Naslov
Rigorous derivation of the effective model describing a non-isothermal fluid flow in a vertical pipe filled with porous medium

Autori
Beneš, Michal ; Pažanin, Igor

Izvornik
Continuum mechanics and thermodynamics (0935-1175) 30 (2018), 2; 301-317

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Darcy-Brinkman-Boussinesq model ; thin pipe ; Newton cooling condition ; asymptotic approximation ; error estimates

Sažetak
This paper reports an analytical investigation of non-isothermal fluid flow in a thin (or long) vertical pipe filled with porous medium via asymptotic analysis. We assume that the fluid inside the pipe is cooled (or heated) by the surrounding medium and that the flow is governed by the prescribed pressure drop between pipe's ends. Starting from the dimensionless Darcy- Brinkman-Boussinesq system, we formally derive a macroscopic model describing the effective flow at small Brinkman-Darcy number. The asymptotic approximation is given by the explicit formulae for the velocity, pressure and temperature clearly acknowledging the effects of the cooling (heating) and porous structure. The theoretical error analysis is carried out to indicate the order of accuracy and to provide a rigorous justification of the effective model.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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