Closure to “Discussion of a Discussion by K. Vafai and S. J. Kim” (1997, ASME J. Heat Transfer, 119, pp. 195–196)

Thermoconvective instability and local thermal non-equilibrium in a porous layer with isoflux-isothermal boundary conditions

“…α f,s = k f,s /(ρc) f,s , t * is time, µ is the dynamic viscosity, K is permeability, ρ is density, g is the modulus of the gravitational acceleration g, β is the thermal expansion coecient, T 0 is the reference temperature, e z is the unit vector for the direction z, ϕ is porosity, and c is the heat capacity per unit mass. The set of boundary conditions can be expressed as [11,12,13] …”

“…On the other hand, unlike in the studies reported in [10,11], we will analyse asymmetric temperature conditions, where the upper wall is kept at constant temperature, while a uniform heat ux is prescribed on the lower wall. The uniform heat ux condition will be formulated according to the Amiri-Vafai-Kuzay Model A [11,12,13]. The latter model is valid when the boundary wall has a nite thickness and a high thermal conductivity.…”

Numerical Simulation of Flow Disturbance and Heat Transfer Effects on the Methanol-Steam Reforming in Miniature Annulus Type Reformers

“…To simplify the analysis, the following assumptions are made: The catalyst particles are assumed to be spherical with a diameter d p , and the catalyst bed is treated as a homogeneous porous medium with porosity ε and permeability K . The flow is assumed to be steady. With the reactants entering the reformer in a flow parallel to the reformer axis at a small mass flow rate and then flowing through a homogeneous catalyst bed, the flow inside the reformer can be assumed to be laminar and axisymmetric. The catalyst bed is in local thermal equilibrium with the surrounding gas mixture. The species in the gas mixture are ideal gases. The hot gas used for heat supply is treated as air. There is no heat generation in the reformer and outer cylinder walls. The reformer, baffle plate, and the outer cylinder are made of the same material. Based on the above assumptions, the governing equations for the mass conservation, fluid flow, energy transport, and mass transfer inside the reformer can be written as − ∇ · ( ρ V⃗ ) = 0 1 normalε 2 ∇ · ( ρ V⃗ V⃗ ) = prefix− ∇ p + 1 normalε · ∇ ( ∇ μ V⃗ ) − normalμ K V⃗ − normalρ C normalF K | V⃗ | V⃗ ∇ · ( ε ρ c p V⃗ T ) = ∇ · ( λ e ∇ T ) + …”

Modeling nonisothermal impregnation of fibrous media with reactive polymer resin

“…The RIM polyurethane resin studied by Reboredo and Rojas (9) is used for the simulation. The fiber medium has the following permeabilities: (1) K , = K, = 1 x lo-' m2 for cases 1 to 4, and The procedure outlined above is an explicit [18][19][20]. The momentum boundary layer for low permeability porous media is small compared with the gapwidth dimension.…”

“…The momentum boundary layer for low permeability porous media is small compared with the gapwidth dimension. Hence, an estimate of h, is obtained from the analytical solution of the energy equation for Darcian flow (18). For this study, the following values are used: h, = 300…”