The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.

### Diffusion penetration time for transient conduction

#### Abstract

The time duration for processes involving transient thermal diffusion can be a critical piece of information related to thermal processes in engineering applications. Analytical solutions must be used to calculate these types of time durations since the boundary conditions in such cases can be effectively like semi-infinite conditions. This research involves an investigation into analytical solutions for five geometries including one-dimensional cases for Cartesian, cylindrical and spherical coordinates. The fourth case involves two-dimensional conduction from a point heat source on the surface of a slab subjected to insulated boundary conditions elsewhere. The mathematical modeling for this case is done in cylindrical coordinates. The fifth case involves a heated surface on the inside of a hole bored through an infinite body, which is a one-dimensional problem in radial coordinates. A sixth case is also mentioned, which is the only two-dimensional configuration discussed, having to do with point heating on a flat plate. For each geometric configuration, a relationship is developed to determine the time required for a temperature rise to occur at a non-heated point in the body in response to a sudden change at a heated boundary. A range of time values is computed for each configuration based on the amount of temperature rise used as a criterion. Plots are given for each case showing the relationships between the temperature rise of interest and the amount of time required to reach that temperature.
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2015
978-1-62410-361-2
Code 157349
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11697/36396`
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