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Reflection and refraction of a transient temperature field at a plane interface using Cagniard-de Hoop approach
1School of EEIE, South Bank University, 103 Borough Road, London SE1 0AA, United Kingdom.
Summary
This study introduces a novel method using the Cagniard-de Hoop technique for transient heat conduction problems. The findings reveal wave-like properties in temperature fields, including reflection and refraction phenomena.
Area of Science:
- Physics
- Thermodynamics
- Mathematical Physics
Background:
- Transient heat conduction in heterogeneous media is complex.
- Existing methods often struggle with the interface between different thermal properties.
Purpose of the Study:
- To develop a new analytical approach for transient heat conduction in two dissimilar half-spaces.
- To investigate wave-like properties of temperature fields and their implications.
Main Methods:
- Utilized Laplace and Fourier transforms for time and space.
- Applied the Cagniard-de Hoop technique for inverting transforms, adapted from elastodynamics.
- Analyzed the heat conduction equation reduced to a Helmholtz equation.
Main Results:
- Derived Green's functions for the temperature field.
- Demonstrated wave phenomena: reflection, refraction, and transmission of temperature fields.
- Showed that temperature rays consistent with Snell's law do not align with heat flux directions.
Conclusions:
- The Cagniard-de Hoop method is effective for transient heat conduction.
- Temperature fields exhibit wave-like behavior, challenging traditional heat flux interpretations.
- Ray tracing requires careful consideration in heterogeneous thermal media.