Investigation and modeling of heat transfer with phase-lag in biological tissues
In this report, the equivalence between the phase-lagging and fractional (fractal) models of anomalous diffusion is investigated. Their respective solutions, each providing its own unique physical description of a heat transfer process, are equated to yield the fundamental correlative solution. The...
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sg-ntu-dr.10356-656962023-03-04T18:33:52Z Investigation and modeling of heat transfer with phase-lag in biological tissues Tan, Jian Hui Vladimir Vladimirovich Kulish School of Mechanical and Aerospace Engineering DRNTU::Engineering::Mathematics and analysis In this report, the equivalence between the phase-lagging and fractional (fractal) models of anomalous diffusion is investigated. Their respective solutions, each providing its own unique physical description of a heat transfer process, are equated to yield the fundamental correlative solution. The simplest form of the expression, however, is not closed-form. Nevertheless, being analytical, numerical methods remain pertinent. The dimensionless diffusivity is then plotted against time for the range of Hurst exponents, elucidating the nuances of the equivalent responses in characterising sub-, super-, as well as the three classical models of heat diffusion. Independent validation of the preceding study is through a numerical algebraic constraint of the zero function solution. A good initial approximation of the three coupled variables is germane to the extraction of any semblance of the exact numerical solution, and wherein accentuates the extreme sensitivity of the equivalent solution. Bachelor of Engineering (Mechanical Engineering) 2015-12-10T02:30:48Z 2015-12-10T02:30:48Z 2015 2015 Final Year Project (FYP) http://hdl.handle.net/10356/65696 en Nanyang Technological University 81 p. application/pdf |
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DRNTU::Engineering::Mathematics and analysis Tan, Jian Hui Investigation and modeling of heat transfer with phase-lag in biological tissues |
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In this report, the equivalence between the phase-lagging and fractional (fractal) models of anomalous diffusion is investigated. Their respective solutions, each providing its own unique physical description of a heat transfer process, are equated to yield the fundamental correlative solution. The simplest form of the expression, however, is not closed-form. Nevertheless, being analytical, numerical methods remain pertinent. The dimensionless diffusivity is then plotted against time for the range of Hurst exponents, elucidating the nuances of the equivalent responses in characterising sub-, super-, as well as the three classical models of heat diffusion. Independent validation of the preceding study is through a numerical algebraic constraint of the zero function solution. A good initial approximation of the three coupled variables is germane to the extraction of any semblance of the exact numerical solution, and wherein accentuates the extreme sensitivity of the equivalent solution. |
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Vladimir Vladimirovich Kulish |
author_facet |
Vladimir Vladimirovich Kulish Tan, Jian Hui |
format |
Final Year Project |
author |
Tan, Jian Hui |
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Tan, Jian Hui |
title |
Investigation and modeling of heat transfer with phase-lag in biological tissues |
title_short |
Investigation and modeling of heat transfer with phase-lag in biological tissues |
title_full |
Investigation and modeling of heat transfer with phase-lag in biological tissues |
title_fullStr |
Investigation and modeling of heat transfer with phase-lag in biological tissues |
title_full_unstemmed |
Investigation and modeling of heat transfer with phase-lag in biological tissues |
title_sort |
investigation and modeling of heat transfer with phase-lag in biological tissues |
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2015 |
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http://hdl.handle.net/10356/65696 |
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1759854624467058688 |