Eventos Anais de eventos
ENCIT 2022
19th Brazilian Congress of Thermal Sciences and Engineering
NUMERICAL APPROXIMATION FOR POROUS PARALLEL FINS WITH RADIATION
Submission Author:
Maria Laura Martins-Costa , RJ , Brazil
Co-Authors:
Vinícius Vendas Sarmento, Maria Laura Martins-Costa, ROGERIO GAMA
Presenter: Maria Laura Martins-Costa
doi://10.26678/ABCM.ENCIT2022.CIT22-0288
Abstract
This work aims to find the temperature distribution of porous fins with insulated tips under the parallel case in a dominant radiation situation. By first using the prevalent mathematical dimensionless models in the literature, the problem is similar to the solid fin case. However, due to the consideration of radiation from another fin and from the base, the model gives rise to an Integro-Differential problem. In order to solve the differential equations, the Finite Difference Method (FDM) is employed, along with the usage of a weighting parameter α which allows for a gradually increasing sequence of elements to numerically converge. For evaluating the integrals, the high-speed Trapezoidal Rule method approximates the heat transfer between the parallel porous fins due to radiation and the heat transfer between the fin and the fin’s base, which is considered to be at a constant temperature. However, it must be noted that the integrals must be solved first. Then by using the previously described method alongside Gauss-Seidel iterations, the problem can be solved for each element of the sequence. After this procedure, the sequence is built (for each element) until it converges according to an established tolerance. The obtained results are in good agreement with the recognized literature, such as, for example, a rise in the emissivity of the porous fins causing the decrease of the temperature distribution even when considering radiation from the fin’s base and from the other parallel fin. The heat transfer from the porous fin to the environment still surpasses both of them in many situations. Another interesting result is the impact of the fin’s base on the temperature distribution. As the length of the base increases, the temperature distribution on the porous fin is also greatly augmented, and the fin’s base influence becomes higher than the effect from the other parallel fin.
Keywords
Nonlinear Heat Transfer, porous fin, Finite Differences, Numerical simulation
