Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using K...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Baghdad
2023-04-01
|
| Series: | Journal of Engineering |
| Subjects: | |
| Online Access: | https://joe.uobaghdad.edu.iq/index.php/main/article/view/1955 |
| _version_ | 1797782904124735488 |
|---|---|
| author | Mishaal Abdulameer Abdulkareem |
| author_facet | Mishaal Abdulameer Abdulkareem |
| author_sort | Mishaal Abdulameer Abdulkareem |
| collection | DOAJ |
| description |
The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal conductivity. It is found that the characteristics of the thermal insulation material and the pressure value between its particles have a major effect on the rate of heat transfer and temperature profile.
|
| first_indexed | 2024-03-13T00:18:32Z |
| format | Article |
| id | doaj.art-9c4e0922da1c48f2923462a6ed419427 |
| institution | Directory Open Access Journal |
| issn | 1726-4073 2520-3339 |
| language | English |
| last_indexed | 2024-03-13T00:18:32Z |
| publishDate | 2023-04-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Journal of Engineering |
| spelling | doaj.art-9c4e0922da1c48f2923462a6ed4194272023-07-11T18:35:16ZengUniversity of BaghdadJournal of Engineering1726-40732520-33392023-04-0120110.31026/j.eng.2014.01.07Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal ConductivityMishaal Abdulameer Abdulkareem The one-dimensional, spherical coordinate, non-linear partial differential equation of transient heat conduction through a hollow spherical thermal insulation material of a thermal conductivity temperature dependent property proposed by an available empirical function is solved analytically using Kirchhoff’s transformation. It is assumed that this insulating material is initially at a uniform temperature. Then, it is suddenly subjected at its inner radius with a step change in temperature. Four thermal insulation materials were selected. An identical analytical solution was achieved when comparing the results of temperature distribution with available analytical solution for the same four case studies that assume a constant thermal conductivity. It is found that the characteristics of the thermal insulation material and the pressure value between its particles have a major effect on the rate of heat transfer and temperature profile. https://joe.uobaghdad.edu.iq/index.php/main/article/view/1955Nonlinear differential equation, analytical solution, thermal conductivity, transient, Kirchhoff’s transformation. |
| spellingShingle | Mishaal Abdulameer Abdulkareem Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity Journal of Engineering Nonlinear differential equation, analytical solution, thermal conductivity, transient, Kirchhoff’s transformation. |
| title | Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity |
| title_full | Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity |
| title_fullStr | Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity |
| title_full_unstemmed | Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity |
| title_short | Analytical Solution of Transient Heat Conduction through a Hollow Spherical Thermal Insulation Material of a Temperature Dependant Thermal Conductivity |
| title_sort | analytical solution of transient heat conduction through a hollow spherical thermal insulation material of a temperature dependant thermal conductivity |
| topic | Nonlinear differential equation, analytical solution, thermal conductivity, transient, Kirchhoff’s transformation. |
| url | https://joe.uobaghdad.edu.iq/index.php/main/article/view/1955 |
| work_keys_str_mv | AT mishaalabdulameerabdulkareem analyticalsolutionoftransientheatconductionthroughahollowsphericalthermalinsulationmaterialofatemperaturedependantthermalconductivity |