Mathematical Analysis for Radiometric Calorimetry of a Radiating Sphere

Area of Science:

• Materials Science
• Thermodynamics
• Heat Transfer

Background:

• Accurate determination of thermal properties is crucial for material science and engineering applications.
• Existing methods for calculating thermal diffusivity and specific heat often rely on simplified assumptions that may not reflect real-world conditions.

Purpose of the Study:

• To derive equations for calculating the temperature dependence of specific heat and thermal diffusivity of spherical samples.
• To account for temperature field non-uniformity and thermal expansion during cooling.
• To develop a universal cooling curve for designing radiative cooling experiments.

Main Methods:

• Derivation of equations based on time-dependent surface temperature and energy loss rates.
• Analysis considering non-uniform interior temperature fields.
• Inclusion of thermal expansion effects, excluding phase changes.

Main Results:

• Developed equations enabling calculation of specific heat and thermal diffusivity from cooling data.
• Established a universal temperature-time cooling curve for the post-transient regime of radiating spheres.
• Demonstrated applicability to various cooling mechanisms maintaining spherical symmetry.

Conclusions:

• The derived equations provide a robust method for determining thermal properties of spherical materials.
• The universal cooling curve serves as a valuable tool for experimental design in radiative cooling.
• The methodology accounts for complexities like non-uniform temperature fields and thermal expansion.