General boundary element method for non-linear heat transfer problems governed by hyperbolic heat conduction equation

The general Boundary Element Method (BEM) for strongly non-linear problems proposed by Liao (1995) is further applied to solve a two-dimensional unsteady non-linear heat transfer problem in the time domain, governed by the hyperbolic heat conduction equation (HHCE) with the temperature-dependent thermal conductivity coefficients which are different in the x and y directions. This paper confirms that the general BEM can be used to solve even those non-linear unsteady heat transfer problems whose governing equations do not contain any linear terms in spatial domain.     

Radial integration BEM for transient heat conduction problems

In this paper, a new boundary element analysis approach is presented for solving transient heat conduction problems based on the radial integration method. The normalized temperature is introduced to formulate integral equations, which makes the representation very simple and having no temperature gradients involved. The Green's function for the Laplace equation is adopted in deriving basic integral equations for time-dependent problems with varying heat conductivities and, as a result, domain integrals are involved in the derived integral equations. The radial integration method is employed to convert the domain integrals into equivalent boundary integrals. Based on the central finite difference technique, an implicit time marching solution scheme is developed for solving the time-dependent system of equations. Numerical examples are given to demonstrate the correctness of the presented approach.     

Analysis of static non-linear response by explicit time integration

In general, a system of linear (or non-linear) algebraic equations is solved on an analogue computer by integrating an appropriately defined system of associated first-order differential equations, the steady-state solution of which is the desired solution of algebraic system. This approach usually works very well so long as the associated dynamical system is stable. The idea of using the same approach numerically is also not altogether new. One can, ‘analogously’, construct a dynamical system associated with a given system of non-linear algebraic equations and solve it numerically by any of a number of explicit time integration schemes. In fact, similar ideas provide the basis for certain ‘dynamic relaxation’ methods, incremental loading methods and the widely acclaimed methods of invariant imbedding.     

A simple spatial integration scheme for solving Cauchy problems of non-linear evolution equations

In this study, we address a new and simple non-iterative method to solve Cauchy problems of non-linear evolution equations without initial data. To start with, these ill-posed problems are analysed by utilizing a semi-discretization numerical scheme. Then, the resulting ordinary differential equations at the discretized times are numerically integrated towards the spatial direction by the group-preserving scheme (GPS). After that, we apply a two-stage GPS to integrate the semi-discretized equations. We reveal that the accuracy and stability of the new approach is very good from several numerical experiments even under a large random noisy effect and a very large time span.     

Extremum principles for some nonlinear heat transfer problems

Summary Recent results on extremum principles for various nonlinear boundary value problems are applied to heat transfer problems involving space radiators such as fins and other parts of spacecraft. The results are illustrated by obtaining quite accurate variational solutions for such problems involving the fourth-power law of radiation.     

A new family of explicit time integration methods for linear and non-linear structural dynamics

A new family of explicit single-step time integration methods with controllable high-frequency dissipation is presented for linear and non-linear structural dynamic analyses. The proposed methods are second-order accurate and completely explicit with a diagonal mass matrix, even when the damping matrix is not diagonal in the linear structural dynamics or the internal force vector is a function of velocities in the non-linear structural dynamics. Stability and accuracy of the new explicit methods are analysed for the linear undamped/damped cases. Furthermore, the new methods are compared with other explicit methods.     

Homogenization of transient heat transfer problems for some composite materials

The article presented is devoted to the homogenization of transient heat transfer problems in some composite materials. The mathematical model used in the FEM computation is based on the effective modules method introduced for periodic composites. The effective heat conductivity is calculated in the closed form; effective heat capacity and mass density for the composite are obtained by simple spatial averaging. Such a homogenization scheme makes it possible to significantly simplify the numerical analysis of transient heat phenomena in various types of composites. Computational experiments performed using symbolic mathematics show the variability of effective heat conductivity for 2D and 3D composites as a function of the reinforcement volume ratio, of composite components conductivity coefficients as well as of the probabilistic moments of material properties versus volume ratio. Finally, using the Finite Element Method program, the comparison of transient heat transfer problem for the real and homogenized composites models is carried out.     

An efficient semi-analytic time integration method with application to non-linear rotordynamic systems

This paper presents a simple and efficient time-integration method for non-symmetric and non-linear equations of motion occurring in the analysis of rotating machines. The algorithm is based on a semi-analytic formulation combining powerful methods of linear structural dynamics applied to non-linear dynamic problems. To that purpose, the total solution is separated into a linear and a non-linear part, and a further partitioning into quasi-static and dynamic parts is performed. Modal analysis is applied to the undamped equations of the dynamic parts. The quasi-static parts contain all degrees of freedom, while a cost-saving modal reduction may be easily performed for the dynamic parts. Duhamel's integral is utilized for the modal equations. The time-evolution of the unknown modal excitations due to the dissipative, non-conservative, gyroscopic and non-linear effects entering Duhamel's integral is approximated during each time-step. The resulting time-stepping procedure is performed in an implicit manner, and the method is examined in some detail, in view of stability and accuracy characteristics. A rotordynamic system serves as a benchmark problem in order to demonstrate the computational advantages of the present method with respect to various other time-integration algorithms.     

On nonlinear problems of heat and mass transfer

A system of nonlinear equations for steady one-dimensional heat and mass transfer problems is considered. Analytical solutions are obtained for certain special cases.     

A comparative study on various time integration schemes for heat wave simulation

The performance of several explicit and implicit time advancement schemes of first-order ODEs are examined for heat wave simulation with different boundary conditions. It is found that the boundary conditions have a considerable influence on the stiffness property of the hyperbolic heat conduction equation, due to the occurrence of thermal shock waves, and hence, according to the type of the enforced boundary conditions, a specific time integration scheme has to be performed in order to obtain an accurate and efficient solution. The results of the considered time integration schemes are also compared with analytical solution and based on the obtained results, some recommendations regarding the numerical simulation of hyperbolic heat conduction are presented.     

Experimental research on heat transfer coefficients for cryogenic cross-counter-flow coiled finned-tube heat exchangers

The aim of present experimental research is to find out the suitable correlations for designing the coiled finned-tube heat exchangers used in cryogenic applications. In order to conduct above experimental study, cross-counter-flow coiled finned-tube heat exchangers were developed in our lab and used in actual refrigeration cycle. The experiments were conducted in the range of effective Reynolds number 500–1900. The effect of diametrical clearance on the prediction of overall heat transfer coefficient is also investigated experimentally. The results from present study were compared in the form of overall heat transfer coefficient. Results of present experimental research indicate that different correlations selected in the study can be used with reasonable accuracy for designing the coiled finned-tube heat exchangers, if they are applied with suitable method of calculation of free-flow cross-sectional area. A more accurate new correlation has also been proposed that fitted experimental data within ±10% error band.     

Experimental heat transfer investigation in heat shield material test facilities

An experimental investigation has been made of the thermal interaction of the gas in a facility for testing heat shield materials. The results are presented in terms of the Nusselt number at the stagnation point of a flat plate, accounting for turbulent fluctuations of the oncoming stream. The data obtained are compared with the theory of reference [4].Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 23, No. 6, pp. 988–992, December, 1972.     

Integrated study of scientific and applied problems on heat transfer enhancement in tubular heat transfer apparatuses

A highly efficient method of enhancing heat transfer in annular swirl-augmented tubes, with gases and liquids flowing in them, under drop and film condensation is developed and investigated.Moscow Aviation Institute, Russian. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 65, No. 1, pp. 25–31, July, 1993.     

Collocation time finite element procedures for integration of strongly nonlinear initial value problems

By use of a collocation time finite element formulation a modification of the well-known generalized midpoint method is derived. The new family possesses an additional free parameter. This allows for significant improvement of the numerical solution in strongly nonlinear situations. Numerical results show the accuracy of the proposed algorithm in comparison to the midpoint method.     

Boundary element solution of heat conduction problems in multizone bodies of non-linear material

A novel algorithm for handling material non-linearities in bodies consisting of subregions having different, temperature dependent heat conductivities is developed. The technique is based on Kirchhoff's transformation. The material non-linearity is reduced to a solution dependent function of unified form added to unknown nodal Kirchhoff's transforms. Assembling of element contributions brings the non-linearity to the right hand sides of the global set of equations. The first step of the solution of this set is the Gaussian pre-elimination (condensation) of linear degrees of freedom. At this stage efficient block solvers can be used. Then, a set of non-linear equations is extracted from the condensed one and solved employing the Newton-Raphson technique. The iteratively solved set consists of the least possible number of equations and its Jacobian matrix is calculated efficiently by taking advantage of the specific form of the equations.     

Using analytical expressions in radial integration BEM for variable coefficient heat conduction problems

In this paper, a new approach using analytical expressions in the radial integration boundary element method (RIBEM) is presented for solving variable coefficient heat conduction problems. This approach can improve the computational efficiency considerably and can overcome the time-consuming deficiency of RIBEM in computing involved radial integrals. The fourth-order spline RBF is employed to approximate unknowns appearing in domain integrals arising from the varying heat conductivity. The radial integration method is utilized to convert domain integrals to the boundary resulting in a pure boundary discretization algorithm. Numerical examples are given to demonstrate the efficiency of the presented approach.