<p>With the recent advances in micro devices, an accurate gas flow and heat transfer analysis becomes more relevant considering the slip effect. A micro-scale, multiple-relaxation-time (MRT) lattice Boltzmann method is employed for its better stability and accuracy in the prediction of gas transport phenomena in porous media. A double distribution function approach is used for the ease of implementation. Slip velocity and temperature jump are captured at the curved boundaries using non-equilibrium extrapolation scheme with the counter-extrapolation method. A pore-scale domain of micro-cylinders, comprised of circle and diamond shapes is studied, respectively. The cylinders are arranged in staggered formation. Gas flows in the domain at a lower temperature than that of the micro-cylinders. Symmetry boundary condition is used to define top and bottom walls of domain. Adiabatic boundary condition is defined at the exit. Permeability and Nusselt numbers are calculated in a wide range of Reynolds number (1-10), Knudsen number (0.01-0.1) and different porosities. Porosity is variated by changing the diameter of obstacles in the pore-scale domain.</p><p>It is found that the permeability values increase with an increase in Knudsen number for all the cases and are also found comparable to the correlations proposed in open literatures. The increasing trend is similar to both cylinder and diamond. However, the permeability increase in circular shaped cylinder is larger than that of diamond one. An increase in surface area for the case of diamond shaped cylinder can be accounted for the reason behind it. As this increase in surface area will lead to a higher friction and resultantly a lower permeability. For heat transfer, Nusselt number increases with increasing in Reynolds number. Similarly, a higher Reynolds number will correspond to an increased velocity through the domain. This increased velocity of the flow will resultantly decrease the bulk gas temperature across the domain. This depreciation in bulk temperature result in a higher temperature gradient near cylindrical surface and hence a higher temperature jump, which in effect results in a surficial thermal resistance and deteriorates the heat transfer process. Nusselt number represents a decrease in the value with the increasing temperature jump. Knudsen number also effects heat transfer in a similar way. As Knudsen number is increased from a no-slip (Kn=0.0) to slip (0.01&lt;Kn&lt;0.1), the gas molecules tend to slip at the boundary of the obstacle which hinders the heat transfer process. Hence, the bulk temperature of gas in slip region is decreases than that in no-slip region. In conclusion, a micro-scale lattice Boltzmann method is presented, which is effective to predict permeability and Nusselt number in confined porous media at pore-scale level for slip flow problems.</p>

Slip Gas Flow and Heat Transfer in Confined Porous Media With Different Shape Cylinders

Paper Proceedings: https://asmedigitalcollection.asme.org/HT/HT2021/volume/84874

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