Local effective emissivity of conical cavities

Area of Science:

• Thermodynamics
• Radiative Heat Transfer
• Mathematical Physics

Background:

• Blackbody cavities are crucial for accurate thermal radiation measurements.
• Calculating effective emissivity in cones is complex due to surface geometry.
• Existing methods have limitations in different cone regions and conditions.

Purpose of the Study:

• To develop a novel, accurate analytical approximation for the local effective emissivity of a diffusely reflecting blackbody cone.
• To compare the new approximation with existing methods, such as Kelley's.
• To extend the approximation to account for temperature gradients along the cone surface.

Main Methods:

• Formulating the problem as an integral equation for local effective emissivity.
• Deriving a new analytic approximate solution for the integral equation.
• Modifying the approximation to incorporate a linear temperature gradient.

Main Results:

• The new approximation provides highly accurate results for the interior of narrow cones, where emissivity approaches unity.
• Kelley's approximation is more suitable near the cone's aperture.
• Both approximations are effective for wide-angle cones.
• The modified approximation quantitatively estimates the impact of temperature gradients.

Conclusions:

• The presented analytic approximation offers a valuable tool for calculating blackbody cone emissivity, particularly in narrow geometries.
• The new method enhances the accuracy of thermal radiation measurements by accounting for geometric and thermal complexities.
• The ability to estimate temperature gradient effects expands the applicability of blackbody cone models.