In this article, we study the effect of adopting a two-temperature and two-velocity model, appropriate to a bidisperse porous medium (BDPM), on the classical Cheng-Minkowycz study of vertical free convection boundary-layer flow in a porous medium. It is shown that the boundary-layer equations can be expressed in terms of three parameters: a modified volume fraction, a modified thermal conductivity ratio, and a third parameter incorporating both thermal and BDPM properties. A numerical simulation of the developing boundary layer is guided by a near-leading-edge analysis and supplemented by a far-field analysis. The study is completed by a presentation of numerical simulations of the elliptic equations in order to determine how the adoption of the BDPM model affects the thermal fields in the close vicinity of the origin.
Rees, D. A. S., Nield, D. A., & Kuznetsov, A. V. (2008). Vertical free convective boundary-layer flow in a bidisperse porous medium. Journal of Heat Transfer, 130(9), 092601-1. https://doi.org/10.1115/1.2943304