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Simulation of boiling heat transfer in small heaters by a coupled cellular and geometrical automata

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Abstract

Automata are entities defined by mathematical states that change following iterative rules representing neighborhood interactions. A model of automata for pool boiling heat transfer simulation consisting in collections of virtual spheres that change their volumes and move around a certain environment is presented. The approach is an alternative technique to describe the turbulent features of boiling phenomena, such as interfacial topological transitions and fluid-wall interaction. The novel computer model presented here is able to capture the essential features underlying boiling heat transfer and crisis above a small heater, showing good agreement with experimental data reported in the open literature.

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Abbreviations

A l :

Fraction of area in direct contact with the liquid

c mc :

Microconvection constant

g :

Gravity acceleration

H :

Convection heat transfer coefficient

h fg :

Latent heat of evaporation

Ja :

Jakob number

k l :

Liquid conduction heat coefficient

k m :

Metal conduction heat coefficient

L :

Characteristic cell length

L c :

Channel length

Nu :

Nusselt number

p :

Breakup probability per time unit

P :

Cell perimeter

p b :

Breakup coefficient (0 < p b  < 1)

Pr :

Prandtl number

\( \dot{q} \) :

Volumetric heat source

q c :

Convection associated heat

q mc :

Microconvection associated heat

q ml :

Microlayer theory associated heat

r :

Bubble radius

r 0 :

Previous bubble radius

Ra :

Rayleigh number

r c :

Critical bubble radius

R cav :

Cavity radius

r d :

Detachment bubble radius

t :

Time

T :

Cellular automata temperature

T sat :

Saturation temperature

T w :

Wall temperature

α l :

Liquid thermal diffusivity

β :

Volumetric thermal expansion coefficient

Δ:

Cell side

Δt :

Time that went since the last bubble detachment

ε :

Heater emissivity

ϕ :

Contact angle

ν :

Liquid kinematic viscosity

σ :

Surface tension coefficient

σ rad :

Stefan–Boltzmann constant

ρ l :

Liquid density

ρ v :

Vapor density

τ :

Time lag associated to each change

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Authors and Affiliations

  1. Centro Atómico Bariloche, Av. Bustillo 9500 S.C. de Bariloche, CP 8400, Rio Negro, Argentina

    C. Marcel, F. Bonetto & A. Clausse

  2. Universidad Nacional del Centro, 7000, Tandil, Argentina

    A. Clausse

Authors
  1. C. Marcel
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  2. F. Bonetto
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  3. A. Clausse
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Correspondence to C. Marcel.

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Marcel, C., Bonetto, F. & Clausse, A. Simulation of boiling heat transfer in small heaters by a coupled cellular and geometrical automata. Heat Mass Transfer 47, 13–25 (2011). https://doi.org/10.1007/s00231-010-0667-6

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  • DOI: https://doi.org/10.1007/s00231-010-0667-6

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