Optimal shape of an anthill dome

Bejan's constructal law revisited

R. G. Kasimova, Yu V. Obnosov, F. B. Baksht, A. R. Kacimov

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

An anthill is modelled as a paraboloid of revolution, whose surface (dome) dissipates heat from the interior of the nest to the ambient air according to the Robin boundary condition, which involves a constant coefficient, given temperature jump and dome's area. The total heat loss of the net is one (integral) component of ants' colony expenditures of energy. Ants, populating the paraboloid, spend also energy individually, by hoisting the load from the ground surface to a certain elevation within the paraboloid and by overcoming a Coulombian resistance, proportional to the trajectory length. In order to count the gross colony expenditures for these mechanical activities all trajectories are integrated over the volume. Ants are assumed to move along the shortest straight lines of their regular sorties between the nest and forest. The three-component energy is mathematically expressed as a closed-form function of only one variable, the paraboloid height-to-width ratio. The minimum of this function is found by a routine of computer algebra. The proposed model amalgamates into a single and relatively simple function, tractable by standard calculus, the property of the whole structure (dome area) with labouring of insects-comrades. The ants are sociobiologically analogized with Bejan's builders of ancient pyramids and contemporary designers of man-made "dream-houses" or "dream-prisons".

Original languageEnglish
Pages (from-to)384-390
Number of pages7
JournalEcological Modelling
Volume250
DOIs
Publication statusPublished - Feb 2013

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dome
ant
expenditure
nest
trajectory
energy
ambient air
boundary condition
insect
temperature

Keywords

  • Ant nest
  • Constructal design
  • Global minimum
  • Heat transfer
  • Mathematical modelling
  • Social insects

ASJC Scopus subject areas

  • Ecological Modelling

Cite this

Optimal shape of an anthill dome : Bejan's constructal law revisited. / Kasimova, R. G.; Obnosov, Yu V.; Baksht, F. B.; Kacimov, A. R.

In: Ecological Modelling, Vol. 250, 02.2013, p. 384-390.

Research output: Contribution to journalArticle

Kasimova, R. G. ; Obnosov, Yu V. ; Baksht, F. B. ; Kacimov, A. R. / Optimal shape of an anthill dome : Bejan's constructal law revisited. In: Ecological Modelling. 2013 ; Vol. 250. pp. 384-390.
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