Method For Heat Transfer Problems Research Articles

A space-time meshfree method for heat transfer analysis in porous material

Abstract Porous material batteries are a new type of battery technology that uses porous materials as electrode materials, with advantages such as long lifespan. In the present study, we manily propose a space-time meshfree method for heat transfer problems in porous material energy storage battery. The thermal behavior is demonstrated based on a numerical solution of the energy conservation equation. A simple space-time meshless collocation scheme, which is based on a new type space-time radial basis function, is presented to get the approximate solution of the energy conservation equation. The energy conservation equation was transferred into a system of linear algebraic equations. By introducing prescribed boundary conditions, the heat transfer analysis in porous material energy storage battery can be shown with numerical results. Numerical discussions show that the proposed meshless collocation method is appropriate to simulate thermal behavior in porous material energy storage battery, while the traditional finite element method failed to provide the reasonable results for the tested examples in this paper.

An integrative SPH method for heat transfer problems involving fluid-structure interaction

An integrative SPH method for heat transfer problems involving fluid-structure interaction

An isogeometric boundary element method for heat transfer problems of multiscale structures in electronic packaging with arbitrary heat sources

We present an isogeometric boundary element method (IGABEM) capable of studying heat transfer problems for multiscale structures in electronic packaging problems. This method offers a number of key improvements compared with current analysis methods available for electronic packaging problems. The method benefits from the accuracy, computational efficiency and CAD integration that have consistently been shown as features of the IGABEM. In addition, the current method can efficiently evaluate the nearly singular integrals caused by multiscale structures, owing to the use of a proposed hybrid integration scheme. By changing a tolerance, the scheme enables engineers to achieve any desired balance between accuracy and computational efficiency as may be appropriate to the situation. To study heat transfer problems with an arbitrary heat source, the radial integral method is used to transform the domain integral to an equivalent boundary integral. Numerical results are compared with available analytical solutions and finite element solutions and demonstrate the effectiveness of the proposed approach.

A non-field analytical method for heat transfer problems through a moving boundary

This paper presents an extension of the non-field analytical method—known as the method of Kulish—to solving heat transfer problems in domains with a moving boundary. This is an important type of problems with various applications in different areas of science. Among these are heat transfer due to chemical reactions, ignition and explosions, combustion, and many others. The general form of the non-field solution has been obtained for the case of an arbitrarily moving boundary. After that some particular cases of the solution are considered. Among them are such cases as the boundary speed changing linearly, parabolically, exponentially, and polynomially. Whenever possible, the solutions thus obtained have been compared with known solutions. The final part of the paper is devoted to determination of the front propagation law in Stefan-type problems at large times. Asymptotic solutions have been found for several important cases of the front propagation.

On a simple and effective thermal open boundary condition for convective heat transfer problems

We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary will not cause an “energy-like” temperature functional to increase over time, irrespective of the state of flow on the open boundary. It is effective in coping with thermal open boundaries even in flow regimes where strong vortices or backflows are prevalent on such boundaries, and it is straightforward to implement. Extensive numerical simulations are presented to demonstrate the stability and effectiveness of our method for heat transfer problems with strong vortices and backflows occurring on the open boundaries. Simulation results are compared with previous works to demonstrate the accuracy of the presented method.

Transient response bounds analysis of heat transfer problems based on interval process model

A transient temperature response analysis method for heat transfer problems with dynamic uncertain parameters is proposed. The time-variant or dynamic uncertain parameters are quantified by an interval process model using only the variation bounds of uncertainty, providing an effective way for problems where probabilistic modeling of the dynamic uncertainties is unfeasible due to lack of sufficient sample data. The interval Karhunen–Loève (K-L) expansion is adopted to represent the interval processes, thus describing accurately the continuous uncertainty over time by a series of interval variables. For convenience of solution, the Laplace transformation is then applied to transform the heat transfer uncertainty analysis over time domain to the complex field, where the analytical solution for the upper and lower bounds of the transient temperature responses can be obtained. Finally, the computational effectiveness and efficiency of the proposed method are verified by three typical numerical examples.

Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

Lattice Boltzmann method for heat transfer problems with variable thermal conductivity

A numerical method for heat transfer problems using collocation and radial basis functions

Simple, mesh/grid free, numerical schemes for the solution of heat transfer problems are developed and validated. Unlike the mesh or grid-based methods, these schemes use well-distributed quasi-random collocation points and approximate the solution using radial basis functions. The schemes work in a similar fashion as finite differences but with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no extra difficulty. © 1998 John Wiley & Sons, Ltd.

APPLICATION OF THE HOMOGRAPHIC APPROXIMATION IN THE ENTHALPY METHOD FOR PHASE CHANGE PROBLEMS

The homographic approximation, in which the Heaviside step function is replaced by a continuous smooth curve, is applied to the enthalpy method for heat transfer problems with isothermal phase change. Both the finite difference and finite element implementations, based on the basic enthalpy, the apparent heat capacity and the source term formulations, are considered. A 1‐D Stefan problem of melting a solid is used as a test problem. The accuracy of the numerical solutions is measured globally using L2 error norms and comparison is made between the solutions using homographic approximation and those using linear approximation. The advantages of using homographic approximation are examined.

A Generalized Finite-Difference Method for Heat Transfer Problems of Irregular Geometries

A Generalized Finite-Difference Method for Heat Transfer Problems of Irregular Geometries