A. Bejan et al., CONSTRUCTAL THEORY OF NATURAL CRACK PATTERN-FORMATION FOR FASTEST COOLING, International journal of heat and mass transfer, 41(13), 1998, pp. 1945-1954
The constructal theory of the origin of geometrical form in natural fl
ow systems is used to predict the formation of crack patterns in solid
s subjected to volumetric cooling by convection. The approach is purel
y theoretical (deterministic), because it starts from the principle of
geometric minimization of resistance to flow, and leads to the existe
nce of optimal distances between successive cracks and, consequently,
optimal crack widths. The analytical part of the paper is based on the
method of intersecting the asymptotes (many cracks vs. few cracks), a
nd anticipates several natural features that had not been explained pr
eviously: cracks are denser when the convective cooling effect is more
intense and/or the initial departure from equilibrium is greater, and
the loops are close to round (or square) in two-dimensional lattices
of cracks. These trends are further illustrated by using a one-dimensi
onal numerical conduction model with equidistant parallel-plate coolin
g channels. (C) 1998 Elsevier Science Ltd. All rights reserved.