Heat transfer in the two-dimensional model

The heat transfer parameters in the two-dimensional model are the effective radial conductivity Xreff and the wall heat transfer coefficient Owaii Reviews of the correlations using the plug-flow assumption can be found in [159] [199] [274] [288]. 

Correlations of the effective radial conductivity usually have the following form  

The wall coefficient is usually correlated as a Nusselt number equation, i.e. 

Both the stagnant and the particle to wall radiation parts are small compared with the turbulent part at industrial syngas conditions even at the high temperatures. For the turbulent part different values of the parameters A, a, and b can be found in the literature [199] [274], depending on particle type, size, and tube-to-particle diameter ratio. 

The constant 8 in the last term changes with the relative values of the two resistances, but it is evident that the two parameters are cross-correlated as expressed by the Biot number  

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