Influence of particles size and concentration in particles cloud radiation by Mie Theory

Abstract

The effects of mean diameter of particles and of particles concentration, for particles cloud, on the radiative heat flux have been analyzed by a mathematical model. The mathematical model for the radiation of particulate media on the surrounding walls, for 3-D rectangular geometry has been developed. The model is based on the Hottel-Cohen Zone Method for the analysis of radiative heat transfer. Total View Factors for radiative exchange have been evaluated by the Monte Carlo Method. Mic Theory has been used for the determination of the radiative properties of particles cloud in the enclosure. Parameters defining the radiative properties by Mie equations arch particles shape, mean diameter of particles, complex refractive index of particles material, density of material, particles concentration and the wavelength of incident radiation. The particles considered have been of spherical shape, In the zone method, the enclosure and its surrounding surfaces are divided into a number of volume and surface zones, each of which is assumed to have uniform properties. A radiative energy balance is written on each zone giving the net radiative heat transfer between that zone and every other volume and surface zone in the system. The Monte Carlo Method is based an probability and statistics. The concept of energy bundles is introduced to simulate the actual physical process of radiation. A statistically meaningful number of energy bundles are followed from initial points of emission through randomly determined paths until the final points of absorption on the system. The mathematical and physical background of the interaction between incident radiation and a single solid particle is the solution of Maxwells wave equations. Gustav Mic solved Maxwell,s wave equations with the appropriate boundary conditions for single cylindrical and spherical particles and the resulting equations are called the Mic equations. The main objectives of the study are: To link numerically Hottel-Cohen zone method and Monte Carlo Method with Mie equations and to create an original 3-D computer code for the prediction of heat flux distribution. Using the code, as the results, the distribution of net radiative heat flux on the surfaces of a cube have been predicted for various values of mean diameter of particles and of particles concentration. The parametric study has been carried out keeping constant: complex refractive index of particles material and density of material. The wavelength of incident radiation was varied as well. It has been concluded, inter alia, that the larger is the mass concentration of particles the higher is the radiative heat flux transferred to the surfaces. The influence of particles diameter on the heat flux is not straight forward and it depends on the wavelength of incident radiation.