Deterministic Numerical Simulations of a Non-Isothermal Blackbody Effective Emissivity using a Coupled Fredholm Integral Equation System

Vishal Ramnath


Nonisothermal blackbody, effective emissivity, Fredholm equation


Radiation thermometry involves the modelling of radiative heat transfer interactions between thermal radiation sources such as blackbodies and thermal radiation detectors such as pyrometers in order to deduce temperatures. When furnaces and heat-baths are modelled as blackbodies the corresponding effective emissivity becomes essential in order to adequately characterise non-ideal systems. Due to the complexity that is involved in such systems analytical formulae are generally only mathematically tractable for isothermal systems and simple geometries. Systems exhibiting more complex geometries and optical/thermal characteristics are then frequently only amenable to further analysis using stochastic based simulation techniques. One of the problems associated with stochastic techniques is that they suffer from a lack of independent verification and validation bench marks for non-isothermal conditions. In this paper we adopt a physical based modelling approach in order to independently determine the effective emissivity of a high temperature blackbody that exhibits a non-isothermal heat distribution by using a deterministic numerical simulation. We model the system in terms of a generalized Fredholm integral equation system and develop a numerical solution approach using a modified collocation method that may incorporate the zonal technique, and briefly contrast the merits of our approach with that of multi-parametric homotopy techniques that are based on the Adomian decomposition method.

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