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Experimental Methodology for Estimation of Local Heat Fluxes and Burning Rates in Steady Laminar Boundary Layer Diffusion Flames

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Local effective emissivity of conical cavities.

J H Shirley, J H Eberly

|March 11, 2010

Summary

A new approximate solution improves calculations for blackbody cone emissivity. This method is accurate for interior surfaces and can estimate temperature gradient effects.

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.

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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.