Analytical Study of Heat Flux Splitting in Micro-channels Filled with Porous Media

Abstract

The conditions of occurring heat flux splitting (bifurcation) phenomenon in a micro-channel filled with a porous medium including internal heat generations within both the solid and fluid phases under the local thermal non-equilibrium (LTNE) condition is analytically studied in the slip regime. The channel walls are subjected to a constant heat flux. Exact solutions for both the dimensionless temperatures of the two phases and the Nusselt number are obtained. Effects of the pertinent parameters such as heat generation parameter (ω), the interphase heat transfer parameter (Vadasz in J Porous Media 15: [249][250][251][252][253][254][255][256][257][258] 2012) or Biot number (Bi), the fluid-to-solid effective conductivity ratio (k), and the temperature jump coefficient (β) on the dimensionless temperature profile (θ ) of the two phases as well as the Nusselt number are investigated. Moreover, the validity of one-equation model (the local thermal equilibrium assumption) is analyzed by comparing the Nusselt number obtained by one-equation model (LTE) with that obtained by the two-equation model (LTNE). Results reveal that the conditions at which the heat flux bifurcation (splitting) occurs in the slip regime is the same as those of the no-slip regime. In addition, a kind of heat flux bifurcation in which the solid and fluid phases have the same dimensionless temperature sign is observed in the slip regime, while it was not previously observe in the no-slip regime. It is discussed that the Nusselt number can increase or decrease with respect to ω and may have either positive or negative values in both the no-slip and slip regimes. The presence of internal heat generation intensifies the role of β in the Nusselt number reduction. In addition, the accuracy of LTE model increases with increased Bi and with decreased β, while it is not a monotonic function of k in the presence of internal heat generation. B Maziar Dehghan

A semi-analytical solution for time-dependent natural convection flow with heat generation/absorption in an annulus partially filled with porous material

“…Yang and Vafai (2010) addressed the effect of constant internal heat generation on the temperature field in the porous region under local thermal non-equilibrium in the fully developed region of a channel filled with a porous material. Their research was further extended to the micro-scale by Dehghan et al (2015) and Mahmoudi (2015) to inspect the thermal response and the Nusselt number in the slip-flow system in which the temperature jump occurrence is also governed at the walls.…”

Microchannels enhanced by porous materials: Heat transfer enhancement or pressure drop increment?

“…To see more discussions on the above-mentioned general boundary condition incorporating the slip-flow regime, one may refer to the following works: Nield and Kuznetsov [29], Kuznetsov and Nield [35], Buonomo et al [38], Dehghan et al [9,39], Harley et al [57], and White [58]. The process of non-dimensionalizing the momentum equation and solution can be found in Dehghan et al [9].…”

“…For the first time under the local thermal nonequilibrium (LTNE) condition, Buonomo et al [38] studied the fully developed heat transfer of a micro-channel filled with a porous material. Most recently, Dehghan et al [39] analyzed the heat flux splitting (or the heat flux bifurcation phenomenon introduced by Yang and Vafai [40]) for a channel fully filled with a porous material under LTNE condition in the slip-flow regime. They also discussed the validity region of the local thermal equilibrium (LTE) condition in the no-slip and slip-flow regimes.…”

On the thermally developing forced convection through a porous material under the local thermal non-equilibrium condition: An analytical study

“…Effects of heat generations/absorptions within the solid and fluid phases of a porous material on the thermal response have been studied by Refs. [33][34][35][36][37] in details.…”