Modelling of radial heat transport in wall-cooled packed beds: Confidence intervals of estimated parameters and choice of boundary conditions

The heat transport in a wall-cooled packed tube in which a hot gas is cooled down is often described with a pseudo-homogeneous one-dimensional or two-dimensional model. Assuming a radially flat inlet temperature profile at the bed entrance can lead to erroneous results, if the actual profile at the entrance is curved. It can cause an apparent length dependence of the effective heat transport coefficients, the so called “length effect”. The reason being that the amount of heat entering the packed bed is overestimated, which is compensated for by higher values for the heat transport coefficients. Using a parabolic inlet temperature profile, as measured in the packed bed at a certain minimal bed length, eliminates the length dependence of the heat transport coefficients. An experimental investigation showed that for the gas flow rates applied. Pe_p ^s= 52 to 785, a wall heat transfer coefficient α_w has to be used for modelling the heat transport with a two-dimensional model. Confidence intervals are given for the effective radial heat conductivity λ_e,r the wall heat transfer coefficient αw and the overall heat transfer coefficient U_u,v. It is shown that λ_e,r and α_w are strongly cross-correlated and have large confidence intervals. Especially at low gas flow rates α_w is difficult to determine accurately. The confidence intervals for U_u,v are much smaller. It is shown that although values for λ_e,r and αw can scatter much for different measurements due to the cross-correlation of these coefficients, the scatter in U_u,v is reduced significantly if this coefficient is calculated with the so called “lump equation”