Modeling of radiative heat transfer in solid oxide fuel cells (SOFC)


Fuel cells are static energy conversion devices that partially convert the chemical energy of fuels directly into electrical energy. There are several types of fuels cells. Solid oxide fuel cells (SOFC) have the advantage that they operate with high efficiency and also can directly convert fossil fuel, and not only hydrogen. The fact that they operate at relatively high temperature (800-1000C) causes specific risks for stress failure due to local overheating. To understand and solve the problems it is necessary to have a good understanding of all heat transfer phenomena in the fuel cell, including radiative heat transfer.  Radiative heat transfer is described by an integro-differential equation for the intensity, describing the processes of emission, absorption and scattering. In flowing media interacting with the radiation field, the energy equation has to be solved including a source/sink term for radiative heat transfer.  This project will generate adequate models based on fundamental physical understanding of the radiative heat transfer phenomena. This concerns both the radiative properties of materials as the propagation of radiation in the cell and towards the environment. Approximations will be needed in relation to the spectral and direction dependence of surfaces and flowing media. 

At TU Delft SOFC's are studied experimentally and by modeling in the Energy Technology section of the Process and Energy department. On the other hand, expertise in modeling of radiative heat transfer in high temperature systems is available in the reactive flows group of the Fluid Mechanics section. In this project the expertise of both groups have been combined. 
The results of the project are reported in the MSc Thesis by Jelle Stam presented by on March 11, 2015.



Solid Oxide Fuel Cells operate at high temperatures, which places stringent requirements on the ceramic materials in these devices. Optimizing the design by thermal stress minimization could increase the life expectancy of a fuel cell. In order to do this it is important to have a detailed understanding of the heat flows and temperature profiles in SOFCs.

Because of the high temperatures it is expected that radiative heat transfer plays an important role in the thermal behavior of the cell. This phenomenon is however often neglected in SOFC modeling. Arguments often used for neglecting thermal radiation are the lack of knowledge of material properties or to save computational time. A literature study on thermal radiation in solid oxide fuel cells shows that the results from past research are not always in agreement. Some articles about radiation in the anode, cathode and electrolyte (or PEN-structure) even show completely contradictory results.

Modeling studies have been performing in multiple steps, all simulations are performed using Ansys Fluent.

The SOFC models are all hydrogen fueled. To study the effects of thermal radiation in the anode, cathode and electrolyte simplified 2D representations of the PEN-structure were developed. Because the material properties are not well known the results are obtained for a wide range of optical properties, on two different geometries. The results show that in the limit of high optical thickness of the anode and cathode the entire PEN-structure can be considered opaque, which means only radiation emitting from the anode and cathode surface will be important. Thermal radiation in the electrolyte has a negligible effect on the temperature profiles in the PEN-structure.

To study the effect of surface-to-surface radiation a 2D model of a planar SOFC is developed. In this model uniform heat sources are used to account for the heat released due to electrochemical reactions and irreversibilities. Since the surface properties are not well known the temperature profiles throughout the domain are obtained for a wide range of optical properties, for both a co-flow and a counter-flow arrangement. The results show that thermal radiation has a very small effect on the temperature profiles in the domain. It was also found that the results are not very sensitive to the surface emissivity. The results are also obtained with the PEN-structure participating in radiative heat transfer, which verifies the statement that these materials can be considered opaque.

To obtain more accurate results and to check the assumption of uniform heat sources a 3D-model of a single channel planar SOFC is developed. This model is also used to study the influence of participating gases. Instead of assuming uniform heat sources the ‘Fuel Cell and Electrolysis’ add-on module is used to model the relevant fuel cell phenomena. The model outputs show that using uniform heat sources is not an accurate assumption. The results also show that radiation has a very small effect on the temperature profiles in the domain, and that the ratio of radiative heat flux to total heat flux is not higher than 9%. Similar to the 2D planar cell model, the results are not sensitive to surface emissivity. The effect of participating gases is studied by considering water vapor as a participating component for the radiative transfer equation. The results show this participating gas has a negligible effect on the temperature profiles in the domain. The reason for small radiation effects is because temperature gradients are small in the direction were radiation has the most effect. Temperature gradients are shown to be dominant in axial direction, or in the direction of the flow, which is important for further studies on thermal stress minimization.

To study the effect of radiative heat transfer in a completely different fuel cell design, a 3D model of an anode supported tubular SOFC is developed. The ‘SOFC with Unresolved Electrolyte’ add-on module is used to model the relevant fuel cell phenomena. It is expected that radiation effects are slightly more important in this tubular SOFC model. However this model does not work optimal yet, and no results with radiative heat transfer have been obtained yet.

The results in this thesis show that radiative heat transfer in single channel SOFCs can be neglected when the temperature field has to be determined for thermal stress minimization.

Supervisors: Prof. dr. D.J.E.M.Roekaerts and Dr. P.V. Aravind.  


Involved People:

Facilities used:



David L. Damm, Andrei G. Fedorov, Radiation heat transfer in SOFC materials and components, Journal of Power Sources, 143, 2005, 158-165


M. Soroush and A. Shamiri, Mathematical modeling of solid oxide fuel cells: A review, Renewable and Sustainable Energy Reviews, 15, 2011, 1893-1917