Constructal optimization for geometry of cavity by taking entransy dissipation minimization as objective

Abstract

The entransy dissipation extremum principle provides new warranty and criterion for optimization of heat transfer. For two cases (body with heat generation and body heated externally) of a solid conducting wall with an open cavity, a dimensionless equivalent thermal resistance based on entransy dissipation definition was taken as the optimization objective to optimize the model constructal geometry. Numerical results validated the necessity and feasibility of the presented method. Comparisons of the numerical results based on minimization of dimensionless maximum thermal resistance and minimization of dimensionless equivalent thermal resistance, respectively, showed that there was no obvious difference between the two results when the volume fraction Φ occupied by cavity was small, but the difference between the two results increased with the increases of Φ and the body aspect ratio H/L for any model. The optimal cavities for bodies heated externally were more slender than those for bodies with heat generation. Heat origin had obvious effect on the global performance of heat transfer. The entransy dissipation of body heated externally increased 2―3 times than that of body with heat generation, indicating that the global performance of heat transfer weakened. The method presented herein provides some guidelines for some relevant thermal design problems.