Title: Constructal theory of critical mass

Authors: Mohammad Yaghoub Abdollahzadeh Jamalabadi

Addresses: Faculty of Marine Engineering, Chabahar Maritime University, Chabahar, Iran

Abstract: The constructal law is now applied in many fields of engineering. It is based on the principle that a finite-size system must evolve to allow greater and greater access to each incoming current to persevere in time (to live). Here, the constructal law is applied to an eigenvalue problem of critical mass. It can have applications in nuclear engineering, natural frequency design of multipart solids and structural dampers. Here, first the problem of optimal shape for critical mass in cylindrical form is solved by constructal theory and benchmarked with an analytical solution. Then, the problem of insertion of an absorber in a fissionable material is optimised and for any mass ratio, the optimal shape is obtained. The results of one group obtained here could be used as an example of more complex geometries, with neutronic groups and reactivity feedback which causes the morphing design throughout the time.

Keywords: constructal theory; eigenvalue problem; one group neutronic; risk assessment; critical mass; optimal design.

DOI: 10.1504/IJNEST.2026.154190

International Journal of Nuclear Energy Science and Technology, 2026 Vol.18 No.3, pp.199 - 208

Accepted: 28 Aug 2025
Published online: 16 Jun 2026 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article