A Semi-Empirical Model for Porous Media Heat Exchanger Design

1 Fellow, ASME Abstract A semi-empirical model for conduction/convection in a thin “fin-like” porous wall of arbitrary composition and thickness is developed. The model assumes one-dimensional conduction in the porous matrix and one-dimensional flow of the coolant through the wall. Closed form solutions are obtained for a uniform composition and thickness porous wall having an insulated tip. Analysis shows that the equivalent unit surface conductance and the effectiveness of the porous wall are always maximum when it is operated with the number of transfer units of the porous matrix greater than two (ntu ≥ 2). Furthermore, if the porous matrix is composed of a packed bed of spherical particles, it is found that, for a given coolant flow rate, the pressure drop across the porous matrix is minimum when ntu ≤ 2. This suggest that for many design requirements, the porous media exchanger should be operated at ntu = 2. Nomenclature A porous wall cross section area, tW As heat transfer surface area cp coolant specific heat d particle diameter F see Eq. (12) G coolant mass velocity h unit surface conductance H porous wall height ke porous media effective conductivity kf coolant conductivity mH see Eq. (13) ntu porous media number of transfer units p pressure Pr Prandtl number q conduction heat transfer rate Re particle Reynolds number ReH coolant Reynolds number St particle Stanton number t porous wall thickness T temperature U equivalent unit surface conductance Vol volume W porous wall width y coordinate β heat transfer surface area-to-volume ratio ε porosity ρ coolant density μ coolant viscosity Θ non-dimensional temperature