A mesh-free Monte-Carlo method for simulation of three-dimensional transient heat conduction in a composite layered material with temperature dependent thermal properties

2018 ◽  
Vol 119 ◽  
pp. 533-541 ◽  
Author(s):  
Reza Bahadori ◽  
Hector Gutierrez ◽  
Shashikant Manikonda ◽  
Rainer Meinke
Keyword(s):  
Monte Carlo ◽  
Thermal Properties ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Transient Heat Conduction ◽  
Layered Material ◽  
Temperature Dependent ◽  
Mesh Free

The Heat-Balance Integral—Further Considerations and Refinements

1961 ◽  
Vol 83 (1) ◽  
pp. 83-85 ◽  
Author(s):  
Theodore R. Goodman
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Surface Temperature ◽  
Heat Balance ◽  
Transient Heat Conduction ◽  
Temperature Dependent ◽  
Integral Methods ◽  
Infinite Slab ◽  
The Heat Balance ◽  
Excellent Accuracy

Integral methods have previously been applied to transient heat conduction in a slab with constant thermal properties. In this paper the method is extended so as to include temperature-dependent thermal properties in the analysis. In addition, it is shown how to improve the accuracy of a solution by increasing the order of the polynomial used to represent the temperature profile. For the case of a prescribed step surface temperature in a semi-infinite slab, a quartic profile is shown to give excellent accuracy.

Simple Numerical Procedure for the Digital Computer Solution of Non-Linear Transient Heat Conduction with Changes of Phase

1966 ◽  
Vol 8 (3) ◽  
pp. 259-263 ◽  
Author(s):  
F. C. Lockwood
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Finite Difference ◽  
Numerical Procedure ◽  
Transient Heat Conduction ◽  
Temperature Dependent ◽  
Computer Solution ◽  
Integral Transformations ◽  
Finite Difference Technique ◽  
Explicit Finite Difference

A practical numerical method is described for the solution of transient heat conduction where the thermal properties are temperature dependent and changes of phase occur. The procedure involves the use of the explicit finite difference technique, for which a stability criterion is given, in conjunction with two integral transformations.

scholarly journals Numerical Method of Transient Heat Conduction with Temperature Dependent Thermal Properties

1972 ◽  
Vol 15 (89) ◽  
pp. 1394-1401 ◽  
Author(s):  
Kozo KATAYAMA ◽  
Masaru HATTORI ◽  
Masashi OKADA ◽  
Shin-ichiro KOTAKE
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Numerical Method ◽  
Transient Heat Conduction ◽  
Temperature Dependent

Multidimensional Inverse Heat Conduction Using the Monte Carlo Method

1993 ◽  
Vol 115 (1) ◽  
pp. 26-33 ◽  
Author(s):  
A. Haji-Sheikh ◽  
F. P. Buckingham
Keyword(s):  
Monte Carlo ◽  
Random Walk ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Three Dimensional ◽  
Inverse Heat Conduction ◽  
Step Size ◽  
Curved Boundaries ◽  
The Monte Carlo Method ◽  
Inverse Heat Conduction Problems

The Monte Carlo method is used to solve inverse heat conduction problems when the surface temperature is spatial and time dependent. The standard random walk is modified to deal with curved boundaries. The proposed random walk has all the characteristics of the floating random walk, except its step size is small. This is a uniquely flexible method with excellent accuracy and it is computationally fast. The method is used to solve one- and three-dimensional heat conduction problems and the results are presented. A procedure is described to improve the accuracy of the solution, then used to calculate heat transfer from a cylindrical surface cooled by a stream of air.

scholarly journals A Monte Carlo Method of Solving Heat Conduction Problems

1980 ◽  
Vol 102 (1) ◽  
pp. 121-125 ◽  
Author(s):  
S. K. Fraley ◽  
T. J. Hoffman ◽  
P. N. Stevens
Keyword(s):  
Monte Carlo ◽  
Heat Conduction ◽  
Monte Carlo Method ◽  
Transport Equation ◽  
Heat Conduction Equation ◽  
Analytical Techniques ◽  
Conduction Equation ◽  
Geometric Complexity ◽  
New Approach ◽  
Temperature Distributions

A new approach in the use of Monte Carlo to solve heat conduction problems is developed using a transport equation approximation to the heat conduction equation. A variety of problems is analyzed with this method and their solutions are compared to those obtained with analytical techniques. This Monte Carlo approach appears to be limited to the calculation of temperatures at specific points rather than temperature distributions. The method is applicable to the solution of multimedia problems with no inherent limitations as to the geometric complexity of the problem.

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