Computational Methods in Radiative Heat Transfer

Overview

• Radiative heat transfer includes an electromagnetic component of heat energy. “Handbook of Food Science, Technology, and Engineering, Volume 3” states, “too often the radiative heat transfer in an operation is neglected because it is considered too difficult to estimate or assumed to be negligible in comparison to the other forms of heat transfer.” Computational models of heat transfer can account for radiative heat transfer when the model is too complex to perform by hand.

Factors

• Radiative heat transfer depends on the rate at which the energy source is emitting radiation. Radiative heat transfer also depends on how well the receiving surface absorbs the radiation. The greatest predictor of radiative heat transfer rates is the temperature difference between the radiation source and receiver. Radiative heat transfer decreases with surface reflectivity. For example, a white surface or shiny surface reflects solar radiative heat back into space rather than absorbing the energy and warming up.

Black Bodies

• Black bodies are theoretical computational models in which the object absorbs all radiation transmitted to it. Black bodies provide a basis of calculating the maximum radiative heat transfer for a set of physical parameters. The term gray bodies refer to any objects that have lower radiative heat transfer than the black body ideal. Radiative heat transfer analysis using black bodies provides a baseline for computational methods and measure for radiative heat transfer efficiency.

Computational Methods

• Finite Element Methods (FEM) and Finite Volume Methods (FVM) can be used to estimate radiative heat transfer. Computer models using Monte-Carlo methods can simulate different potential surfaces of the object and the odds of each surface occurring, providing a most likely estimate of radiative heat transfer. Computational Fluid Dynamics (CFD) models permit users to model situations with conduction, convection and radiative heat transfer occurring at once.

Equations

• Radiative heat transfer rates are calculated using the Stefan-Boltzmann Law. The Stefan-Boltzmann Law applies to all radiation wavelengths. The radiation heat transfer coefficient begins with the temperature difference between the emitting and receiving surfaces measured in absolute temperature from absolute zero. The difference in temperature is quadrupled and multiplied by the Stefan-Boltzmann constant and the area of the emitting body. Computer programs can convert temperatures in other units to absolute temperatures before calculating the radiative heat transfer rate.