis–Hastings), are implemented and compared with the Ordinary Least Squares solution. Simulated temperature measurements are used in the inverse analysis. The nodal strategy relies on the availability of temperature measurements with fine spatial resolution and high frequency, typical of nowadays infrared cameras. The effects of both the measurement errors and of the model errors on the inverse problem solution are also analysed.     

A discrete mechanics approach to dislocation dynamics in BCC crystals

A discrete mechanics approach to modeling the dynamics of dislocations in BCC single crystals is presented. Ideas are borrowed from discrete differential calculus and algebraic topology and suitably adapted to crystal lattices. In particular, the extension of a crystal lattice to a CW complex allows for convenient manipulation of forms and fields defined over the crystal. Dislocations are treated within the theory as energy-minimizing structures that lead to locally lattice-invariant but globally incompatible eigendeformations. The discrete nature of the theory eliminates the need for regularization of the core singularity and inherently allows for dislocation reactions and complicated topological transitions. The quantization of slip to integer multiples of the Burgers’ vector leads to a large integer optimization problem. A novel approach to solving this NP-hard problem based on considerations of metastability is proposed. A numerical example that applies the method to study the emanation of dislocation loops from a point source of dilatation in a large BCC crystal is presented. The structure and energetics of BCC screw dislocation cores, as obtained via the present formulation, are also considered and shown to be in good agreement with available atomistic studies. The method thus provides a realistic avenue for mesoscale simulations of dislocation based crystal plasticity with fully atomistic resolution.     

Stresses in a tubular bone exposed to heat radiation from a distant heat source

The paper deals with the development of a mathematical model for studying the distribution of stresses generated in a long tubular bone specimen due to a radiating heat source situated at a very large distance. The model is particularly suitable for examining the effect of solar radiation on long bones. The expressions for the radial and circumferential stresses derived on the basis of the mathematical analysis are computed numerically for a particular bone specimen and the variation of the stress-components with radial and angular distances are studied.     

A numerical study of mixed convection in a horizontal channel with a discrete heat source in an open cavity

This article aims to numerically investigate mixed convection heat transfer in a two-dimensional horizontal channel with an open cavity. A discrete heat source is considered to be located on one of the walls of the cavity. Three different heating modes are considered which relate to the location of the heat source on three different walls (left, right and bottom) of the cavity. The analysis is carried out for a range of Richardson numbers and cavity aspect ratios. The results show that there are noticeable differences among the three heating modes. When the heat source is located on the right wall, the cavity with an aspect ratio of two has the highest heat transfer rate compared to other cavity heating modes. Moreover, when the heat source is located on the bottom wall, the flow field in the cavity with an aspect ratio of two experiences a fluctuating behaviour for Richardson number of 10. The results also show that at a fixed value of Richardson number, all three different heating modes show noticeable improvements in the heat transfer mechanism as the cavity aspect ratio increases.     

Thermal stresses induced by a point heat source in a circular plate by quasi-static approach

The present paper deals with the determination of quasi-static thermal stresses due to an instantaneous point heat source of strength g_pi situated at certain circle along the radial direction of the circular plate and releasing its heat spontaneously at time t = τ. A circular plate is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary of r = b. The governing heat conduction equation is solved by using the integral transform method, and results are obtained in series form in terms of Bessel functions. The mathematical model has been constructed for copper material and the thermal stresses are discussed graphically.     

Simultaneous melting and evaporation due to an area heat source

A numerical method to solve the heat transfer problem of simultaneous melting and evaporation due to an area heat source is presented. The method enables the calculation of the propagation of the melting crater with time and the amount of material erosion in the process of electrical discharge machining. Computations were carried out to compare between removal of several metals.     

The moving, plane heat source in an elastic medium

Summary This note presents an exact solution for the stress and displacement field in an unbounded and transversely constrained elastic medium resulting from the motion of a plane heat source travelling through the medium at constant speed in the direction normal to the source plane.Nomenclature mass density - diffusivity - thermal conductivity - Q heat emitted by plane heat source per unit time per unit area - speed of propagation of plane heat source - shear modulus - Poisson's ratio - T temperature - _x, _y, _z normal stress components - u _x, u_y, u_z displacement components - c speed of irrotational waves - t time - x, y, z Cartesian coordinates - =x–vt moving coordinate     

The thermal stress system associated with a moving heat source

Summary A derivation is given of the thermal stress system associated with a source of heat moving with uniform velocity through an infinite medium.