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Solutions for heat conduction in a solid with temperature dependent thermal conductivity

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Název: Solutions for heat conduction in a solid with temperature dependent thermal conductivity
Autoři: Amirul Irfan
Přispěvatelé: Ang Whye-Teong, School of Mechanical and Aerospace Engineering, MWTAng@ntu.edu.sg
Informace o vydavateli: Nanyang Technological University
Rok vydání: 2025
Sbírka: DR-NTU (Digital Repository at Nanyang Technological University, Singapore)
Témata: Engineering
Popis: Thermal conductivity of a material can be a function of temperature. It can be related to temperature linearly, exponentially or in some cases it is an independent constant. When considering the function of temperature in thermal conductivity mathematically, it will result in a complicated partial differential equation. In order to solve for the solutions of thermal conductivity that is dependent on temperature, Kirchoff’s Transformation is used to linearize the partial differential equation, into a linear and homogeneous Laplace Equation. Using Methods of Separating Variables to solve for solutions where single non homogeneous boundary conditions is applied to a two-dimensional rectangular block, at steady state with no internal heat generation. Afterwards, using Principle of Superposition, we are able to superimpose the gathered solutions from the single to multiple non-homogeneous boundary conditions on a single block. Once the formulas to evaluate the temperature distribution within the block for constant, linear and exponential relations of thermal conductivity to temperature is found, the author uses MATLAB for a numerical example to compare the effects of different parameters. The author finally discussed the significance of thermal conductivity in real world applications. ; Bachelor's degree
Druh dokumentu: other/unknown material
Popis souboru: application/pdf
Jazyk: English
Relation: https://hdl.handle.net/10356/200763
Dostupnost: https://hdl.handle.net/10356/200763
Přístupové číslo: edsbas.9CD67092
Databáze: BASE
Popis
Abstrakt:Thermal conductivity of a material can be a function of temperature. It can be related to temperature linearly, exponentially or in some cases it is an independent constant. When considering the function of temperature in thermal conductivity mathematically, it will result in a complicated partial differential equation. In order to solve for the solutions of thermal conductivity that is dependent on temperature, Kirchoff’s Transformation is used to linearize the partial differential equation, into a linear and homogeneous Laplace Equation. Using Methods of Separating Variables to solve for solutions where single non homogeneous boundary conditions is applied to a two-dimensional rectangular block, at steady state with no internal heat generation. Afterwards, using Principle of Superposition, we are able to superimpose the gathered solutions from the single to multiple non-homogeneous boundary conditions on a single block. Once the formulas to evaluate the temperature distribution within the block for constant, linear and exponential relations of thermal conductivity to temperature is found, the author uses MATLAB for a numerical example to compare the effects of different parameters. The author finally discussed the significance of thermal conductivity in real world applications. ; Bachelor's degree