METHOD FOR SOLVING TRANSIENT HEAT-TRANSFER PROBLEMS INCLUDING COMPUTER PROGRAMS AND AN ANALYSIS OF FORM-SURFACE FACTORS

1969 ◽  
Author(s):  
Donald C. Todd
Keyword(s):  
Heat Transfer ◽  
Computer Programs ◽  
Transient Heat Transfer ◽  
Transfer Problems

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

Solving Transient Heat Transfer Problems by the Convolution Type Semi-Analytical DQ Method

2012 ◽  
Vol 204-208 ◽  
pp. 4315-4319
Author(s):  
Jian She Peng ◽  
Guang Bing Luo ◽  
Liu Yang
Keyword(s):  
Heat Transfer ◽  
Variational Principle ◽  
Initial Conditions ◽  
Point Of View ◽  
Convolution Type ◽  
Transient Heat Transfer ◽  
New Equation ◽  
Analytical Series ◽  
Transfer Problems ◽  
Convolution Method

The convolution-type Gurtin variational principle is known as the only variational principle that is, from mathematics point of view, totally equivalent to the initial value problem system. In this paper, the governing equation of bars is first transformed to a new equation containing initial conditions by using convolution method. Then, a convolution-type semi-analytical DQ approach, which involves differential quadrature (DQ) approximation in space domain and an analytical series expansion in time domain, is proposed to obtain the transient response solution. The transient heat transfer examples show the proposed method is a very useful and efficient tool in transient heat transfer problems.

A Space-Time Meshless Method for Heat Transfer Problems With High Discontinuities

2013 ◽  
Author(s):  
Arthur Da Silva ◽  
Tonino Sophy ◽  
Ali Kribèche
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Source ◽  
Weight Function ◽  
Meshless Method ◽  
Space Time ◽  
Transient Heat Transfer ◽  
Source Power ◽  
Spurious Oscillations ◽  
Transfer Problems

The aim of this research is the development of a space-time driscretization method based on Diffuse Approximation Meshless method. This method, devoted to transient heat transfer problems presenting high temporal discontinuities, avoids any Finite-Difference time stepping procedure. The space-time discretization proposed here seems to be convenient for continuous transient heat transfer. Nevertheless, for problems including temporal discontinuities, some spurious oscillations, whose amplitudes depend on source power, appear. A new weight function respecting the principle of causality, based on a modification of the involved node’s selection and a normalisation of the distances, is developed. The use of this new weight function both improves the accuracy and vanishes the oscillations. The method is validated by a source free transient heat transfer problem presenting convective exchanges. Then problems including a constant and a discontinuous heat source are solved. Temperatures fields obtained when using the classical weight function are closer to those obtained with a backward Finite Difference scheme when the heat source is continuous. In case of discontinuous sources, when using the classical weight function, temperature fields present some spurious oscillations which disappear when choosing the new one. The proposed method associated to a grid refinement procedure will lead to adaptive grids in space and/or time, independently.

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