Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-9, 2016, DOI:10.5098/hmt.7.31

Abstract The two dimensional phase change problem was solved using the extended finite element method with a Lagrange formulation to apply the interface boundary condition. The Lagrange multiplier space is identical to the solution space and does not require stabilization. The solid-liquid interface velocity is determined by the jump in heat flux across the i nterface. Two methods to calculate the jump are used and c ompared. The first is based on an averaged temperature gradient near the interface. The second uses the Lagrange multiplier values to evaluate the jump. The Lagrange multiplier based approach was shown to be more robust… More >

A. Zoubir^a , R. Agounoun^a,*, I. Kadiri^b, K. Sbai^a , M. Rahmoune^a

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-6, 2016, DOI:10.5098/hmt.7.35

Abstract Boiling heat transfer process is important because it is a way to increase the flux density transmitted at low temperature differences. To quantify the thermal exchanges, we performed an experimental study of the nitrogen pool boiling, in transient conditions, on a horizontal brass ribbon for a fixed flux density. The results show that there is no break between the monophasic convection zone and the nucleated boiling region. In the nucleated boiling zone, the temperature variations are very small. We also note that the overheating required to trigger boiling increases with the time delay after the activation of nucleation sites. More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a, Donald Ziegler^c, Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.7, pp. 1-11, 2016, DOI:10.5098/hmt.7.40

Abstract A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were… More >

Dave Martin^a,b,† , Hicham Chaouki^a,b, Jean-Loup Robert^a , Donald Ziegler^c , Mario Fafard^a,b

Frontiers in Heat and Mass Transfer, Vol.10, pp. 1-11, 2018, DOI:10.5098/hmt.10.18

Abstract A model for two dimensional solidification problems including convection was developed by coupling the Stefan problem with the Stokes problem. The extended finite element method (XFEM) was used to capture the strong discontinuity in velocity and pressure as well as the jump in heat flux at the phase change interface. The melting temperature and no-slip condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration algorithm. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface. More >