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Monte Carlo method for exchange among diffuse-gray surfaces

DOI: 10.1615/thermopedia.000071

MONTE CARLO METHOD FOR EXCHANGE AMONG DIFFUSE-GRAY SURFACES

John R. Howell

1. INTRODUCTION

Radiation problems are ideally suited for using the Monte Carlo method. Here, we examine radiant exchange between surfaces in the absence of a participating medium.

The general expression for the radiant emissive power of a surface element is

(1)

In this expression, ε(λ, T, θ, φ, r) is the monochromatic directional emissivity, Iλb is the blackbody spectral intensity, and θ and φ are the angular directions (Fig. 1).

Spherical coordinate system.

Figure 1.  Spherical coordinate system.

Equation (1) places no restriction on the wavelength, direction, or temperature dependence of the emissive power. However, from this point, the discussion is limited to application of the method to diffuse-gray surfaces. Extension to directional-spectral surfaces can be explored in the references.

2. DIRECT SIMULATION MONTE CARLO

Direct simulation Monte Carlo simulate ...

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