TY - JOUR
T1 - Thermal dispersion driven by the spontaneous imbibition process
AU - Bautista, O.
AU - Méndez, F.
AU - Bautista, E. G.
PY - 2010/12
Y1 - 2010/12
N2 - In this work, we have theoretically analyzed the thermal dispersion process under the influence of the spontaneous imbibition of a liquid trapped in a capillary element, considering the presence of a uniform temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature T0 and pressure P0. Suddenly, the lower part of the porous medium touches a liquid reservoir at temperature Tl and pressure P0. This contact between both phases, in turn causes spontaneously the imbibition process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and Nusselt numbers. The above results are shown by taking into account the influence of three dimensionless parameters: the ratio of the characteristic thermal time to the characteristic imbibition time, β, the ratio of the hydrostatic head of the imbibed liquid to the characteristic pressure difference for the imbibition front, α, and the ratio of the dispersive thermal diffusivity to the effective thermal diffusivity of the medium, Ω. The predictions show that temperature profiles and the heat transfer process are strongly dependent on thermal dispersion effects, indicating a clear deviation in comparison with the case of Ω=0 that represents the absence of the thermal dispersion.
AB - In this work, we have theoretically analyzed the thermal dispersion process under the influence of the spontaneous imbibition of a liquid trapped in a capillary element, considering the presence of a uniform temperature gradient. The capillary element is represented by a porous medium which is initially found at temperature T0 and pressure P0. Suddenly, the lower part of the porous medium touches a liquid reservoir at temperature Tl and pressure P0. This contact between both phases, in turn causes spontaneously the imbibition process. Using a one-dimensional formulation of the average conservation laws, we derive the corresponding nondimensional momentum and energy equations. The numerical solutions permit us to evaluate the position and velocity of the imbibition front as well as the temperature profiles and Nusselt numbers. The above results are shown by taking into account the influence of three dimensionless parameters: the ratio of the characteristic thermal time to the characteristic imbibition time, β, the ratio of the hydrostatic head of the imbibed liquid to the characteristic pressure difference for the imbibition front, α, and the ratio of the dispersive thermal diffusivity to the effective thermal diffusivity of the medium, Ω. The predictions show that temperature profiles and the heat transfer process are strongly dependent on thermal dispersion effects, indicating a clear deviation in comparison with the case of Ω=0 that represents the absence of the thermal dispersion.
KW - Convective heat transfer
KW - Porous medium
KW - Spontaneous imbibition
KW - Thermal dispersion
UR - http://www.scopus.com/inward/record.url?scp=77954035019&partnerID=8YFLogxK
U2 - 10.1016/j.apm.2010.04.016
DO - 10.1016/j.apm.2010.04.016
M3 - Artículo
SN - 0307-904X
VL - 34
SP - 4184
EP - 4195
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 12
ER -