2015/03/16 by Theodoros Leontiou, Leontiou, Theodoros, Marios M. Fyrillas +1
Engineering · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Classical Physics (physics.class-ph) #Composite Structure Analysis and Optimization #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Heat Transfer and Optimization #Topology Optimization in Engineering #physics.class-ph #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.1503.05148
13 pages, 5 figures
arxiv created 2015/03/16 · openalex publication_date 2015/03/16 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the heat transfer problem associated with a periodic array of extended surfaces (fins) subjected to convection heat transfer with a uniform heat transfer coefficient. Our analysis differs from the classical approach as (i) we consider two-dimensional heat conduction and (ii) the base of the fin is included in the heat transfer process. The problem is modeled as an arbitrary two-dimensional channel whose upper surface is flat and isothermal, while the lower surface has a periodic array of extensions/fins which are subjected to heat convection with a uniform heat transfer coefficient. Using the generalized Schwarz-Christoffel transformation the domain is mapped onto a straight channel where the heat conduction problem is solved using the boundary element method. The boundary element solution is subsequently used to pose a shape optimization problem, i.e. an inverse problem, where the objective function is the normalized Shape Factor and the variables of the optimization are the parameters of the Schwarz-Christoffel transformation. Numerical optimization suggests that the optimum fin is infinitely thin and that there exists a critical Biot number that characterizes whether the addition of the fin would result in an enhancement of heat transfer. The existence of a critical Biot number was investigated for the case of rectangular fins. \bf It is concluded that a rectangular fin is effective if its thickness is less than 1.64 k/h, where the h is the heat transfer coefficient and k is the thermal conductivity. This result is independent of both the thickness of the base and the length of the fin.