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

Transient Heat Conduction in a Rod of Finite Length With Variable Thermal Properties

1960 ◽  
Vol 27 (4) ◽  
pp. 617-622 ◽  
Author(s):  
W. H. Chu ◽  
H. N. Abramson
Keyword(s):  
Thermal Properties ◽  
Heat Conduction ◽  
Finite Length ◽  
Thermophysical Properties ◽  
Numerical Procedure ◽  
Transient Heat Conduction ◽  
Theoretical Solution ◽  
Rod Of Finite Length

This paper presents a theoretical solution for transient heat conduction in a rod of finite length with variable thermal properties. A numerical procedure is developed and the results of one example are presented and compared with the corresponding solution for the case of constant properties. Application to the problem of determination of thermophysical properties is discussed briefly.

Research on Heat Conductivity with a Time-Varying Heat Source

2014 ◽  
Vol 698 ◽  
pp. 637-642
Author(s):  
Anton Eremin ◽  
Ekaterina Stefanyuk ◽  
Liubov Abisheva
Keyword(s):  
Heat Conduction ◽  
Heat Source ◽  
Heat Balance ◽  
Integral Method ◽  
Approximate Analytical Solution ◽  
Heat Conduction Problem ◽  
Time Varying ◽  
Heat Sources ◽  
Plate Temperature ◽  
The Heat Balance

Using additional boundary conditions in the integral method of the heat balance, an approximate analytical solution to the heat conduction problem for an endless plate with time-varying heat sources has been found. It is shown that with any heat source capacity an unlimited plate temperature increase takes place in the course of time.

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