GREEN'S FUNCTION SOLUTION TO HEAT TRANSFER OF A TRANSPARENT GAS THROUGH A TUBE

A heat transfer analysis of a transparent gas flowing through a circular tube of finite thickness is presented. This study includes the effects of wall conduction, internal radiative exchange, and connective heat transfer. The natural mathematical formulation produces a nonlinear, integrodifferential equation governing the wall temperature and an ordinary differential equation describing the gas temperature. This investigation proposes to convert the original system of equations into an equivalent system of integral equations. The Green's function method permits the conversion of an integrodifferential equation into a pure integral equation. The proposed integral formulation and subsequent computational procedure are shown to be stable and accurate.     

Solution of nonlinear transient conduction equation by a modified boundary integral procedure

We apply a modified boundary integral procedure known as the Green element method (GEM) to solve problems arising from nonlinear conduction in a homogeneous isotropic medium. The method is based on the solution of an integral version of the governing partial differential equation over a priori defined subdomains. In addition, a piecewise interpolation of the dependent variable is associated with every nodal positions of the problem domain. By adopting this finite element concept in addition to its boundary integral formulation, GEM arrives at a slender coefficient matrix which is easy to handle numerically, and at the same time offers a more straightforward methodology for handling nonlinearity with the boundary integral theory. This procedure resumes with the conversion of the governing partial differential equation into its integral representative followed by typical finite element features such as scalar interpolation, and domain discretization. The integral equations are solved for each element, and the results assembled to yield the scalar profile over the problem domain. To establish the numerical accuracy of the numerical method thus developed, examples dealing with 1-D and 2-D scalar conduction in a homogeneous domain are solved and compared with those existing in literature.     

一种计算预混层流平面火焰速度的新算法

首次运用类似SIMPLE方法的控制容积积分法的思想,对层流预混平面火焰控制方程的各项分类处理,对源项线性处理。并运用于对甲烷－空气的一维层火焰计算,表明这种新方法易收敛,计算效率高。     

Three-Dimensional Temperature and Thermal Stress Analysis of an Inhomogeneous Layer

In this article we present a technique for analytical solution of three-dimensional heat-conduction and thermal-stress problems for an elastic layer whose thermophysical and mechanical properties are arbitrary functions of the transversal coordinate. This technique is based on direct integration of the original heat-transport and thermoelasticity equations and allows for reducing the original problems to solution of the governing Volterra integral equations of second kind. The obtained governing equations are solved by making use of the resolvent kernel.     

Thermal Stresses in Anisotropic and Radially Inhomogeneous Annular Domains

This paper presents an analytical approach for construction of solutions to the plane quasi-static, non-axially-symmetric elasticity and thermoelasticity problems for cylindrically anisotropic and radially inhomogeneous hollow cylinders and disks subjected to in-plane external force loadings and temperature distribution. This approach is based upon the direct integration of equilibrium equations, which are independent of material properties. The original problems are reduced to integral equations of Volterra type. By application of the resolvent technique, solutions of the governing integral equations are constructed in explicit form, which is convenient for analysis and appropriate for various kinds of inhomogeneity.     

A Green element treatment of isothermal flow with second order reaction

The present work addresses the problem of a tubular reactor in which axial diffusion is accompanied by nonlinear kinetics. The governing equations are solved by a new integral formulation which relies on the Green's second identity. The formulation fundamental solution is applied to the highest order derivative term of the governing equation before implementing the singular integral theory of the Boundary element method (BEM) in an element-by-element fashion. The technique which is essentially domain based provides a friendly interface with the finite element method (FEM) while at the same time retains the second order convergence of BEM. Physically realistic results obtained by applying the technique to flow involving nonlinear kinetics serve to demonstrate the usefulness and accuracy of this technique.     

A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack

Abstract

This article constructs a new model of nonlocal thermoelasticity which resolves a dynamical problem of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is being subjected to a prescribed temperature distribution and stress. In the context of three-phase lag model of generalized thermoelasticity, the governing equations have been solved employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm’s integral equation of the first kind. These integral equations have been solved employing the Maple software package, while the numerical inversion of the Laplace transform is carried out with the help of Bellman method. Numerical computations for a copper material are performed and demonstrated graphically. The results provide a motivation to further investigate the problem and draw concluding remarks due to the influence of nonlocality also.     

装甲车辆柴油机调速系统的仿真模型

发展一个装甲车辆柴油机调速系统的仿真模型。将发动机任一工况下调速器齿杆位置与油门开度和转速联系起来,建立了调速系统静力学和动力学方程;动力学方程用2个一阶微分方程表示,引入连续性函数sigmoid函数代替非连续性函数sign函数,从而能够方便地应用数值积分方法求解动力学方程,并且避免了计算结果的小范围振荡。对一台装甲车辆柴油机调速系统的仿真实例显示,这个模型具有可以仿真装甲车辆柴油机调速系统静态与动态工况和计算调速系统性能参数的能力。     

Cross flow on transient double‐diffusive natural convection in inclined porous trapezoidal enclosures

This paper investigates the cross‐diffusion effects subject to exponential variable boundary conditions on transient double‐diffusive natural convection flow in an enclosure. The flow domain is a two‐dimensional inclined trapezoidal cavity filled with a porous medium. The top wall is assumed to be insulated and permeable, while the enclosure's bottom wall is subject to exponential varying temperature and concentration. The prescribed temperature and concentration are different at the vertical walls. Conservation equations are used as the governing equations. The finite element Galerkin weighted residual method, in association with the Newton‐Raphson scheme is employed to solve the system of coupled nondimensional equations. The numerical tests are confirmed with existing literature and are found to be in excellent agreement. The simulations results for stream functions, isotherms, and isoconcentrations are discussed for the various flow parameters. A sensitivity analysis using the response surface method suggests that the average Nusselt and Sherwood numbers are more sensitive to the cross‐diffusion effects. It is further observed that the cross‐diffusion terms stabilize the sensitivity to the angle of inclination.     

Influence of Soret and Dufour on mixed convection flow across a vertical cone

This contribution examines the influence of Soret and Dufour on an incompressible viscous fluid flow across a vertical cone. The flow model is framed in the form of mathematical governing equations and a nondimensionalization is performed on them for ease of the numerical computations' examination; the obtained nonsimilarity equations are solved numerically through the bivariate Chebyshev spectral collocation quasi-linearization method. Outcomes of the flow characteristics, velocity, temperature, concentration, skin friction rate, heat, and mass transfer rates are analyzed with the variations of governing parameters, Prandtl number, buoyancy parameter, Schmidt number, buoyancy ratio, Soret and Dufour parameters at various stream-wise spots of the flow. To certify the exactness of the listed computations, we performed a comparison with prior published computations, which were found with great agreement, and the residual analysis study was also portrayed to reflect the convergence and stability of the adopted numerical technique.     

Calculation of Turbulent Boundary Layers Using the Dissipation Integral Method

INTRODUCTIONCalculation and prediction of turbulent boundarylayers (TBL) are among the most challenging tasksof present fluid mechanics. A strong demand existsfor robust, easy-to-handle and in terms of computingeffort cheap algorithms which can be used for technical applications. Most of the difficulties occur withthe comprehensive modelling of turbulence and, despite growing computer capabilities, with the limitedcomputing capacity. If the approaches to turbulenceare analysed, a sketch …     

Conjugate free convection from long vertical plate fins in a non-Newtonian fluid-saturated porous medium

The problem of conjugate free convection from long vertical fins in a non-Newtonian fluid-saturated porous medium has been investigated exploiting the boundary layer approximation. The governing equations based on the power-law model appropriate for the Darcy flow are solved exploiting an integral method. The effects of the fin shape exponent and power-law index parameters on the flow and heat transfer characteristics are discussed.     

THERMOELASTICITY OF ANISOTROPIC CYLINDRICAL SHELLS

The quasistatic thertnoelastic equations for radially monoclinic cylindrical shells are solved in closed form for arbitrary temperature distributions and boundary conditions. In addition to both mechanical and thermal material anisotropy, the effects of shear deformation are admitted in the governing shell field equations. The solution to the governing thermomechanical noncanonical field equations is obtained through the use of integral transformations employed in conjunction with the application of adjoint differential operators. To illustrate the substantial effects of mechanical and thermal material anisotropy, the results of several numerical experiments are studied in detail.     

SOLUTION OF STEADY PERIODIC HEAT CONDUCTION BY THE FINITE-ELEMENT METHOD

This paper describes the use of the finite-element technique to solve problems of steady periodic heal conduction. The concept of a complex variable can be used to reduce the governing unsteady heat conduction equation to two noncoupled Poisson equations. The validity of the present method is confirmed with a one-dimensional problem for which an analytic solution exists. Numerical solutions for a three-dimensional problem are presented to illustrate the capability of the method.     

Natural convection in a thin,inclined, porous layer exposed to a constant heat flux

Thermally driven flow in a thin, inclined, rectangular cavity—filled with a fluid-saturated, porous layer—is studied analytically and numerically. A constant heat flux is applied for heating and cooling the two opposing walls of the layer while the other two walls are insulated. On the basis of the Darcy-Oberbeck-Boussinesq equations, the problem is solved analytically, in the limit of a thin layer, using asymptotic expansions and an integral form of the energy equation. Solutions for the flow fields, temperature distributions and Nusselt numbers are obtained explicitly in terms of the Rayleigh number and the angle of inclination of the cavity. A numerical study of the same phenomenon, obtained by solving the complete system of governing equations, is also conducted. A good agreement is found between the analytical predictions and the numerical simulation.     

A critical investigation into the heat and mass transfer analysis of counterflow wet-cooling towers

This study gives a detailed derivation of the heat and mass transfer equations of evaporative cooling in wet-cooling towers. The governing equations of the rigorous Poppe method of analysis are derived from first principles. The method of Poppe is well suited for the analysis of hybrid cooling towers as the state of the outlet air is accurately predicted. The governing equations of the Merkel method of analysis are subsequently derived after some simplifying assumptions are made. The equations of the effectiveness-NTU method applied to wet-cooling towers are also presented. The governing equations of the Poppe method are extended to give a more detailed representation of the Merkel number. The differences in the heat and mass transfer analyses and solution techniques of the Merkel and Poppe methods are described with the aid of enthalpy diagrams and psychrometric charts. The psychrometric chart is extended to accommodate air in the supersaturated state.     

Dynamic analysis of cracks under thermal shock considering thermoelasticity without energy dissipation

This article reports a study of a cracked finite isotropic medium under nonclassic thermal shock based on thermoelasticity without energy dissipation. The time history of stress intensity factors as well as the temperature distribution around the crack tip is analyzed thoroughly. The fully coupled governing equations are discretized in the space by employing the extended finite-element method. The Newmark method is used as the time integration scheme to solve discretized equations. The stress intensity factors, which are extracted using the interaction integral method, are compared with other theories of thermoelasticity. The results of a cracked plate under temperature shock demonstrate that the stress intensity factors based on thermoelasticity without energy dissipation are significantly greater than those based on classic and Lord–Shulman models, whereas the peaks of stress intensity factors under heat flux shock are nearly equal for various theories of thermoelasticity. Furthermore, a mobile cold region is created along slanted crack in the temperature distribution, in which the temperature is less than the applied thermal boundary condition.     

Unsteady heat conduction involving phase changes for an irregular bubble/particle entrapped in a solid during freezing – An extension of the heat-balance integral method

Temperature distributions in the molten layer and solid with distinct properties around a bubble or particle entrapped in the solid during unidirectional solidification are determined by applying a heat-balance integral approximation method. The present model can be used to simulate growth, entrapment or departure of a bubble or particle inclusion in solids encountered in manufacturing and materials processing, MEMS, contact melting processes, drilling, etc. In this work, the proposed heat-balance equations are derived by integrating unsteady elliptic heat diffusion equations and introducing the Stefan boundary condition. Due to the time-dependent irregular shapes of phases, coefficients of assumed quadratic temperature profiles are considered to be functions of longitudinal coordinate and time. Temperature coefficients in distinct regions therefore are determined by solving equations governing temperature coefficients derived from heat-balance equations, imposing boundary conditions, and introducing a fictitious boundary condition. The computed temperature fields show agreement with predictions from the finite-difference method. Since the number of independent variables is reduced by one, this work provides an effective method to solve unsteady elliptic diffusion problems experiencing solid–liquid phase changes in irregular shapes.     

Simulation of a Turbulent Impinging Jet into a Layer of Porous Material Using a Two–Energy Equation Model

This article presents numerical results for a turbulent jet impinging against a flat plane covered with a layer of permeable and thermally conducting material. Distinct energy equations are considered for the solid porous material attached to the wall and for the fluid that impinges on it. Parameters such as Reynolds number, porosity, permeability, thickness, and thermal conductivity of the porous layer are varied in order to analyze their effects on the local distribution of Nu. The macroscopic equations for mass, momentum, and energy are obtained based on volume-average concept. The numerical technique employed for discretizing the governing equations was the control volume method with a boundary-fitted nonorthogonal coordinate system. The SIMPLE algorithm was used to handle the pressure-velocity coupling. Results indicate that inclusion of a porous layer eliminates the peak in Nu at the stagnation region. For highly porous and highly permeable material, simulations indicate that the integral heat flux from the wall is enhanced when a thermally conducting porous material is attached to the surface.     

ANALYSIS OF MOVING BOUNDARY PROBLEM FOR BUBBLE COLLAPSE IN BINARY SOLUTIONS

Bubble collapse in a binary solution with simultaneous heat and mass transfer is studied under a nonspherically symmetrical condition. A numerical technique is presented in this paper that is suitable for solving the axisymmetric moving boundary problem. Making use of the boundary-fitted curvilinear coordinate system and the Lagrangian method, this finite difference technique is able to dynamically track the evolving bubble shape and size during the collapsing process through adaptive grid regeneration. The grid moving velocity is incorporated as an integral part of the governing equations. The numerical results demonstrate that the combined effect of zero shear stress condition, the decreasing curvature, and short life span results in the absence of a wake behind a collapsing bubble.