scholarly journals Analytical Solutions to 3-D Bioheat Transfer Problems with or without Phase Change

10.5772/52963 ◽  
2012 ◽  
Author(s):  
Zhong-Shan Deng ◽  
Jing Liu
Keyword(s):  
Phase Change ◽  
Analytical Solutions ◽  
Bioheat Transfer ◽  
Transfer Problems

Analytical solutions of some heat transfer problems in mining practice

2014 ◽  
Vol 50 (1) ◽  
pp. 81-86 ◽  
Author(s):  
N. N. Smirnova ◽  
N. V. Nikolaeva ◽  
V. N. Brichkin ◽  
V. B. Kuskov
Keyword(s):  
Heat Transfer ◽  
Analytical Solutions ◽  
Transfer Problems

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2004 ◽  
Vol 126 (6) ◽  
pp. 937-945 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith ◽  
Ramin K. Rahmani
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase-change problems. Several isothermal phase-change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust, and efficient for the numerical modeling of phase-change problems.

scholarly journals Unconditional Stability of a Numerical Method for the Dual-Phase-Lag Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
M. A. Castro ◽  
J. A. Martín ◽  
F. Rodríguez
Keyword(s):  
Numerical Method ◽  
Numerical Solutions ◽  
Unconditional Stability ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Stability Properties ◽  
The Stability ◽  
Transfer Problems ◽  
Uniformly Bounded

The stability properties of a numerical method for the dual-phase-lag (DPL) equation are analyzed. The DPL equation has been increasingly used to model micro- and nanoscale heat conduction in engineering and bioheat transfer problems. A discretization method for the DPL equation that could yield efficient numerical solutions of 3D problems has been previously proposed, but its stability properties were only suggested by numerical experiments. In this work, the amplification matrix of the method is analyzed, and it is shown that its powers are uniformly bounded. As a result, the unconditional stability of the method is established.

scholarly journals Conjugate Problems in Convective Heat Transfer: Review

2009 ◽  
Vol 2009 ◽  
pp. 1-27 ◽  
Author(s):  
Abram Dorfman ◽  
Zachary Renner
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Analytical Solutions ◽  
Modern Approach ◽  
Current Time ◽  
Aerospace Systems ◽  
The One ◽  
Transfer Problems ◽  
Technology Processes

A review of conjugate convective heat transfer problems solved during the early and current time of development of this modern approach is presented. The discussion is based on analytical solutions of selected typical relatively simple conjugate problems including steady-state and transient processes, thermal material treatment, and heat and mass transfer in drying. This brief survey is accompanied by the list of almost two hundred publications considering application of different more and less complex analytical and numerical conjugate models for simulating technology processes and industrial devices from aerospace systems to food production. The references are combined in the groups of works studying similar problems so that each of the groups corresponds to one of selected analytical solutions considered in detail. Such structure of review gives the reader the understanding of early and current situation in conjugate convective heat transfer modeling and makes possible to use the information presented as an introduction to this area on the one hand, and to find more complicated publications of interest on the other hand.

Phase Change Heat Transfer Problems

2014 ◽  
pp. 3647-3666 ◽  
Author(s):  
Jerzy Banaszek ◽  
Miroslaw Seredynski
Keyword(s):  
Heat Transfer ◽  
Phase Change ◽  
Phase Change Heat Transfer ◽  
Transfer Problems

Application of the Conservation Element and Solution Element Method in Numerical Modeling of Three-Dimensional Heat Conduction With Melting and/or Freezing

2003 ◽  
Author(s):  
Anahita Ayasoufi ◽  
Theo G. Keith
Keyword(s):  
Numerical Modeling ◽  
Heat Conduction ◽  
Fluid Mechanics ◽  
Phase Change ◽  
Numerical Method ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Solution Element ◽  
Explicit Numerical Method ◽  
Element Method

The conservation element and solution element (CE/SE) method, an accurate and efficient explicit numerical method for resolving moving discontinuities in fluid mechanics problems, is used to solve three-dimensional phase change problems. Several isothermal phase change cases are studied and comparisons are made to existing analytical solutions. The CE/SE method is found to be accurate, robust and efficient for the numerical modeling of phase change problems.

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