**Modelling of coupled Heat transfer - Application to
Porous media at high temperatures**

Raj Narayan Konduru^{1},
Olivier Farges^{1}, Vincent
Schick^{1}, Yves Gaillard^{2}, Patrick Hairy^{2}, Gilles Parent^{1}

^{⋆} : raj-narayan.konduru@univ-lorraine.fr

^{1} University of
Lorraine, LEMTA, F-54000, Nancy, France

^{2} CTIF - 44 avenue de
la Division Leclerc - F-92318 SEVRES CEDEX

**Mots clés :** Porous Media, Radiation, Conduction,
Convection, Monte Carlo, Deterministic, Coupling.

**Résumé :**

In the current context of greenhouse gas reduction, the improvement of energy efficiency in industries using high temperature processes (metallurgy, iron and steel, cement, glass) requires, among other things, the development of high temperature heat recovery/storage/transport solutions. For high temperature heat recovery on an industrial scale, the use of porous materials could be an interesting solution due to their high specific surface area. For better heat recovery, the foams should be designed to have a lower pressure drop and a high temperature difference between the inlet and outlet of an element filled with such foams. Numerical methods are used to solve the heat and fluid flow through the porous heat exchanger that provides the solution. Two different types of steady-state numerical simulations have been performed on the Kelvin cell foam that solve for conjugate heat transfer, i.e. the coupling of conduction, convection and radiation. One is the deterministic method which solves using the finite volume method with density variation based on temperature and pressure changes (equation of state) using the OpenFOAM toolkit and the other is the Monte Carlo – Meshless method keeping a constant density using the reference based algorithm adapted to our case. We performed simulations at 0.1 m/s and 2 m/s at imposed temperatures of 373 K, 473 K and 1073 K. We found that the error between the two methods increases as the velocity and the imposed temperature increase. We also found that the Monte Carlo method takes very little computation time compared to the deterministic methods.

Work In Progress