Application of constructal theory for the construction of an arrangement of heated blocks inserted in a channel subject to flows with forced convection

Abstract

This work shows an analysis of the construction of the geometric arrangement of blocks mounted on the surfaces of a channel subject to a laminar, incompressible flow, with forced convection in a two-dimensional domain. The construction is carried out through a construction function based on the system performance indicator, i.e., the heat transfer rate from the arrangement to the fluid flow. For the assembly of the arrangement, a methodology based on the principles of the Constructal Theory is used. To solve the convection problem, the mass, momentum and energy conservation equations are solved with the Finite Volume Method, more precisely using the FLUENT software. The objective of this work is to understand how the construction of the initial blocks of the array (N = 3 blocks) occurs in an area occupied by the channel in flows with forced convection and Reynolds and Prandtl numbers of ReH  = 100 and Pr = 0.71. The best and worst cases for N = 2 led to an increase of 93.21% and 28.59%, respectively, compared to the N = 1 case. Results demonstrated that the construction that led to the best thermal performance was the configuration where there is the highest momentum between blocks (intensifying the convective heat transfer coefficient) and with the lowest interaction between the thermal boundary layers, which is in agreement with the principle of optimal distribution of imperfections.