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Analysis of heat flux bifurcation inside porous media incorporating inertial and dispersion effects – an exact solution. (English) Zbl 1231.80033

Summary: The phenomenon of heat flux bifurcation inside a porous medium is analyzed by studying the convective heat transfer process within a channel partially filled with a porous medium under local thermal non-equilibrium conditions. Either the thermal dispersion effect or the inertial effect are considered in the physical model. Exact solutions are derived for both fluid and solid temperature distributions for three interface thermal models at the porous-medium-fluid interface. The required conditions for validity of each interface thermal model are obtained, and the conditions under which the different interface thermal models yield equivalent solutions are given. The range of validity of the local thermal equilibrium condition is established, and the phenomenon of heat flux bifurcation inside a porous medium is established and proven for the first time in the literature. Furthermore, the Nusselt number is obtained and investigated for pertinent parameters. The ranges of physical parameters in which the thermal dispersion effect and the inertia effect are important are established.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
76S05 Flows in porous media; filtration; seepage
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