# Monte Carlo method for exchange among diffuse-gray surfaces

## MONTE CARLO METHOD FOR EXCHANGE AMONG DIFFUSE-GRAY SURFACES

### 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).

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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#### References

1. Farmer, J. T. and Howell, J. R., Comparison of Monte Carlo strategies for radiative transfer in participating media, Advances in Heat Transfer, vol. 31, Hartnett, J. P. and Irvine, T. F. (eds.), pp. 333-429, Academic Press, New York, 1998.
2. Haji-Sheikh, A. and Howell, J. R., Monte Carlo methods, Handbook of Numerical Heat Transfer, 2nd ed., Minkowycz, W. J., Sparrow, E. M., and Murthy, J. Y. (eds.), pp. 249-296, Wiley, Hoboken, NJ, 2006.
3. Howell, J. R., The Monte Carlo Method in Radiative Heat Transfer, J. Heat Transfer, vol. 120, pp 547-560, 1998.
4. Howell, J. R., Application of Monte Carlo to heat transfer problems, Adv. Heat Transfer, vol. 5, pp. 1-54, 1968.
5. Modest, M. F., Radiation Heat Transfer, 2nd ed., Academic Press, San Diego, 2003.
6. Siegel, R. and Howell, J. R., Thermal Radiation Heat Transfer, 5th ed., Taylor and Francis, New York, 2010.
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