In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (N u cl = 4.12 and f Re cl = 24) are used to define heat transfer increment ratio (ε th = N u p /N u cl ) and pressure drop increment ratio (ε p = f Re p / f Re cl ) and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer and pressure drop increment ratios are used to define an overall performance (ε = ε th /ε p ) to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for a partially porous filled channel, the value of ε is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k r ) when k r > 2. For a fully porous material filled channel, the value of ε is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls.

In this study, path-percolation theory was applied to randomly generate porous media, and effective porosities of these domains were determined. A statistical approach was pursued to determine effective porosity with confidence levels of 95%, 97%, and 99%. Furthermore, the Lattice-Boltzmann method was applied to obtain the velocity distribution throughout the porous channels to evaluate effective tortuosity. Two dimensional lattices with nine velocity components were utilized for fluid flow simulations. A new effective diffusivity model for porous media was developed using the effective porosity and tortuosity determined by pathpercolation and Lattice-Boltzmann theories, respectively. Diffusion behavior of gasses in porous media as a function of porosity is typically unpredictable when the porosity is below 0.6, but the developed diffusion model as a function of effective porosity is shown to be useful in all effective porosity ranges.

a b s t r a c tAn analytical study on laminar and fully developed forced convection heat transfer in a parallel-plate horizontal channel filled with an anisotropic permeability porous medium is performed. The principal axis of the anisotropic porous medium is oriented from 0 to 90 degrees. A constant heat flux is applied on the outer wall of the channel. Both clear (Newtonian) fluid and Darcy viscous dissipations are considered in the energy equation. Directional permeability ratio parameter A * is defined to combine both the effect of the dimensionless permeability ratio parameter K * ¼(K 1 /K 2 ) and orientation angle 4 into one parameter.The effects of the parameter A * , the Darcy number Da and the modified Brinkman number Br * on the heat transfer and fluid flow characteristics in the channels are investigated and presented in graphs. The obtained results show that the parameters A * , Da and Br * have strong effects on the dimensionless normalized velocity and temperature profiles as well as on the Nusselt number. It is found that for a particular value of A * , called as critical value A cr * , the external heat applied to the surface of the channel is balanced by the internal heat generation due to viscous dissipation and the bulk mean temperature approaches the wall temperature. Hence, the Nusselt number approaches infinity for the critical values A cr * .

In this work, single-component single-phase, and single-component multi-phase Lattice-Boltzmann models were developed to investigate the effects of liquid formation on mass transfer in porous channels via path-percolation theory. A two-dimensional lattice with nine velocity components was used in both lattice-Boltzmann models. A confidence level of 99% was utilized to obtain statistical results of porosity, effective porosity, and tortuosity of the system with 0%, 10%, and 20% liquid formation. Velocity distributions in randomly generated inhomogeneous porous channels with different solid-liquid-vapor combinations were analyzed. The statistical results show that the porosity range of the initially generated porous media lies between the specified error limit of 0.001 determined by the confidence level study for all three cases with 70%, 80%, and 90% target porosity. When target porosity decreases, the difference between porosity and effective porosity increases and the effective porosity range gets wider than the range of porosity. Effective diffusion coefficient decreases with increase in liquid formation, since the effective porosity decreases. An application programming interface called OpenMP was implemented on the developed serial in-house program and the effects of 1 to 4 threads on program performance and efficiency were investigated. The maximum speedup and performance gained are 3.3553 and 1.275 GFlops for 4 threads of a personal computer with a 38.4 GFlops peak performance.

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