casualguitar said:
Ideal. These final model equations seem to be extremely close to the ones you developed in model 1. I'll post them this evening (currently away from my pc):
Multiplying the spatially discretised model equations by ##A_C\Delta z##:
Individual species mass balance:
##m_{m,j}\frac{\partial y_i}{\partial t} = \dot{m}_{j-1}(y_{j-1} - y_j) - \dot{M}_{i,j}''a_sA_C\Delta z + y_{i,j}*A_C\Delta z\sum_{j=1}^{n_c}\dot{M}_j^"a_s##
Individual species heat balance:
##m_{m,j}c_{p,j}\frac{\partial T_g}{\partial t} = \dot{m}_{j-1}c_{p,j-1}(T_{j-1} - T_j) - q_{g,I,j}a_sA_C\Delta z##
Overall mass balance to the gas phase:
##\frac{\partial m}{\partial t} = m_{j-1} - m_j -A_C\Delta z\sum_{i=1}^{n_c}{\dot{M}_{i,j}^"a_s}##
And then the two equations that do not have spatial derivatives, the species mass balance for deposition at the interface, and the heat balance to the bed:
##\frac{\partial M_i}{\partial t} ={\dot{M}_i^"a_s}##
##\rho_s(1-\epsilon_g)C_{p,s}\frac{\partial T_b}{dt}=q_{I,b}a_s##
I have left ##A_C\Delta z## in three of the terms that I did not know how to simplify. I could sub in V/n here but I would guess there is a better way to get rid of the ##A_C\Delta z## term?
Edit: I also have started re-reading the model from the beginning (cleaning up our comments into a word document), and reading back over the earlier comments with the new knowledge of how these early equations were developed into the equations we now have. A lot of the smaller bits that didn't really make sense (like how they got their individual species mass balance) now do make sense
Edit 2: Also quite funny (in my view) that I seem to respond with 'I fully understand your post' quite often and then continue to misunderstand what you've said for a number of further posts. Apologies about that, will aim to do better