TY - JOUR A2 - De Bartolo, Samuele AU - Martins-Costa, Maria Laura AU - Vendas Sarmento, Vinícius AU - Moraes de Lira, Allan AU - Saldanha da Gama, Rogério M. PY - 2020 DA - 2020/08/26 TI - Temperature Distribution in Porous Fins, Subjected to Convection and Radiation, Obtained from the Minimization of a Convex Functional SP - 8613717 VL - 2020 AB - This work proposes a convex functional endowed with a minimum, which occurs for the solution of the thermal radiation and natural convection heat transfer problem in a rectangular profile porous fin with a fluid flowing through it. The minimum principle ensures the (mathematically demonstrated) uniqueness of the solution and allows the problem simulation by employing a minimization procedure. Darcy’s law with the Oberbeck–Boussinesq approximation simplifies the momentum equation. The energy equation assumes thermal equilibrium between the porous matrix and fluid, allowing comparisons with previous authors’ models, which accounts for the effects of a porosity parameter, a radiation parameter, and a temperature ratio on the temperature. Results for very long fin and finite-length fin with insulated tip were successfully compared with previous works. Closed-form exact solutions for two limiting cases (no convection and no thermal radiation) are also presented. SN - 1024-123X UR - https://doi.org/10.1155/2020/8613717 DO - 10.1155/2020/8613717 JF - Mathematical Problems in Engineering PB - Hindawi KW - ER -