@article{PAR00020089,
  title = {{S}tudy of the effect of thermal dispersion on internal natural convection in porous media using {F}ourier series},
  author = {{F}ahs, {M}. and {G}raf, {T}. and {T}ran, {T}. {V}. and {A}taie-{A}shtiani, {B}. and {S}immons, {C}. {T}. and {Y}ounes, {A}nis},
  editor = {},
  language = {{ENG}},
  abstract = {{N}atural convection in a porous enclosure in the presence of thermal dispersion is investigated. {T}he {F}ourier-{G}alerkin ({FG}) spectral element method is adapted to solve the coupled equations of {D}arcy's flow and heat transfer with a full velocity-dependent dispersion tensor, employing the stream function formulation. {A} sound implementation of the {FG} method is developed to obtain accurate solutions within affordable computational costs. {I}n the spectral space, the stream function is expressed analytically in terms of temperature, and the spectral system is solved using temperature as the primary unknown. {T}he {FG} method is compared to finite element solutions obtained using an in-house code ({TRACES}), {O}pen{G}eo{S}ys and {COMSOL} {M}ultiphysics ({R}). {T}hese comparisons show the high accuracy of the {FG} solution which avoids numerical artifacts related to time and spatial discretization. {S}everal examples having different dispersion coefficients and {R}ayleigh numbers are tested to analyze the solution behavior and to gain physical insight into the thermal dispersion processes. {T}he effect of thermal dispersion coefficients on heat transfer and convective flow in a porous square cavity has not been investigated previously. {H}ere, taking advantage of the developed {FG} solution, a detailed parameter sensitivity analysis is carried out to address this gap. {I}n the presence of thermal dispersion, the {R}ayleigh number mainly affects the convective velocity and the heat flux to the domain. {A}t high {R}ayleigh numbers, the temperature distribution is mainly controlled by the longitudinal dispersion coefficient. {L}ongitudinal dispersion flux is important along the adiabatic walls while transverse dispersion dominates the heat flux toward the isothermal walls. {C}orrelations between the average {N}usselt number and dispersion coefficients are derived for three {R}ayleigh number regimes.},
  keywords = {{N}atural convection ; {T}hermal dispersion ; {D}arcy's law ; {F}ourier series solution ; {COMSOL} multiphysics ; {P}arameter sensitivity analysis ; {N}usselt number},
  booktitle = {},
  journal = {{T}ransport in {P}orous {M}edia},
  volume = {131},
  numero = {2},
  pages = {537--568},
  ISSN = {0169-3913},
  year = {2020},
  DOI = {10.1007/s11242-019-01356-1},
  URL = {https://www.documentation.ird.fr/hor/{PAR}00020089},
}