Monte Carlo Method for Calculating View Factor of Truncated Cone Radiators

Abstract

To address radiative heat transfer problems, the determination of view factors is crucial. In this study, the focus is placed on the calculation of the view factor using the Monte Carlo method, specifically for truncated cone radiators. Although reference books offer theoretical relations for computing the view factor, a new approach employing the Monte Carlo method is utilized to ensure the accuracy of the general solution. To measure the accuracy, three types of cases are considered: positive, negative, and zero-angle truncated cones with a fixed disk (ring) at the base of the cone. The results are presented for various ratios between the height of the truncated cone and the radii of the ring and base side of the cone. Additionally, the impact of different angles of the truncated cone on the view factor is investigated. In the zero-angle case, five different L/r1 are examined, in the positive angle case, seven different positive angles in two different L/r1 are studied, and in the negative angle case, three negative angles in three different L/r1 are studied. For positive angles, the maximum difference between the results of Monte Carlo method and theoretical method is 42.81% and occurred in L/r1 equal to 5 and 40 degrees. While for zero-angle the maximum difference is 30.16% and occurred in L/r1 equal to 10. In the negative angle case, the maximum difference is 36.66% and occurred in L/r1 equal to 0.2 and -15 degrees.

Keywords

• radiation
• ray tracing method
• monte carlo method
• configuration factor
• frustum
• cone angle